Patching of heat pulse velocity data

CHAPTER 1 INTRODUCTION

1.7 Outline of document

2.4.5 Patching of heat pulse velocity data

Tree transpiration data loss during a field experiment can result from low battery

voltages, corrosion of heater probes, and cracks around heater and thermistor probes and subsequent large wound widths.

Dyeet al. (2001) found good agreement between daily sapflow (total transpiration) measured with the HPV technique and the product of the average daily water vapour pressure deficits es - e and the daylight hours, for a number of tree species. This relationship has been used by Dyeet al. (2001) to accurately patch missing sap flow data.

2.5 A description ofthe Penman-Monteith equation

Penman (1948) derived a fonnula to account for the energy required to sustain

evaporation and a mechanism to remove water vapour. The original Penman equation for reference evaporation(Eo) over a open water surface is given as:

2.20

whereRnis the net irradiance, L1 (kPa

Qe

^l) is the slope of the saturation water vapour pressure vs temperature curve at the surface temperature (To), ris the psychrometric constant (kPa

Qe

^{l) and}

2.21

wheree_{s -} eais the daily averaged water vapour pressure deficit (kPa) and the wind function, f(u), given by:

f(u)=

0.27 (1

+u/l00)

whereuis the daily averaged windspeed (mS-I)(Rosenberg,et aI., 1983).

2.22

The Penman equation was later modified by Monteith (1963, 1964) to give the Penman-Monteith combination equation. The Penman-Monteith equation combines a

"radiative" and "aerodynamic" component to calculate the Penman-Monteith reference evaporation(ETa):

ET =Ll(R^IIS-GJ+ I

*

Mw

(e, -eJ

o A(Ll+r) R(Ta+273.15)r_v (Ll+r)

2.23 ETo

=

"radiative" component+"aerodynamic" component

whereRnsis the calculated daily radiant density, Gsthe calculated daily soil heat flux density,

i

is the apparent psychrometric constant,Mwthe molar mass of water,Rthe

universal gas constant, Ta the daily average air temperature and r_vthe combined aerodynamic and canopy resistance to water vapour:

2.24

wherer_a is the aerodynamic resistance for heat transfer andre the canopy resistance (Campbell; undated; Oke, 1978; AlIenet aI., 1998; Monteith and Unsworth, 1990;

Metelerkamp, 1993).

The net radiant density(R ns) is estimated from the solar radiant density (Rs)

2.25

where the net radiant density,Rn, is the sum of the net radiant density and the net long- wave radiant density, where

as

is the reflection coefficient of the crop andL_nithe atmospheric radiant emittance minus the crop emittance at daily average air temperature. Under clear skies,Lni(kW m-²) is given by:

L_nic =0.0003Ta -0.107 2.26

withTa as the daily average air temperature(DC). Under cloudy skiesL niapproaches zero. Cloudiness is estimated from the ratio of measured to potential daily total solar radiant density during daylight hours(R/Ro). A cloudiness function,f(R/R o)^is computed:

f(Rs1R )=1- [ 1 ] 2.27

I

Ra 1+0.034 exp (7.9RsIRa)

The daily net isothermal long-wave radiant density(Lni ) is then calculated as:

2.28

The cloudiness function (Eq. 2.27) requires the computation of the potential solar radiant density on a horizontal surface outside the earth's atmosphere,Ro:

R_o

=

^{1.36 sin}cp

where 1.36 kW m-²is the solar constant, and tpthe solar elevation:

sincp

=

^{sindsinI+cosdcosIcos [15}(t -to)]

2.29

2.30

wheredis the solar declination angle, Ithe latitude at the site,tthe local time andtothe time of solar noon. A polynomial is used forsin d:

sind=-0.37726-0.105564} + 1.2458/ -0.75478/ +0.13627/-0.00572/ 2.31

where} is the day of the year (DOY) divided by 100 (DOY/IOO) anddis the declination. The cosine ofdis computed from the trigonometric identity:

cosd=(1-sin²d)05 2.32

The time tis the datalogger local time less half the time increment from the lastET_o computation. The time of solar noon, to, is given by:

2.33

withLe the longitude correction and tethe "equation of time". The longitude correction is calculated by determining the difference between the longitude of the site and the longitude of the standard meridian. The longitude correction is given as:

Le

=

(Ls - L)/15 ^2.34

The "equation of time" is an additional correction to the time of solar noon that depends on the day of year. Two equations are used to calculatete: one for the fIrst half of the year (for Day ~ 180,where)

=

DaY/lOO):

t_e=-0.04056-0.74503}+0.08823/ +2.0515/ -1.8111/ +0.42832/ 2.35

and one for the second half of the year (for Day> 180,where)= (DOY-180)/100):

t_e = -0.05039-0.33954} +0.04084/ + 1.8928/ -1.7619/+0.4224/ 2.36

Evaporation occurs mainly during daylight hours when the net irradiance is the main driving force of the evaporation and is positive. The soil heat flux density can be estimated as a fraction of the net irradiance. For a complete canopy cover,G_s is assumed to be approximately 10 % of the net radiant density.

During the night R_s= 0and Gsis assumed to be50%of the net irradiance.

G_s =0.5R_n

2.37

2.38

The Penman-Monteith equation has been applied successfully over different surfaces (crops and forests) of optimal or limited water supply where the resistance required, is known (Campbell, undated; Rosenberg et al., 1983).

CHAPTER 3

IN SITU SOIL WATER CONTENT AND SOIL WATER POTENTIAL MEASUREMENT TECHNIQUES

3.1 Introduction

Several techniques exist to measure in situ soil water content and soil water potential.

These techniques include gravimetric, nuclear, electromagnetic, tensiometric,

hygrometric and remote sensing techniques (Zazueta and Xin, undated). Some sensors allow long-term monitoring of soil water content or soil water potential through the availability of dataloggers and electronic equipment. These sensors and microprocessor systems can be left unattended to do numerous measurements per day, and collect data automatically. These sensing techniques have a distinct advantage over the widely used neutron probe technique (Herkelrath and Delin, undated) which requires the presence of an operator. However, of all these techniques, none is completely satisfactory.

Most of the techniques relate more easily measured soil properties to the water content or the water potential of the soil. For example, the water content reflectometer technique relates the dielectric constant of the soil to the soil water content, whereas the heat dissipation technique relates the thermal conductivity and heat capacity

(temperature change) to the soil water potential, and the thermocouple psychrometric technique relates the soil humidity to the soil water potential. The three techniques mentioned here will be discussedinmore detail below.

3.2 Definitions