Advantages and disadvantages of the thermocouple psychrometer

CHAPTER 1 INTRODUCTION

1.7 Outline of document

3.5.4 Advantages and disadvantages of the thermocouple psychrometer

• time consuming data analysis, and

• required specialised equipment for excitation and measurements (SOWACS, undated).

3.6 Summary

Chapter 3 concludes the discussion of the techniques used in the short-term, site- specific field experiment. The following chapter(Chapter 4) describes the theory behind the Soil Water Atmosphere Plant model applied in the long-term soil water balance modelling.

CHAPTER 4

THE SOIL WATER ATMOSPHERE PLANT (SWAP) MODEL

4.1 Introduction

SWAP, the Soil Water Atmosphere Plant model, simulates the hydrological processes at a field scale (Fig. 4.1). The water flow and solute transport processes in the vadoze zone are influenced by plant growth during the season. Van Damet al. (1997) and Van Dam (2000) describe the processes applied in SWAP in detail. These processes

include: soil water flow, solute transport, soil heat flow, daily evapotranspiration, crop growth, field irrigation and drainage, surface water and multilevel drainage at a sub- regional scale and discharge in a regional system.

The processes used in our simulations (soil water flow; daily evapotranspiration and crop growth) will be described briefly.

} _\~ - ^.

Transpiration

I

Pereola'on

J j

i

Precipitation

Fig. 4.1 Hydrological processes used in the simulations with the Soil Water Atmosphere Plant (SWAP) model (SWAP, undated)

4.2 A description of the most important processes applied in SWAP 4.2.1 Soil water flow

Soil water flows as a result of differences in pressure heads(h) within the soil. The one dimensional flow of soil water in the vertical direction can be described by Darcy's equation:

q=_K(h)a(h+z)

az

^4.1

whereqis the soil water flux density (mm d-^I)2,K(h)the hydraulic conductivity (mm d-^I) which is dependent on soil water pressure headh(mm), andzthe vertical coordinate (mm).

Darcy's equation is subsequently combined with the continuity equation for soil water:

a6^v

=_ aq

^{-S (z)}

at az

^{a 4.2}

where Ovis the volumetric soil water content (mm³mm-³),t is the time (d) andSais the actual soil water extraction rate by plant roots (mm³mm-³d-^I). Invoking the chain rule of calculus we have:

a6_v a6_v ah - - = - - -

at ah at

and combining equations 4.1 and 4.2, yields:

arK(h)

ah

⁺

1

¹¹

ae

at

^v =C(h)ah=

at az az ~-s

^{a (z)}

2The outputs by the SWAP model in cm d-I were converted to mm d-^I•

4.3

-.:C....:..:h.::.ap!;..;t...:..e_r4 60

?t

where C is the differential soil water capacity(dB/dh)(mm-I). Eq. 4.3 is Richards' equation, which simulates vertical soil water movement in the soil profile using soil hydraulic functions.

4.2.2 Daily evapotranspiration 4.2.2.1 Introduction

SWAP uses a two-step approach to estimate potential evapotranspiraiton. Firstly, the potential evapotranspiration³is estimated with the Penman-Monteith equation for a daily time step:

4.4

= ET_rad +ET_aero

whereETrad and ETarea refer to the radiation and aerodynamic terms of the Penman- Monteith equation and is also described in Section 2.5.

Secondly, the actual evapotranspiration is calculated and includes the reduction of the rootwater uptake due to water and salt stress.

4.2.2.2 Potential transpiration of a fully covered soil and the potential evaporation of a bare soil

SWAP uses the Penman-Monteith equation to calculate the:

• _p~tential evapotranspiration of a wet canopy completely covering the soil (ET",o),

•

potential evapotranspiration of a dry canopy completely covering the soil(ET_po), and

3The Penman-Monteith evapotranspiration refers to the evapotranspiration from a dry, extensive, uniform canopy, optimally supplied by water as defined by Alien et at. (1998) and in section 2.2.5.

• potential evaporation of a wet bare soil(Epo).

SWAP also allows for the calculation of reference potential evapotranspiration(ETref) using methods other than the Penman-Monteith method. This reference

evapotranspira:tion is converted into potential evapotranspiration of a dry canopy using a canopy factor(kc):

4.5

Her~_however, SWAP equates the potential evapotranspiration for a dry crop, wet crop or wet soil. SWAP assumes that the potential evapotranspiration of a wet(ETwo) and a dry^(ETpo)canopy completely covering the soil is equal, and that the potential evaporation of a wet, bare soil(Epo)is equal to the potential evapotranspiration of a dry canopy completely covering the soil.

4.2.2.3 Potential transpiration and evaporation of a partially covered soil

SWAP separates potential evapotranspiration into evaporation and transpiration, and uses a physically-based approach to estimate the reduction in the potential transpiration and the potential evaporation. The potential evapotranspiration is partitioned into evaporation and transpiration using either the leaf area index or the soil cover fraction as a function of the crop development stage.

The potential soil evaporation under a crop is calculated using the Penman-Monteith equation, neglecting the aerodynamic term (Eq. 4.4). Neglecting the soil heat flux density, and assuming an exponential decrease in net irradiance below the crop, this potential evaporation(Ep ) is given as a function of the leaf area index(LAJ) as used by Ritchie (1972):

E = ET e^-ICg,UI

p P 4.6

where -K_gr is the product of the extinction coefficient of diffuse and direct visible irradiance, or alternativelyE_p is given as a function of the soil cover fraction (SC):

The potential transpiration rate(T_{p )} is given by:

T =ETP P

(l-~

ET ^l_E

I

^P

PO)

wherePiis the rainfall interception by a canopy.

4.2.2.4 Actual soil evaporation

4.7

4.8

The soil evaporation of a wet soil equals the potential soil evaporation(E_{p )}and is determined by the atmospheric demand. For a drying soil, with a decreasing hydraulic conductivity, the potential soil evaporation is reduced to actual soil evaporation.

The actual soil evaporation is determined as the minimum of the potential soil

evaporation(Ep ),the maximum evaporation according to Darcy's equation(Ema.lj, or the actual soil evaporation calculated using an empirical function(Ea)of Black (1969) or Boesten and Stroosnijder ( 1986) (cited by Van Damet al., 1997).

4.2.2.5 Actual plant transpiration

The maximum root water extraction rate over the rooting depth is equal to the potential transpiration rate(Tp). The potential root water extraction rateSp(d-^I) at a certain soil depth z is:

S (z)= llrool(z) T

P

IO

_Jr ^P

rool(z) dz

-Drool

4.9

where Jr,.OOIis the root length density (m m-\Droot(mm) is the rooting depth, and where the potential transpiration rate Tpis reduced through stresses (water or salinity) to the actual root water flux densitySa(z)(d-^I):

4.10

where ~is the reduction factor due to water stresses, and 0;.5is the reduction factor due to salinity stresses.