United States 

Department of 

Agriculture 

Forest Service 

Intermountain 

Forest and Range 

Experiment Station 

Ogden, UT. 84401 

Research Paper 

I NT-293 

July 1982 

A Calibration Model 

for Screen-caged 

Peltier Thermocouple 

Psychrometers 

Ray W. Brown and Dale L. Bartos 

This file was created by scanning the printed publication.

Errors identified by the software have been corrected;

however, some errors may remain.
THE AUTHORS 

RAY W. BROWN is a plant physiologist on the MinedLand Reclamation research project at the Forestry 

Sciences Laboratory in Logan, Utah. He joined the staff 

of the lntermountain Station in 1965. He holds a B.S. 

degree in forestry and an M.S. degree in range ecology 

from the University of Montana, and a Ph.D. in plant 

physiology from Utah State University. His main research 

responsibilities include plant water relations and minedland revegetation in alpine and other high-elevation lifezones. 

DALE L. BARTOS is a range scientist with the aspen 

ecology research work unit at Logan, Utah. He joined the 

lntermountain Station in 1972. Bartos holds B.S. and M.S. 

degrees from Fort Hays Kansas State University, and a 

Ph.D. degree in range science from Colorado State 

University. His principal interests include researching 

and modeling the dynamics of the aspen ecosystem. 

ACKNOWLEDGMENTS 

We extend a very special note of appreciation to 

Chester E. Jensen, mathematical statistician, for his tireless assistance, guidance, and encouragement throughout the entire study. Although Chet's efforts were particularly helpful during the model development phase of 

the research, he also provided expert assistance during 

both the planning stage and the manuscript review stage. 

Also, thanks are given to Ross D. Parry, group leader of 

computer science, for his assistance in preparing the 

FORTRAN program in appendix I and the tabular printouts in appendix II. 

To J. M. Collins, forestry technician, we extend thanks 

for assistance with the data collection and the hundreds 

of hours involved in "setting up psychrometer runs," the 

cleaning, drying, and reassembling of calibration 

chambers, water baths, and other apparatus used. We 

also appreciate the assistance of Bryan D. Williams, 

forestry technician, in programing the Hewlett-Packard 

9845-B computer. 

The use of trade, firm, or corporation names in this 

publication is for the information and convenience of the 

reader. Such use does not constitute an official endorsement or approval by the U.S. Department of Agriculture of any product or service to the exclusion of 

others that may be suitable. 

RESEARCH SUMMARY 

Calibration is one of the most important steps in using 

thermocouple psychrometers for estimating water potential. Unfortunately, the calibration process has numerous 

problems, including: (1) the logistics of calibrating large 

numbers of psychrometers; (2) applying isothermai calibration data to unstable thermal environments; (3) 

projecting limited calibration data to extended ranges of 

temperature and water potential; and (4) visually interpolating and extrapolating data from hand-drawn curves. 

A mathematical model of psychrometer calibration was 

developed that should alleviate most of these problems 

and enhance calibration accuracy. The model applies to 

a water potential range of 0 to about -80 bars, a ternperature range of 0" to 40" C (32 " to 104" F) and to 

Peltier cooling times of from 15 to 60 sec. In addition, the 

model includes a correction for the effects of temperature gradients on psychrometer performance as reflected 

by zero-offsets ranging from-60 to + 60 microvolts. 

Within the limits established, this model is applicable to 

screen-caged psychrometers constructed with 0.0025-cm 

(0.001-inch) diameter chromel-constantan thermocouples 

that employ a Peltier cooling current of 5 ma. Techniques 

of psychrometer calibration and cleaning are discussed 

together with the details of the model, its application, 

and limitations. 

CONTENTS 

Page 

Introduction .......................................... 1 

Review of Theory and Concepts ....................... 2 

Thermocouple Psychrometers. ..................... .2 

Measurements of Water Potential .................. 3 

General Cali bration Procedures .................... .3 

The Role of Temperature Gradients.. ............... .3 

Methods and Procedures. ............................ .4 

Isothermal Calibration ............................. .4 

Nonisothermal Cali brat ion ......................... .6 

Results and Discussion ............................... 7 

Psychrometer Responses .......................... .7 

The Predictive Model ............................. .12 

Model Verification. ................................ 14 

Verification of the Isothermal Model.. ............ 15 

Verification of the Entire Model .................. 17 

Guides for Users.. .................................. .20 

Calibration. ...................................... .20 

Model Application ................................ .21 

Data Acquisition ................................. .21 

Conclusions.. ...................................... .22 

Publications Cited ................................... 23 

Appendix I. Computer program in BASIC and 

FORTRAN ........................................ .25 

Appendix II. Computer printout of model ............. .32 
United States 

Department of 

Agriculture A Calibration' Model 

Forest Service 

Intermountain 

Forest and Range Experiment Station 

for Screen-caged 

Ogden, UT. 84401 

Research Paper Peltier Thermocouple I NT-293 

July 1982 Psychrometers 

Ray W. Brown and Dale L. Bartos 

INTRODUCTION 

Thermocouple psychrometers are useful instruments 

for measuring the water potential of soils, plant tissues, 

and other media in the laboratory and the field. Unfortunately, they must be carefully calibrated under elaborately controlled conditions to insure accurate data. The 

calibration process involves establishing the relationship 

between microvolt output and known water potentials 

over a range of temperatures. These relationships are 

usually represented, for each psychrometer, as sets of 

hand-drawn curves that form the basis for estimating 

water potential from known microvolt and temperature 

data. However, calibration is time consuming, expensive, 

and subject to multiple errors when many psychrometers 

are used. 

Calibration errors are commonly associated with using 

improper techniques, applying laboratory data to unstable thermal environments, and interpolating data from 

hand-drawn curves. Because the reliability and accuracy 

of a thermocouple psychrometer are defined by the 

quality of its calibration, it is essential that one use 

proper techniques tempered with stringent adherence to 

detail and procedure (Brown 1970; Meyn and White 1972; 

Rawlins 1966; Slavik 1974; Wiebe and others 1971). In 

addition, it is usually recommended that each psychrometer be calibrated individually because common 

methods of construction often result in some variability 

among units that may affect their calibration characteristics (Wiebe and others 1971). However, in recent years 

the field use of thermocouple psychrometers in large 

numbers has become a common research method. This 

seriously complicates the logistical procedures of calibration when attempting to include the entire range of 

variables likely to be encountered under field conditions 

for dozens, or perhaps hundreds, of psychrometers. 

Serious problems arise when attempting to relate laboratory calibrations made under isothermal conditions to 

field data collected in unstable thermal environments. 

Although the errors caused by temperature gradients 

have long been recognized (Rawlins and Dalton 1967), the 

normal practice has been to ignore them. Not until Wiebe 

and others (1977) and Wiebe and Brown (1979) quantified 

the errors caused by temperature gradients could 

suggestions be made of how to avoid them, or otherwise 

minimize their effects. They defined the magnitudes of 

temperature gradient errors and identified various flaws 

in psychrometer design that aggravate them. Michel 

(1979)#subsequent ly studied temperature gradient effects 

on psychrometer calibration over narrow ranges of microvolts and temperatures. 

Four primary variables can be identified as influencing 

estimates of water potential with thermocouple 

psychrometers: (1) the microvolt output of the psychrometer; (2) the equilibrium temperature of the sample and 

the psychrometer; (3) the Peltier cooling current and 

length of cooling time; and (4) the influence of temperature gradients on psychrometer output. Although psychrometers may differ slightly in their calibration characteristics, generally they all have highly predictable responses to these variables within certain limits (Brown 

1970; Meyn and White 1972; Michel 1979; Rawlins 1966; 

Wiebe and others 1971). Also, calibration characteristics 

of psychrometers remain rather stable if the thermocouple is kept clean and its geometric position remains 

unaltered. For example, Brown and Johnston (1976) found 

that calibration outputs of psychrometers changed only 

1.2 percent after 40 months of continuous field exposure. 

This strong predictability of response to the four primary variables, together with the long-term stability of 

calibration characteristics, suggests that mathematical 

modeling may be useful in circumventing some of the 

problems associated with psychrometer calibration. A 

model would provide the interactive form and internal 

scales for the relations involved, and would express the 

average performance of the population of psychrometers 

used in its development. Also, a model would ideally be 
applicable to psychrometets of other pbpulations that are 

constructed with similar materials and techniques. Gross 

adjustment of the model using a small number of wellcontrolled calibration measurements would suffice to 

make the model applicable to any new pSyChrometer or 

group of psychrometers. The limits of accuracy would be 

established by the range of variability among the psychrometers, and could be predicted by model verification. 

If these linlits are acceptable, the mddel could prove to 

be highly useful for establishing the calibration characteristics of large numbers of psychrometers with a 

minimum of time, expense, and possible error due to 

interpretation of hand-fitted and drawn relationships. 

Further, using the assumption that the unique characteristics of each psychrometer can be identified with only 

one or a few calibration points, their responses over the 

entire range of the four primary variables could be predicted within prescribed limits of error using the model. 

Estimates of water potential with from one to any 

number of psychrometers could then be automated by 

computer programing methods. Although at first glance it 

may appear that some level of accuracy may be sacrificed by this method, most errors associated with manual 

data manipulation would be eliminated. 

The potential value of psychromet& calibration modeling has long been recognized (Rawlins 1972; Van Haveren 

and Brown 1972). Unfortunately, only the efforts of Meyn 

and White (1972) have been documented in detail. Their 

model was based on the performance of only eight 

psychrometers, and related microvolt output to a narrow 

range of water potentials (0 to about -46 bars) over a 

restricted temperature span, 8" tb 25 " C (46,4" to 77" F). 

In addition, their model was valid for only one Peltier 

cooling time under isothermal conditions. Michel (1979) 

attempted to predict the effects of temperature gradients 

on psychrometer estimates of water potential, but only 

studied narrow ranges of these two variables between 

20" and 30" C (68" to 86" F). 

The model developed here is designed to predict 

estimated potentials over the range of envirohmental 

conditions most likely to be encountered in the field. 

Generally, the model predicts water potentizils aver the 

range of sensitivity of chromel-conStaritan beltier psychrometers, or from 0 to about -80 bars. Also, it apglies to 

an ambient temperature range of 0" to 40" C (32" to 104" 

F) for Peltier cooling times of 15 to 60 sec, and for temperature gradient conditions that create about -e 1 " C 

(& 1.8" F) temperature differerlce between the sensing 

and reference junctions af the psychrometer (zero-offset 

of -e 60 microvolts). In addition, the predictive model was 

used to evaluate the following hypotheses: 

1. The microvolt response of any given psychrometer 

(of similar design criteria to those used here) to water 

potential, temperature, Peltier cooling time, and temperature gradients can be modeled arld predicted to within at 

least the limits of error normally expected with handdrawn calibration curves. 

2. The normal limits of error encountered in calibration 

can be redueed by adjusting the model over the range of 

appropriate variables as a function of a few calibration 

points for any individual psychrometer of similar design. 

3. The time and expense normally devoted to hand 

calibration can be significantly reduced by modeling 

calibration. 

4. Large quantities of either field or laboratory data 

can be analyzed more quickly and with fewer errors using 

the model-concept than with conventional methods. 

Recent technology advances in electronic instruments 

permit the use of such a model in microprocessor 

circuitry with field-operated meters and data storage and 

retrieval systems. This capacity can significantly reduce 

the amount of data processing required, and permits 

nearly instantaneous evaluation of data outputs. 

REVIEW OF THEORY CONCEPTS 

The development of a model for thermocouple psychrometer calibration depends, in part, upon an understanding of the basic concepts of these instruments. In 

addition, it is essential to recognize the role of the different variables that affect the performance of psychrometers. 

Thermocouple Psychrometers 

The theory of how thermocouple psychrometers 

operate has been described in detail (Spanner 1951; 

Rawlins 1966; Dalton and Rawlins 1968; Peck 1968,1969; 

Brown 1970; Wiebe and others 1971; Brown and Van 

Haveren 1972; Scotter 1972; and Slavik 1974). Basically, 

psychrometers are used to infer the water potential of 

soils, plant tissues, and other media from measurements 

of equilibrium vapor pressure. Instruments have been 

designed for use in closed systems within a sealed 

chamber and for in situ use in the field. 

Although a variety of design features have been developed, all Peltier thermocouple psychrometers now 

used have the same basic ingredients. They consist of a 

thermocouple constructed of 0.00254 - cm (0.001 -inch) 

diameter chrome1 and constantan wires welded to form a 

sensing junction. A short distance back from the sensing 

junction these wires are each attached to separate 

copper lead wires of large diameter, forming the reference junctions of the psychrometer. The sensing junction 

and two reference junctions form the essential constituents of a thermocouple psvchrometer. 

The primary differences among types of psychrometers 

are the design and material used to construct the protective housing around the thermocouple. Usually the choice 

of material and the design of the housing are determined 

by the intended use of the psychrometer, although there 

are some exceptions. Materials used include ceramic, 

stainless steel screen, and solid stainless steel or Teflon 

tubing with a screen end window. The various advantages and disadvantages of these have been discussed 

(Wiebe and Brown 1979; Wiebe and others 1971; Wiebe, 

Brown, and Barker 1977; Brown and Van Haveren 1972; 

Brown 1970). 
Measurements of Water Potential 

Prior to measuring water potential, the psychrometer is 

suspended in a closed system containing soil, plant 

tissue, or other media. Vapor pressure equilibrium is 

reached when the water potential of the medium and the 

vapor pressure of the air around it are in dynamic 

equilibrium. Under isothermal conditions the temperatures of the medium, the air, and the psychrometer are all 

equal. 

When these conditions are achieved, water potential 

measurements are made using the Peltier effect. A small 

electrical current (about 5 ma) is passed through the 

psychrometer circuit from the constantan to the chromel 

side of the thermocouple for a brief time (usually about 

15 sec). This current causes the sensing junction to cool 

slightly below ambient temperature (the maximum efficiency of chromel-constantan thermocouples is about 

0.6" C [I .08" F] below ambient temperature). If the 

thermocouple is cooled below the dew-point of the 

atmosphere surrounding it, water vapor in the air will 

condense on the sensing junction. Following a specified 

cooling time the current is terminated, and the 

condensed water on the junction immediately begins to 

evaporate back into the surrounding atmosphere. During 

this phase the thermocouple is again cooled, but now as 

a function of the rate of evaporation, which is a function 

of the vapor pressure of the atmosphere and hence of the 

water potential of the medium. In this manner the Peltier 

effect allows a thermocouple psychrometer to be used as 

a wet-and-dry bulb instrument. 

If the atmosphere adjacent to the thermocouple is at 

the saturated vapor pressure, the ambient temperature 

and the dew-point temperature will be identical, and thus 

water will not evaporate from the sensing junction. This 

situation corresponds to saturation or a 0 bar water 

potential, and will be detected as a 0 microvolt output on 

the meter. However, if a vapor pressure deficit exists in 

the surrounding atmosphere, evaporative cooling of the 

wet sensing junction will occur at a rate directly related 

to the magnitude of the deficit. This corresponds to a 

drier situation than saturation, and will be detected as a 

microvolt output from the thermocouple. Thus, the drier 

the water potential of the medium, the greater will be the 

microvolt output from the psychrometer. If the water 

potential is drier than about -85 bars, however, the dewpoint temperature will likely be more than 0.6" C (1 .O8" F) 

below the ambient temperature. At this point and beyond, 

the efficiency of the Peltier effect is no longer great 

enough to condense sufficient water on the sensing 

junction to achieve stable readings. This represents the 

approximate lower limit of sensitivity for chromelconstantan thermocouple psychrometers. 

General Calibration Procedures 

Thermocouple psychrometers can be calibrated by 

suspending the instrument in a sealed chamber containing a water vapor source of known water potential at a 

constant temperature (Barrs 1968; Brown 1970; Brown 

and Van Haveren 1972; Campbell 1972; Meyn and White 

1972; Rawlins 1966, 1972; Slavik 1974; Wiebe and others 

1971). Normally an electrolyte solution such as NaCl or 

KC1 of known molality is used as a vapor source. The 

relationship between water potential and solution concentration at various temperatures is available from 

standard tables (Lang 1967; Wiebe and others 1971: 

Brown and Van Haveren 1972) 

A piece of filter paper saturated with the solution is 

sealed with the psychrometer in the chamber. Calibration is usually performed in a water bath under isothermal conditions because both psychrometer output 

and water potential are temperature-dependent variables. 

Psychrometer outputs in microvolts are then plotted 

against water potential in bars for several different 

temperatures to yield a family of curves. Since the relationship between psychrometer output and water 

potential is not linear throughout the entire range, several 

different salt solutions are used for each of several 

temperatures. 

The importance of careful and precise calibration technique has been stressed (Rawlins and Dalton 1967; 

Brown 1970; Wiebe and others 1971 ; Meyn and White 

1972). Everything known about psychrometer responses 

is based on calibration. Electrolyte solutions must be 

prepared with great care, and all materials used including the psychrometers, chambers, filter paper, and 

other accessories must be thoroughly and rigorously 

cleaned. In addition, care must be exercised in maintaining precise temperature control to minimize the 

effects of temperature gradients and to accurately 

establish the relationship between psychrometer output 

and temperature. 

The Role of Temperature Gradients 

Temperature gradients are a natural phenomenon 

(Wiebe and others 1977). Although thermocouple psychrometers are designed and calibrated for use under 

isothermal conditions, in situ applications in the field 

invariably lead to problems associated with temperature 

gradients. Thermal instability in a system leads to, 

ammg other phenomena, the movement. of water vapor 

from warmer to cooler regions. Essentially, temperature 

gradients cause errors in estimates of water potential by 

disrupting the thermal stability between the sensing 

junction of the psychrometer and the evaporating sample 

surface, or between the sensing and reference junctions 

(Rawlins and Dalton 1967; Wiebe and others 1977; Wiebe 

and Brown 1979; Michel 1979). 

Wiebe and Brown (1979) analyzed differences in temperature between the sample and the psychrometer and 

showed that temperature gradients may cause several 

types of errors: (1) if the average sample surface and the 

sensing junction temperatures differ, their vapor 

pressures will be identical but their relative vapor pressures will differ; (2) water may condense at, or evaporate 

from, the surface being measured by the psychrometer 

depending upon the direction of heat movement; and (3) 

water may become trapped within solid chambers consisting of "end-window" type designs. They concluded 
that these errors can be minimized with proper psychrometer design criteria: (1) concentric geometry with the 

sensing junction located in the middle or toward the 

distal end of a cylindrical or spherical sample surface; (2) 

use of single-junction thermocouples that permit detection of thermal gradients; (3) use of materials with low 

heat conductivity; and (4) miniaturization of components 

consistent with stability, ruggedness, and ease of construction. 

Among the commercially available designs that currently meet these criteria are the ceramic cup and screencagea units of Wescor and the stainless steel screencaged units of J. R. D. Merrill. Although these units 

minimize errors due to temperature differences that may 

occur oetween the psychrometer and the sample, such 

errors may still occur. 

The null-output in microvolts of a psychrometer under 

true isothermal conditions prior to Peltier cooling will be 

zero. This indicates that the net microvoltage outputs of 

both the reference and the sensing junctions counterbalance each other, a phenomenon referred to as the 

Seebeck effect (Van Haveren and Brown 1972). However, 

when a temperature gradient exists within the psychrometer (the temperatures of the reference junctions and 

sensing junctions are not equal), the null-output will 

either be positive or negative depending upon the 

direction of heat movement. This null-output in microvolts 

has been termed the "zero-offset" (for instance, the 

microvolts of offset from zero) by Wiebe and others 

(1977), Wiebe and Brown (1979), and Michel (1979) and is 

used to detect the presence and magnitude of temperature gradients. 

The output generated by chromel-constantan thermocouples is about 60 microvolts per degree (33.3 microvolts per degree Fahrenheit) in the temperature range of 

0" to 70" C (32" to 104" F) (Omega Engineering, Inc. 1976). 

Thus, an offset from zero of +60 microvolts would 

indicate that the sensing junction was about 1 " C (1.8" F) 

cooler than the reference junctions, and conversely, a-60 

microvolt offset indicates the sensing junction is 1 " C 

(1.8" F) warmer. Although the precise magnitude of a 

temperature gradient may not always be known, its 

relative magnitude and direction can be calculated by 

knowing the offset from zero (Michel 1979) and the 

distance between the sensing and reference junctions. 

Generally, positive offsets result in water potential est imates that are too dry (microvolt outputs are too high), 

whereas negative offsets yield readings that are too wet 

(microvolt outputs are too low). 

METHODS AND PROCEDURES 

The influences of the four primary variables on psychrometer performance incorporated in the model were 

investigated using two different calibration procedures. 

Isothermal calibration was used to determine the effects 

on psychrometer output of (1) water potential, (2) 

equilibrium temperature, and (3) Peltier cooling time. The 

fourth variable, temperature gradients, was assessed by 

nonisot hermal calibration met hods. 

Isothermal Calibration 

The methods of isothermal calibration used in this 

study follow the general procedures discussed above 

with a few modifications. A total of 24 screen-caged 

single-junction thermocouple psychrometers (fig. 1) were 

used that had been selected at random from a total 

population of 270 units (Brown and Collins 1980). These 

units are identical to those constructed by various commercial companies (J. R. D. Merrill, EMCO, and Wescor) 

in all respects affecting psychrometers operation and 

function. Some unique design features were added, 

which have since been adopted by these companies, but 

they do not affect the basic characteristics of chromelconstantan instruments. Therefore, it is anticipated that 

the data collected in this study are representative of 

similar screen-caged psychrometers employing a protective housing that provides a 360" evaporative surface 

concentric to the sample surface. 

PVC INSULATED CABLE 

MYLAR SHIELD 

MELTABLE, SHRINK 

TUBING LINER 

POLYPROPYLENE SHRINK 

TUBING LINER 

COLOR-CODED INSULATION 

EPOXY RES l N 

TEFLON PLUG 

COPPER-CONSTANTAN JUNCT 

(soldered) 

CHROMEL 

(0.0025 cm) 

WELDED 

JUNCTION I I 

"\200 MESH OUTER Ll NER 'I 

!I I 

I1 

-STAINLESS STEEL SCREEN CAP 

Figure 1 .-Screen-caged singlejunction Peltier thermocouple psychrometer used to develop the calibration model (after Brown and Collins 

1980). 
The same 24 psychrometers were used throughout this 

phase of the study. Each psychrometer was sealed in a 

stainless steel chamber identical to those described by 

Brown and Collins (1980) and illustrated in figure 2. With 

the lower cap removed, the entire sidewall of the 

chamber around the psychrometer was lined with a 

Whatman No. 1 filter paper strip previously cut to size. 

The filter paper was then saturated with a NaCl solution 

dispensed from a drop-bottle, with the excess poured off 

and discarded. Then the lower cap was immediately replaced over the chamber and sealed. 

Tt PSYCHROMETER CABLE 

15 O ANGLE (modificatiofir 

SUKCICAl. TURiNG 

REDUCER ORlFl CE (mcdifica4ion~ 

15 O ANGLE (modification) 

SCREEN CAGE, PSYCHROMETER 

SAMPLE CHAVBER 

, 1 cm , 

Scale 

Figure 2.-Stainless steel calibration 

chamber with sealed psychrometer in 

place (after Brown and Collins 1980). 

A summary of the NaCl molalities and temperatures 

used in this study appears in table 1, together with the 

water potentials of the solutions. Each solution was prepared separately with reagent grade NaCl (see Brown and 

Van Haveren 1972, pages 302-308 for detailed procedures). The 0 molality solution consisted of distilleddeionized water. 

A Forma Scientific refrigerated water bath (model 2324) 

was used to maintain constant temperature control 

within limits of & 0.01 " C (0.018" F). We used a modified 

top on the bath that provided a rubber seal around both 

the lead wires of the psychrometers and the rim of the 

reservoir to reduce the effects of evaporative cooling on 

batn temperature. The temperature stability within the 

bath was monitored regularly using four separate 

measuring systems: (1) two National Bureau of Standards 

calibrated mercury4 n-glass thermometers to the nearest 

0.01 " C (0.018" F); (2) a thermistor and electronic digital 

thermometer; (3) a differential copper-constantan thermocouple with.a 5-cm (2-inch) span between junctions; and 

(4) the copper-constantan thermocouple circuit in each of 

the 24 psychrometers. The bath demonstrated excellent 

stability at all temperatures under continuous use, and 

the differential thermocouple never indicated a greater 

temperature difference than 0.0025" C (0.0045" F) 

between its junctions. 

Table 1.-Summary of water potentials in bars for NaCl 

molalities and temperatures used in calibration (after 

Lang 1967) 

NaCl Temperature 

molality 0°C 7.5" C 15°C 25°C 35" C 

- Water lootential, bars - - - - 

0.0 0.0 0.0 0.0 

-8.60 -8.84 -9.15 -9.46 

-21.36 -22.00 -22.81 -23.62 

-29.98 -30.91 -32.10 -33.28 

-43.1 8 -44.59 -46.40 -48.1 5 

-66.06 -68.37 -71.34 -74.1 1 

-75.50 -78.20 -81.70 -84.90 

-80.35 -83.30 -87.00 -90.40 

-85.30 -88.40 -92.40 -96.00 

-90.25 -93.60 -97.80 -101.60 

After the 24 psychrometers were sealed within their 

chambers they were immersed in the bath. About a 35-cm 

(14-inch) section of lead wire above the calibration 

chamber was also submerged into the circulating water 

to reduce the effects of heat conduction along the wires. 

Temperature equilibration between the water bath and 

the chambers was usually achieved within 30 min, but 

vapor pressure equilibrium within the chambers usually 

required from 2 to 6 hours. Temperature equilibrium was 

detected as a 0 microvolt offset on the microvoltmeter 

(Wiebe and others 1977; Wiebe and Brown 1979), and 

vapor pressure equilibrium was assumed when two reproducible water potential outputs were read 1 hour apart. 

The 0 (distilled-deionized water) and 0.2 molal solutions 

required longer equilibration times, whereas the more 

concentrated solutions required shorter times. Also, in 

general, vapor pressure equilibration was slower at cool 

temperatures and faster at warm temperatures. 

In an effort to reduce variability, all 24 psychrometers 

were calibrated simultaneously with the same solution. 

The microvolt outputs of each psychrometer were 

measured with an SB-Systems 600 meter to the nearest 

0.1 pV, and temperature was recorded to the nearest 

0.1 " C (0.18" F). Questionable readings were checked only 
after 30 min reequili bration time. The psychrometer outputs were recorded beginning with the 0" C (32" F) 

temperature first, and then followed successively with 

each next higher temperature up to 35" C (95" F). We 

found it convenient to immerse the set of psychrometers 

in the 0" C (32" F) bath late in the afternoon and allow 

them to equilibrate overnight. After the readings were 

recorded the next morning, the bath temperature was 

resef at 7.5" C (45.5" F). The data at this temperature 

were then recorded when vapor pressure equilibrium had 

been reached, and the process was repeated for each 

successive temperature. Using this procedure, from 3 to 5 

days were required to collect the calibration data for 

each solution. 

Chances of water vapor condensation within the 

chambers were reduced somewhat by sequentially increasing the temperature after each set of readings. 

However, the first set of readings of 0" C (32" F) may 

have been affected by water condensation, which would 

in part explain the much longer equilibration process at 

this temperature. Once condensate forms within the 

chamber, reevaporation of the liquid drops and the establishment of vapor pressure equilibration are severely 

slowed. 

All psychrometers and calibration chamber 

components were thoroughly cleaned and dried each 

time the NaCl solutions were changed. Each component 

was sprayed with electronic tuner cleaner (LPS Instant 

Cleaner, LPS Research Labs., Inc., Los Angeles, CA 

90025) to remove grease and other contaminants. Then 

all components were washed vigorously with distilleddeionized water. A squeeze-bott le with a narrow-neck 

spout was used to force water into the screen-cage of the 

psychrometers to remove all traces of tuner cleaner, salt 

solution, or other contaminants. The components were 

blown dry with filtered compressed air at 60 psi, and then 

completely dried at 80" C (176" F) in a forced-draft oven 

overnight. After the components had cooled to room 

temperature, maintained between 20" and 25" C (68" to 

77" F) the rubber o-ring seals were treated with a thin 

coat of Dow Corning silicone grease to facilitate proper 

sealing and movement of parts, and then reassembled. 

With the lead wires connected to the meter, psychrometer outputs in microvolts as a function of water 

potential and temperature were measured with Peltier 

cooling times of 15, 30, and 60 sec. For our psychrometers we used the optimum Peltier cooling current, 

which had been previously determined to be 5 ma. 

Generally the optimum current for chromel-constantan 

thermocouples of this type is between 3.5 and 5 ma 

(Merrill and Rawlins 1972). In this manner, data were 

assembled for inclusion in the model to describe the 

influence of the first three primary variables on psychrometer performance. 

Nonisothermal Calibration 

The objective of this phase of the study was to assess 

the effects of temperature gradients on psychrometer 

response to known potential and temperature conditions. 

Six psychrometers of the original 24 were randomly 

selected and imbedded in a sand column saturated with 

one of the NaCl solutions. We originally had attempted to 

use nine psychrometers, but the logistics of the technique proved to be too complex to permit accurate 

assessment of each instrument in unstable thermal 

environments. The sand column was contained in a plexiglass tube 11.4 cm in diameter by 35.6 cm length (4.5 

inches by 14 inches) fitted with sealable stainless steel 

plates at both ends 

The sand used in the column was a No. 3 grit that had 

been washed to remove salts and other foreign matter 

and then dried. The sand was presaturated with an NaCl 

solution and then allowed to drain while in a sealed 

plastic bag to reduce evaporation. This moistened sand 

was lightly packed in the plexiglass tube until it was 

nearly half full, and then the psychrometers were positioned half way between the two end plates of the 

column and perpendicular to them. Three of the psychrometers were placed with their sensing junctions facing 

up and the other three facing down (180 degrees in the 

other direciton, but parallel to each other). Opposing 

placement of the psychrometers provided nearly equal, 

but opposite zero-offsets, when a temperature gradient 

passed through the system. The psychrometers were 

positioned about 1 cm (0.39 inch) apart, and moist sand 

was lightly packed around them to hold them in place. A 

30-cm (1 2-inch) section of lead wire of each psychrometer 

was coiled at the same location, but away from the zone 

of immediate influence on the psychrometers, to minimize the effects of heat conduction along the wires. The 

remainder of the tube was then filled, but care was taken 

to pack the sand lightly around the psychrometers to 

insure intimate contact with them. The lead wires of the 

psychrometers extended up through the sand column 

and exited the plexiglass tube near the top. The top plate 

was sealed in place with self-tapping.screws, and RTV 

silicone rubber was used to insure a watertight seal. 

The entire tube was submerged in the water bath and 

allowed to reach temperature and vapor pressure equilibrium. Usually about 3 hours were required to reach 

temperature equilibrium within the large mass of sand, 

but between 24 and 48 hours were required to achieve 

vapor pressure equilibrium. Under these conditions, the 

zero-offset was first verified at 0 microvolts, and then the 

water potential and temperature data were recorded. 

These data served to verify psychrometer consistency 

between the isothermal and nonisothermal calibration 

methods. In virtually all cases the same outputs were 

recorded for given water potentials and temperatures in 

both experiments. The same NaCl solutions (up to 1.5 m 

NaCI), temperature range, and Peltier cooling times were 

used in both the isothermal and nonisothermal experiments. 
To achieve nonisothermal conditions around the psychrometers, the sand column was elevated to different 

levels part way out of the water bath. It was found that, 

with care, the thermal stability in the sand column could 

be disrupted and a new temperature gradient induced 

while maintaining a fairly stable ambient temperature 

around the psychrometers. The difference in temperature 

between the water bath and the laboratory room was 

thus used as the source of temperature gradients in the 

sand column. By adjusting the level of the column in the 

water, and by tilting it to various angles, virtually any 

magnitude of temperature gradient could be achieved. 

With these kinds of manipulations, reasonably constant 

temperature gradients could be induced, as indicated by 

the zero-offset output from the psychrometers. Both 

positive and negative zero-offsets of large magnitvde 

were easily achieved. As discussed by Michel (1979), 

positive zero-offsets were generally indicated when the 

sensing junction was cooler than the reference junctions, 

and negative offsets when the sensing junction was 

warmer than the reference junctions, which is the reverse 

of how Wiebe and others (1977) reported their zero-offset 

observations. 

Wiebe and others (1977) explained that the magnitude 

of the zero-offset only provides an estimate of the magnitude of temperature gradients. They showed that call 

culated values of temperature gradients based on the 

thermocouple thermal constant (60 microvolts per 

degree) and the dimensions of the therpocouple can vary 

slightly from measured temperature gradients. They 

suggested that the sensing and reference junctions likely 

respond to the "average" temperature of the psycqrometer cavity. This explanation is quite plausible since the 

two reference junctions may be at different temperatures 

while the sensing junction may be at yet another 

temperature. Thus, the direction of heat movement within 

the psychrometer cavity can influence the magnitude of 

the zero-offset microvoltage with virtually infinite variations. 

Therefore, we did not measure the actual temperature 

gradients within the sand column with separate thermocouples since such data are of little or no value for 

developing a predictive model, and since the opportunity 

to do so under field conditions is rarely available (except 

where two or more psychrometers are stacked in the 

soil). Rather, we relied on the assumption that, for given 

water potentials and ambient temperatures, each level of 

zero-offset would yield an error of consistent magnitude. 

Our preliminary studies to verify this, together with the 

final analyses of the data, showed that the assumption 

was correct. However, of even greater importance is the 

fact that zero-offsets and associated estimates of water 

potential could be repeatedly reproduced for each set of 

temperature and NaCl molality conditions. Michel (1979) 

similarly found that zero-offsets affect water potentials in 

a predictable manner, and concluded that they can be 

used to correct the estimates of water potential made 

under thermal gradients. Our data and experience 

suggest that zero-offsets alone are of little value as 

direct measures of temperature gradients, as originally 

suggested by Wiebe and others (1977), but are essential 

for adjusting microvolt outputs to correct estimates of 

water potential directly affected by the temperature 

gradient. 

An attempt was made lo allow the system to achieve a 

stable thermal gradient before data were collected, but 

the time required to reach stability varied with different 

temperature condition?. Usually an hour or more waq 

required to achieve stable temperature gradients for each 

new position of the sand column in the water bath. When 

a desired level of temperature gradient (or, more correctly, zero-offset) was reached, the zero-qffset, water 

potential estimate in microvolts, and the ambient 

temperature for each psychrometer were recorded. Prior 

field experience suggested that most observed zerooffsets commonly occur within the range of about -60 to 

+ 60 mi~;rovolts. These extremes of zerg-offset were 

therefore selected as the limits for the predictive model, 

although occasioqal field observations may strgy well 

beyond these limit$. 

RESULTS AND DISCUSSION 

Psychrometer Responses 

The psychrometer calibration data collected under isothermal conditions are summarized in table 2 and figure 

3 a, b, and c. Generally these data show that the 24 psychrometers used here display the same calibration characteristics as those of different design and manufacture 

(Brown 1970; Meyn and White 1972; Wiebe and others 

1971). The mean microvolt outputs increase with longer 

Peltier cooling times and with increasing temperatures. 

Outputs increase from 0 microvolt at 0 molality (0 bar 

water potential) to a maximum near 1.8 molal (about -75 

to-90 bars, depending upon temperature), and then 

decrease sharply beyond this point. Thermocouple psychrometers with similar design features as thoqe used 

here are most sensitive in the range of 0 to about -80 

bars, and sensitivity increases with temperature. At water 

potentials drier than about -80 bars their sensitivity 

declines rapidly, and the variability among psychrometers increases substantially. Bey~nd the region of 

maximum microvolt output, the variability among psychrometers is so great that it is of little or no predictive 

interest. Therefore, only the water potential region of 

maximum sensitivity (0 to about -80 bars) was included in 

the predictive calibration model. The 1.9 and 2.0 molal 

data in table 2 are only included here to illustrate the 

rapid decline in psychrometer output at these dry water 

potentials. 

It is interesting to note the low microvolt outputs for 

the 0 molal (0 bar) solution. Other workers have frequently reported small positive outputs of about 0.2 to 

0.5 microvolt at 0 bar water potential, p~esumably due to 

water absorption on chamber walls or heating of the 

reference junctions during Peltier cooling (Meyn and 

White 1972; Wiebe and others 1971). We found that the 

theoretical output of 0 microvolt could be achieved 

routinely if we adhered to scrupulous cleaning procedures and long eqy ilibration times of 15 to 20 hours. 

7 
WATER POTENTIAL, BARS 

Figure 3a.-Calibration curves for isothermal 

conditions with 15-sec cool time. Standard deviation shown for each set of data. 

WATER POTENTIAL, BARS 

Figure 3b.-Calibration curves for isothermal 

conditions with 30-sec cool time. Standard deviation shown for each set of data. 

Table 2.-Summary of isothermal calibration data for each NaCI molality, temperature ("C), and Peltier cooling time (seconds). Values shown are 

in microvolts. The upper value in each row is the mean (2) for the 24 psychrometers, and the lower value is the standard deviation (sd) 

Temperature and cooling time (seconds) 

NaCl 0 "C 7.5 "C 15°C 25 "C 35 "C 

molality 15 30 60 15 30 60 15 30 60 15 30 60 15 30 60 
WATER POTENTIAL, BARS 

Figure 3c.-Calibration curves forkiothermal 

conditions with 60-sec cool time. Standard deviation shown for each set of data. 

The standard deviations (sd) in table 2, and illustrated 

in figure 3, indicate both the variability among the 24 

psychrometers and the ranges of water potentials and 

temperatures over which they display their greatest 

consistency. Generally the psychrometers were most 

variable at the extreme water potentials and at the cooler 

temperatures studied. However, in most cases the standard deviations were 10 percent or less of the mean 

outputs at water potentials ranging from about -10 to-80 

bars throughout the temperature range studied. Also, 

longer Peltier cooling times resulted in less variability. 

The relationships between psychrometer output and 

zero-offset obtained from nonisothermal calibration were 

established for each temperature regime, NaCl solution 

(up to 1.5 m), and Peltier cool time. An example of one 

such relationship for the six psychrometers used is illustrated in figure 4 for 25" C (77" F) at 0.5 m NaCl using 15- 

sec Peltier cool time. As was typical for all such relationships, the outputs of the six psychrometers used in the 

nonisothermal calibration at an offset of 0 microvolts 

were within the limits of 2 1 sd of the mean output of all 

24 psychrometers calibrated under the same conditions 

shown in table 2. The example in figure 4 illustrates that 

under positive zero-offset conditions, psychrometer outputs tend to be higher than under isothermal conditions. 

But, under negative zero-offset conditions, outputs tend 

to be lower than those under isothermal conditions 

(Wiebe and others 1977; Michel 1979). This relationship is 

strongly linear for all conditions studied with r2 values 

ranging between 0.82 and 0.99 (table 3). The intercepts 

(b), slopes (a), and r2 values of the psychrometer output 

versus zero-offset relationship for other water potentials 

and temperatures at 15-sec cool time are shown in table 

3. Similar data were also collected for the 30- and 60-sec 

MICROVOLTS, ZERO- OFFSET 

Figure 4.-Relationship between psychrometer output in microvolts and 

zero-offset at 25" C for 0.5 m NaCl solution and 15-sec cool time. 
cool times, but the level of sampling was not as intensive. 

The data in table 3 clearly show a strong effect of 

water potential on slope over the entire range of conditions sampled. Except at 0 bar water potential, the slopes 

increased with increasing temperature and decreasing 

water potential. Michel (1979) found this effect of 

temperature but found no effect of water potential. 

Michel (1979) studied narrower ranges of water potential 

(-5to -20 bars), temperatures (20 " to 30" C [68 " to 86 " F]), 

and zero-offsets (-5 to + 8 microvolts), and it is highly 

possible that the effects of water potential were masked 

by the variability among his observations. This leads to 

the conclusion that psychrometer output errors are the 

same at different water potentials. By selecting similarly 

narrow ranges within our own data (see fig. 4, between-5 

and + 8 microvolts of zero-offset), we were able to 

calculate slope values that resemble those presented by 

Michel (1979). It is apparent that a clearer and more 

accurate assessment of psychrometer response is 

possible when broader ranges of conditions are studied. 

As a result, his suggestion that each microvolt of zerooffset is accompanied by an error of 1.75 bars water 

potential, although accurate for his instruments, does not 

apply to psychrometers similar to those used here. It is 

now evident that a fixed level of error is not consistent 

with how screen-caged thermocouple psychrometers like 

those used in this study respond to these variables. 

The magnitude of errors in psychrometer output 

caused by zero-offset (temperature gradients) is affected 

by both temperature and water potential. The effect of 

temperature is illustrated in figure 5, wherein the slopes 

of the curves relating output and zero-offset (table 3) 

were used to construct the relationship between psychrometer error and zero-offset. In this illustration, the data 

for the 0.5 m NaCl solution and the 15-sec cool time are 

displayed at temperatures ranging from 0" to 40" C (32" 

to 104" F). The y-axis represents the error in microvolts of 

psychrometer output for the range of zero-offsets and 

temperatures studied, and shows that psychrometer outputs are too high when positive zero-offset conditions 

Table 3.-Intercepts (b), slopes (a), and r2 values for psychrometer microvolt out~ut vs. zero-offset for 15-second 

cool time 

Temperature, NaCl molal solution 

"C 0 0.5 1 .O 1.5 

b 0.01 8 3.944 7.191 9.884 

0 a .011 .014 .029 .038 

r2 .905 .899 .886 .884 

ZERO- OFFSET. MICROVOLTS 

Figure 5.-Relationship between psychrometer error in microvolts and zerooffset for 0.5 m NaCl and 15-sec cool time for temperatures ranging between 

0" and 40" C. 
prevail, and are too low when negative zero-offset 

conditions prevail. Also, the size of the error is magnified 

as the temperature increases from 0" to 40" C (32" to 

104" F), and as the zero-offset deviates further from 0 

microvolts. 

An example of the effect of temperature gradients 

(expressed as zero-offset) and water potential on 

psychrometer output is shown in table 4 for 25" C (77" F) 

and 15-sec cool time. The number of observations (n) 

shown for each zero-offset from 0 to -160 microvolts 

represents only a small sample of all the observations 

made at other temperature gradients under these conditions. The mean psychrometer outputs in microvolts (x) 

and their corresponding standard deviations (sd) 

illustrate, for this range of water potentials (0 to -71.3 

bars), the general response and the range of variability 

that psychrometers display under temperature gradient 

conditions. Under isothermal conditions (0 zero-offset), 

the data are very similar to those shown in table 2 for the 

same conditions. Of considerable interest is the apparent 

lack of psychrometer response to temperature gradients 

at 0 bar water potential. This same effect was noted at 

the other temperature regimes studied, indicating that 

psychrometers are relatively insensitive to temperature 

gradients (between r 60 microvolts) under saturated 

conditions. Apparently vapor pressure differences within 

the psychrometer cavity are insufficient to cause a 

psychrometer response to temperature gradients under 

saturated conditions. However, as the water potential 

declines, psychrometer output progressively deviates 

from the expected isothermal output as zero-offset increases or decreases from 0 microvolt (the slope data in 

table 3 also show the same effect). The same basic rela. 

tionships were also observed for all other temperatures 

and cooling times studied. The magnitudes of deviation 

in psychrometer output from isothermal calibration 

values tend to be greater at warmer temperatures and 

under longer Peltier cooling times, and are smaller at 

cooler temperatures and short cooling times. 

The effect of temperature gradients (zero-offset) on 

psychrometer output is highly complex, and yet bears 

some rather subtle characteristics. Figure 6 illustrates 

the 0 to -t60 microvolt zero-offset data from table 4, and 

shows just how large an error zero-offset can cause in 

estimates of water potential with thermocouple 

I, *, 

WATER POTENTIAL, BARS 

Figure 6.- Effect of zero-offset at + 60, 

0, and -60 microvolts on psychrometer 

output at 25" C and 15-sec cool time. 

Table 4.-Effect of zero-offset and water potential on psychrometer output at 25°C with 15-second Peltier cool time. Number of observations (n), 

mean psychrometer output in microvolts (g), and one standard deviation (sd) are shown 

Water ~otential. bars 

0 - 22.8 - 46.4 - 71.3 

Zero- (0 rn NaCI) (0.5 m NaCI) (1.0 m NaCI) (1.5 m NaCI) 

- - - offset n - 

x sd n x sd n x sd n x sd 

0 21 0.1 0.1 20 10.4 0.3 20 20.5 0.5 15 29.2 0.5 

- 5 6 .1 .1 9 10.0 .2 9 19.7 .4 9 28.0 .6 

+ 5 6 .1 .1 9 10.6 .1 9 20.9 .4 9 29.3 .6 

- 15 9 .2 .1 6 9.8 .3 6 18.3 .6 6 27.0 .7 

+ 15 9 .I .1 6 11.4 .3 6 21.5 .6 6 30.6 .8 

- 30 9 .1 .1 6 8.8 .4 6 17.1 .5 8 24.7 1.3 

+ 30 9 1 .1 6 11.9 .6 6 23.5 .7 8 33.6 1.1 

- 60 10 .2 .1 15 6.9 .5 12 14.9 .9 12 20.5 1.4 

+60 10 .1 .1 15 14.3 .7 12 26.7 1.4 12 36.5 1.6 
psychrometers. In its simplest form a reading of 15 

microvolts under isothermal conditions (for the example 

in fig. 6) would indicate a water potential of about -33 

bars. However, if a temperature gradient resulting in a 

zero-offset of + 60 microvolts existed, the actual water 

potential for that reading would only be-25 bars. Had the 

zero-offset been ignored (which is a common practice), 

an error of 8 bars in the estimate would have resulted. On 

the other hand, if a-60 microvolt zero-offset occurred, the 

actual water potential would have been -47.5 bars, 

resulting in an error of about 14.5 bars if the correction 

were not made. The subtlety here is that for a given water 

potential, temperature, zero-offset, and cooling time, only 

one unique microvolt output is possible (within certain 

limits and assuming no condensation has occurred 

within the psychrometer). For instance, if the water 

potential was-25 bars in the example of figure 6, an 

output of 15 microvolts could only occur if a zero-offset 

of + 60 microvolts also occurred simultaneously. Had 

there been no zero-offset (isothermal conditions), the 

psychrometer output could have only been about 11.5 

microvolts (+ some acceptable level of error). Conversely, if the medium was at-47.5 bars, the psychrometer output could only be about 20.6 microvolts if the 

offset was 0, or 15 microvolts if it was -60. 

The progressively diverging zero-offset curves away 

from the isothermal calibration curve were not entirely 

anticipated. This relationship is particularly noticeable at 

the extreme zero-offsets such as those illustrated in 

figure 6. Of particular interest is the similarity of zerooffset curves to isothermal curves of other temperatures 

relative to 25" C (77" F). For example, the + 60 and -60 

microvolt zero-offset curves bear a striking similarity to 

the 35" and 15" C (95" and 59" F) temperature curves, 

respectively, shown in figure 3a. Although a comparison 

of their relative slopes (for instance,-0.284 at 15 " C 

[59 " F] and -0.289 and -60 microvolts, and -0.482 at 35 " C 

r95" F] and -0.51 1 at + 60 microvolts) shows they are not 

identical, their similarity suggests a possible relationship. Under a positive zero-offset, when the sensing 

junction is cooler than the reference junctions, psychrometer sensitivity (microvoltslbar) is enhanced somewhat 

as if temperature had been increased. But, under negative zero-offsets, sensitivity is depressed in a similar 

manner as if temperature had been decreased. 

The validity of a predictive model for thermocouple 

psychrometers is based on the assumption that the relationships among temperature, water potential, cooling 

time, and temperature gradients are all reproducible for 

any given similar psychrometer, and that the variability 

among units is acceptably small. The data, such as those 

illustrated in figures 3, 4, 5, and 6, and those shown in 

tables 2. 3, and 4 appear to meet these criteria. Large 

numbers of observations made with numerous psychrometers, together with their relatively small standard 

deviations, indicate these relationships are all highly 

predictable. 

The Predictive Model 

The relationships between psychrometer outputs in 

microvolts and water potentials in bars form the basis of 

the predictive model. The data in table 2 and illustrated in 

figure 3a, b, and c, define the approximate limits of the 

isothermal portion of the model. Generally, the model is 

applicable within the temperature range of 0" to 40" C 

(32" to 104" F) for water potentials ranging from 0 to 

about -80 bars. The effects of both Peltier cooling time 

between 15 and 60 sec (for a 5-ma current), and zerooffset between-60 and + 60 microvolts are also incorporated. Appropriate power functions and e-transforms 

were fitted to the data by least squares methods (Jensen 

and Homeyer 1970; 1971; Jensen 1973,1976,1979). The 

resulting model had an r2 of 0.99 and performs acceptably throughout the required range of imposed 

conditions. 

The overall modeling rationale was one of expressing 

microvolts (MV) as a calibrated function of water potential in bars (WP), temperature in degrees centigrade 

(Temp), and length of Peltier cooling time (Sec). The resulting function was then solved for WP, the final item of 

predictive interest. 

For each of the 15 temperature and cooling time 

combinations, the curves of microvolts over water 

SP WATER POTENTIAL, BARS 

I SP-WP I 

Figure 7.-Generalized relationship 

between microvolt output and water 

potential showing the relative positions of the curve peak (SP) and the 

scaled difference (UI) in microvolts at 

peak height. 
potential were clearly defined by the array of observation 

means. All 15 trends were smoothed manually (fig. 3a, b, 

and c) and the entire relationship was described mathematically. Each curve over water potential was of the 

composite form: height of the peak (upper intercept, UI), 

minus a relatively flat power function (1.18 5 N 5 1.36) of 

the absolute difference between the point in water potential at which the curve peaked (SP) and some specified 

WP (for example, ISP - wpJN) (fig. 7); scaled to the difference between UI and zero (= UI), for example 

(UIIISPIN) * ISP - WPIN, or in total, 

The inputs N, UI, and SP in equation 1 were found to 

vary over both temperature and time. For example, N 

varied sigmoidally over temperature (fig. 8) as follows: 

where the inflection point ( I) varied as a power function over time, so that 

I = 0.45 + 0.000333(Sec) + (1.9846 x 10-19) 

* (Sec)lo, (3) 

and M varied as a sigmoid over time, 

UI varied as a flat power function over temperature, 

such that 

UI = INTI + 0.017288 * YP, * (Temp)'.' (5) 

where INTI and YP, change over time; 

INTI = 12.1 - 0.003475 (60-Se~)l.6~ (6) 

and 

YP, = 39.2 - 0.0004346 (60-Se~)2.~5 (7) 

The point in the range of WP at which the curves peak 

(SP) varied as a flat power function of temperature, where 

SP = INT, -YP2 * 0.0001 71 85 (40-Tem~),.~~ (8) 

where INT2 and YP2 changed over time so that; 

and 

YP, = 8.4 + 2.734 x (60-Se~)~-~~ (10) 

microvolt readings are either increased or decreased 

from those with no gradient, depending upon the extent 

of the gradient and its direction. A measure of difference 

and direction is available in zero-offset microvolts (OMV), 

quantified in figure 5 as to its effect on the microvolt 

reading. Note that the effect changes with the average 

temperature of the medium. For convenience, this effect 

is called zero-offset error (ZOE) and is described mathematically from figure 5 as: 

ZOE = 0.015 (OMV) + 0.001471 (TEMP) (OMV) (11) 

Correction of ZOE to that for cooling times other than 

15 sec is provided by the ratio 

(MVSIMV,,) * ZOE, 

where MVS is the MV for whatever temperature and 

cooling time is specified, and MV,, is the MV at the same 

temperature and at the 15-sec cooling time. Both MVS 

and MV15 were collected at WP = -22.5 bars. A water 

potential of -22.5 bars is a compromise between the 

extremes of the entire water potential range studied, and 

represents the point at which the zero-offset effects were 

studied in the laboratory. Since the effects of zero-offset 

on psychrometer output are linearly related to changes in 

temperature, they are proportional at any water potential 

and temperature to an arbitrarily fixed point, here set at 

-22.5 bars. 

TEMPERATURE, "C 

Figure 8.-Sigmoid relationship 

between N and temperature for 0" to 

40" C. 

The model to this point is applicable only under isothermal conditions. Where temperature gradients exist, 
The isothermal MV in equation 1 is then multiplied by 

the ratio 1 IC to arrive at MV corrected for ZOE, where 

C = MVS 

and where C now provides a proportional correction to 

MV for any combination of WP, Temp, or See. Note that 

when ZOE is negative, C will be less than 1 .O, and MV in 

MVlC becomes larger to compensate for the negative 

errors (fig. 5). When ZOE is positive, C will be greater than 

1.0 and MV in MVlC becomes smaller to compensate the 

positive errors. 

Finally, having multiplied the left side of equation 1 by 

1IC to arrive at MVIC, we solved the resulting equation for 

observed microvolts (applicable under either isothermal 

or nonisothermal conditions), 

where, 

[(UI * C) - MV] ISP-,WPI~ = 

A 

thus, the predicted water potential (WP) can be solved as 

A 

within the limits SP 5 WP 5 0. 

The following parameters must be supplied to predict 

water potential with the model: 

MV = microvolts psychrometer output, 

OMV = zero-offset (-60 to + 60 MV), 

Temp = temperature (0" to 40" C), and 

Sec = seconds cooling time (15 to 60 sec). 

A program of the predictive model in FORTRAN and 

BASIC is presented in appendix I, together with a list of 

programing steps. We have successfully used the 

Monroe Model 1880, the Hewlett-Packard 98458 desk-top 

computer, and the Amdahl 470 VI6-I1 to predict water 

potentials over the entire range of the model. A limited 

computer printout of predicted water potentials is presented in appendix II for cooling times of 15, 30, and 60 

seconds and for the temperature range of 0" to 40" C 

(32" to 104" F), with psychrometer output in microvolts for 

zero-offsets ranging from -60 to + 60 microvolts. 

The model is represented in three-dimensional form in 

figure 9 for the 60-sec cool time only. The relationships 

among the various factors are represented as surfaces 

for the extreme limits of zero-offset (from -60 to + 60 

WATER POTENTIAL (Bars) 

Figure 9.-Three-dimensional representation of 

model characteristics showing the relationships 

among water potential, microvolt output, temperature, and zero-offset for 60-sec cool time. Shorter 

cooling times are not shown because of their 

relatively small effect. 

microvolts). Shorter cooling times would slightly lower 

the slopes of each surface, but the total effect is too 

small to illustrate effectively at the scale shown. This 

illustration shows the limits of the data in appendix II as 

well as the relative shapes of the surfaces for the conditions represented by the model. 

Model Verification 

The general form and internal scales of the various 

relationships used in the model are presumed to apply to 

any individual or group of psychrometers similar to those 

used here. Uncorrected estimates of water potential by 

the model have been found quite reasonable, even for 

psychrometers not previously used. In fact, the isothermal portion of the model (under conditions of 0 zerooffset) appears to estimate water potentials quite adequately for virtually all designs of chromel-constantan 

psychrometers, including screen-caged, ceramic cup, and 

Teflon or stainless steel end-window types. However, the 

nonisothermal portions of the model (used when zerooffsets occur) may be more applicable for screen-caged 

units. 

Nevertheless, the model contains some bias peculiar 

to the group of psychrometers used in its development, 

and to the process of hand-fitting the curves to the data 

points. It is expected that the predictability of the model 

would be strengthened if the bias were eliminated or 

reduced by employing a correction coefficient that would 

adjust for the unique characteristics of the specific 

psychrometer or group of psychrometers to be used in a 
given application. A ratio of the actual water potential (or 

sum of actual water potentials where a group of psychrometers is used) to that estimated by the model 

provides a convenient correction coefficient. Thus, 

where B is the correction coefficient, tWP is the sum of 

actual water potentials (of NaCl solutions used in caliA 

bration), and ZWP is the sum of estimated water potentials by the model for the microvolt outputs of the psychrometers being used. Model bias is then adjusted for 

that particular data set by 

A 

WPadj = B * WP (1 7) 

where WPadi is the adjusted water potential in bars. 

When B = 1.0, the model estimate of water potential is 

identical to the actual value; but when B is less than 1.0, 

the model is estimating a drier water potential; and when 

B is greater than 1.0, it is estimating a wetter water 

potential. The adjustment is accomplished by multiplying 

the estimated water potential by B (equation 17). 

Theoretically, psychrometers of uniform physical and 

chemical structure would all respond to water potentials 

and temperatures identically, and hence could be 

modeled more accurately. Unfortunately, psych-rometers 

are not all identical; each has its own unique characteristics. Therefore, it is probably unrealistic to expect that 

the water potential of any psychrometer can be predicted 

with great accuracy throughout its entire range of sensitivity, regardless of t he correction coefficient used. 

However, it is expected that model adjustments like 

those shown in equation 17, made either for each individual or for an entire group of psychrometers, will provide readily acceptable levels of accuracy (at least within 

the limits normally obtained from hand-drawn calibration 

curves). 

The relative conformity of water potentials estimated 

by the model with those of the NaCl solutions (actual) 

used in calibration was assessed in two stages: (1) for 

the isothermal data of the original 24 psychrometers, and 

(2) for both the isothermal and nonisothermal data from a 

different set of psychrometers not previously used. The 

ability of the model to estimate water potentials from 

thermocouple psychrometer outputs over the ranges of 

temperature, zero-offset, and cool-time durations specified was determined. 

Verification of the Isothermal Model 

Comparisons of the actual and estimated water potentials under isothermal conditions over the temperature 

and water potential ranges studied are provided in table 

5a, b, and c for the 15-, 30-, and 60-sec cool time durations, respectively. Actual water potentials are those of 

the NaCl solutions, and the estimated water potentials 

are those predicted by the model from the mean microvolt outputs shown in table 2. The adjusted estimates of 

water potential were calculated for each cooling time 

duration for all temperatures and NaCl solutions between 

0.2 and 1.7 molal. The correction coefficient from equation 16 was calculated as the ratio of the sum of all 

actual water potentials to the sum of all estimated water 

potentials for each cooling time. 

Separate correction coefficients (B values) could have 

been calculated for each NaCl solution and temperature, 

which would likely have reduced or eliminated the difference between the actual and adjusted estimates. 

However, this would be impractical for most applications 

since psychrometers are rarely used exclusively for a 

given set of water potential and temperature conditions. 

Under most situations it is not known beforehand what 

conditions a psychrometer will encounter; hence the correction coefficient for a specified cooling time duration is 

more practical. 

The departures between the actual and estimated 

water potentials in table 5a, b, and c represent bias in the 

model (for example, variability among the 24 psychrometers used to develop the isothermal model. imprecise 

hand fitting of curves to the data, and any errors that 

may have occurred in calibration or other procedures). 

The adjusted estimate effectively reduces (and in some 

cases nearly eliminates) the departure from the actual 

water potential for the particular set of psychrometers 

used. However, a new adjusted estimate may be required 

for another group of instruments to minimize such 

departures. Had the data throughout the tables been calculated for any one psychrometer only, the departures 

between actual and adjusted estimates would have all 

been relatively small. Although model bias can be minimized substantially in some cases by adjusting the data 

for each individual psychrometer, it may be more practical to treat an entire population together in cases where 

large numbers of units are required. In such instances 

the departures between the actual and estimated water 

potential can be minimized by carefully selecting psychrometers with similar calibration characteristics. 

The differences between the actual water potentials 

and those estimated by the model in table 5a, b, and c 

were entirely expected as a result of the hand-fitting 

procedures used. It is particularly reassuring, however, 

that the model estimates can be adjusted with such 

precision. The sums listed below of the actual, 

estimated, and adjusted estimates of water potential for 

each cooling time from the tables illustrate how 

equations 16 and 17 can be used to adjust the model 

output for a group of psychrometers. 

Table 5a Table 5b Table 5c 

(15 sec) (30 sec) (60 sec) 

t actual 1270.56 1270.56 1270.56 

Z: estimated 1236.23 1276.48 1284.1 1 

t act./ Z: est. 1.02777 0.99536 0.98945 

t adj. est. 1270.50 1270.50 1270.54 

Departure 

(tact. -t adj. est.) 0.06 0.06 0.02 

The ratio of the sum of the actual to the sum of the estimated water potentials is the correction coefficient used 

to compute the adjusted estimated water potential for 

each cooling time. The departures between the actual 

and the adjusted estimates represent rounding-off errors 

in the computations. Note that the corrections required are 

relatively small; the largest is only 2.77 percent (for the 

15-sec cool time). 
Table 5a.-Actual water potentials (bars) of NaCl solutions with 15-second cool time, estimated water potentials by the model, the adjustedestimate of water potential, and the ratio of the actual to the adjusted-estimate for isothermal conditions 

NaCl Water Temperature 

molality potential 0 "C 7.5 "C 15°C 25 "C 35 "C 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

*Beyond the range of the model. 

Table 5b.-Actual water potentials (bars) of NaCl solutions with 30-second cool time, estimated water potentials by the model, the adjustedestimate of water potential, and the ratio of the actual to the adjusted-estimate for isothermal conditions 

NaCl Water Temperature 

molality potential 0 "C 7.5 "C 15 "C 25 "C 35 "C 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 
Table 5c.-Actual water potentials (bars) of NaCl solutions with 60-second cool time, estimated water potentials by the modei, the adjustedestimate of water potential, and the ratio of the actual to the adjusted-estimate for isothermal conditions. 

NaCl Water Temperature 

molality potential 0 "C 7.5 "C 15°C 25 "C 35 "C 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

actual 

estimated 

adj. est. 

ratio 

In general, the data in table 5a, b, and c show that the 

greatest proportional bias in the isothermal model occurs 

at the highest water potentials (0.2 m NaCI) for all temperatures between 0" to 35" C (32" to 95" F). Other than 

at 0.2 m NaCI, there appears to be no consistent effect of 

water potential, or of temperature, on the difference 

between the actual and the adjusted estimate of water 

potential. The departure between these two quantities 

generally is less as cooling time duration increases from 

15 sec to 60 sec, but the relationship is not always 

consistent for every set of conditions. However, these 

data do show that favorable adjustments of the estimated water potentials can be made by use of the suggested correction coefficient, and that such adjustments 

will reduce model bias in estimating water potential of a 

population of psychrometers. 

Verification of the Entire Model 

The performance of the model and the relative effectiveness of the correction coefficients for adjusting estirnated water potentials were evaluated to verify the 

applicability of the model. Eight randomly selected psychrometers that had not previously been used were calibrated over the same ranges of conditions for which the 

model was developed. The model was then used to generate estimated water potentials for each set of conditions based on the microvolt outputs from these psychrometers. Table 6a, b, and c shows the values for 

actual, estimated, and adjusted-estimated water potentials for each temperature, NaCl molality zero-offset (+ 60. 

0, -60 microvolts), and cooling time duration. Correction 

coefficients were computed from equation 16 for each 

cooling time and were then used to calculate the 

adjusted-estimate of water potential using equation 17, 

similar to the procedures described above. 
The sums of the dctual, estimated, and adjusted estimates of water potential, together with the correction 

coefficients and departures for table 6a, b, and c are 

listed below. 

Table 6a Table 6b Table 6c 

(1 5 sec) (30 sec) (60 sec) 

t actual 1270.56 1270.56 1270.56 

1 estimated 1237.38 1281.04 1288.59 

t act.11 est. 1.02681 .99182 .98601 

t adj. est. 1270.56 1270.58 1270.55 

Departure 

(1 act.-I: adj. est.) .OO -.02 .O1 

Note that only the data for 0 zero-offset was used to 

compute the correction coefficients in each table in order 

to test the adjustment procedure at the extreme zerooffsets. Under normal circumstances, most users would 

calibrate their psychrometers for isothermal conditions 

only, and would rely on model adjustment with the correction coefficient to remedy any model bias where zerooffsets occur. This, for example, results in reasonably 

small departures between the actual and adjusted estimates of water potential in table 6. However, even 

smaller departures should result on the average, when 

the ratio applied is based on all the data in the tables, 

including + 60 and -60 microvolts. Such computations 

are shown below to demonstrate the slightly smaller 

ratios. 

Table 6a Table 6b Table 6c 

(1 5 sec) (30 sec) (60 sec) 

1 actual 3258.38 381 1.68 3663.58 

1 estimated 321 8.31 3806.98 3676.1 1 

t act.12 est. 1.01245 1.00123 ,99659 

1 adj. est. 3258.38 381 1.66 3663.57 

Departure 

(t act.-t adj. est.) .OO --02 -.01 

It is somewhat questionable, however, for a user to go 

through the elaborate calibration under nonisothermal 

conditions, particularly in view of the relatively small 

errors that would result from isothermal calibration alone. 

The data in table 6 show, in general, that the greatest 

bias in the model occurs at the extremes of the water 

potential ranges studies (0.2 m and 1.7 m NaCI). The 

adjusted-estimates of water potential are usually within 

-1- 5 percent of the actual values, even for the extreme 

ends of the water potential and zero-offset ranges 

studied. However, the isothermal data are generally predicted more precisely than either zero-offset extreme. The 

largest departure of the adjusted-estimate from the actual 

water potential is 9.26 bars, and occurs for the + 60 

microvolt zero-offset at 60-sec cool time, 35 " C (95 " F) 

and 1.7 m NaCl (table 6c). Overall the -60 microvolt zerooffset data tend to depart most from the actual water 

potential (the largest departure here is in table 6a, for the 

15-sec cool time at 15 " C (59" F) for the 0.2 m 

NaCl solution). Because of bias, the model tends to predict lower water potentials than the actual values at the 

extreme zero-offsets, and yields adjusted estimates that 

are also slightly lower. Illustrating this point is the 

majority of lower adjusted estimate values than actual 

ones in table 6a for the + 60 and -60 microvolt zero-offset 

data. 

Although overall trends in the data for each cooling 

time duration are probably most meaningful, inconsistencies for any one data set are abundant in table 6. For 

example, in table 6a (15-sec cooling time duration), the 

1.5 m NaCl solution at 7.5" C (45.7" F) data show that the 

two extreme zero-offset water potentials were predicted 

more precisely than the 0 zero-offset water potential, 

even though the reverse appears to be the general rule 

for the data set as a whole. These readily apparent 

anomalies reflect the variability among psychrometers 

when calibrated in groups where the data are averaged. 

Because this variability is retained, even after adjustment 

with the correction coefficient, adjusted estimates of 

water potential can be expected to differ from actual 

values. This effect tends to suggest that psychrometers 

should be treated as individuals rather than averaged in 

large groups. However, the intended application and 

desired level of precision required should form the basis 

for that decision. If the level of precision achieved in 

table 6 is sufficient for the given application, then that 

method of calibration should be used. The time and 

expense of converting raw microvolt data are greatly 

reduced when psychrometers can be calibrated and 

treated in groups. 

The variability among psychrometers and model bias is 

lessened as the cooling time duration is increased from 

15 sec to 60 sec (table 6a, b, c). Adjusted estimates of 

water potential for isothermal data tend to lie within + 3 

percent of the actual values regardless of cooling time 

duration. However, the zero-offset data show a relatively 

strong effect of increased cooling time duration wherein 

water potentials are generally underestimated at 15 sec 

(table 6a) and only slightly overestimated at 60 sec (table 

6c). In general, 30-sec cooling time duration (table 6b) 

appears to provide the best estimates of water potential 

in terms of departure between the actual and adjusted 

estimates. 

The data in table 6 show that the model adequately 

(within k 1 sd) predicts water potentials of psychrometers 

that were not used in its development. Further, these 

data show that the correction coefficient from equation 

16 provides a simple and relatively accurate method of 

adjusting the model estimates for any given data set. 

Estimates of water potential under isothermal conditions 

appear to be quite accurate for either large groups (table 

5) or small groups (table 6) of psychrometers. Water 

potential estimates for nonisothermal conditions. 

although perhaps not as accurate as those for isothermal conditions, appear to be adequate when a longer 

cooling time is employed. Although only data for the 

extreme zero-offset conditions are displayed (+ 60 and 

-60 microvolts), these represent the maximum expected 

departures from actual water potentials, and hence the 

"worst possible'' case. On the other hand, zero-offset 

data closer to 0 microvolt tend to deviate less, and thus 

are less variable than those at + 60 and -60 microvolts. 
Table 6a.-Actual water potentials (bars) of NaCl solutions with 15-second cool time, estimated water potentials by the model, the adjustedestimate of waterpotential, and the ratio of the actual to the adjusted-estimate for + 60, 0, and - 60 microvolt of zero-offset for eight 

new psychrometers 

Temperature 

NaCl Water 0 "C 7.5 "C 15°C 25 "C 35 "C 

molality wotential +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 

actual 

0.2 estimated 

adj. est. 

ratio 

actual 

.5 estimated 

adj. est. 

ratio 

actual 

.7 estimated 

adj. est. 

ratio 

actual 

1.0 estimated 

adj. est. 

ratio 

actual 

1.5 estimated 

adj. est. 

ratio 

actual 

1.7 estimated 

adj. est. 

ratio 

'Beyond the range of the model. 

Table 6b.-Actual water potentials (bars) of NaCl solutions with 30-second cool time, estimated water potentials by the model, the adjustedestimate of water potential, and the ratio of the actual to the adjusted-estimate for + 60, 0, and - 60 microvolt of zero-offset for eight 

new psychrometers 

- - 

Temperature 

NaCl Water 0 "C 7.5 "C 15 "C 25 "C 35 "C 

molality potential +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 

actual 8.36 8.36 8.36 8.60 8.60 8.60 8.84 8.84 8.84 9.15 9.15 9.15 9.46 9.46 9.46 

0.2 estimated 8.63 8.03 8.49 8.99 9.00 8.53 9.82 8.24 9.94 9.54 8.79 9.31 9.41 8.63 9.96 

adj.est. 8.51 7.92 8.38 8.87 8.88 8.42 9.69 8.13 9.82 9.42 8.68 9.19 9.28 8.51 9.83 

ratio .982 1.056 .998 ,970 .968 1.021 .912 1.087 .900 .971 1.054 ,996 1.019 1.112 .962 

actual 20.70 20.70 20.70 21.36 21.36 21.36 22.00 22.00 22.00 22.81 22.81 22.81 23.62 23.62 23.62 

.5 estimated 20.52 21.24 22.14 21.03 22.38 20.49 23.16 22.20 22.06 23.66 23.14 24.36 23.23 23.28 22.47 

adj.est. 20.25 20.97 21.85 20.76 22.09 20.23 22.86 21.92 21.78 23.35 22.84 24.04 22.93 22.98 22.18 

ratio 1.022 .987 .947 1 .029 .967 1 .056 .962 1.004 1.01 0 .977 .999 .949 1 .030 1 .028 1 .065 

actual 29.01 29.01 29.01 29.98 29.98 29.98 30.91 30.91 30.91 32.10 32.10 32.10 33.28 33.28 33.28 

.7 estimated 28.86 29.78 30.57 31.93 30.75 31.35 30.95 31.37 29.16 33.22 32.1 1 32.03 32.91 33.25 35.48 

adj.est. 28.49 29.40 30.18 31.52 30.35 30.95 30.55 30.97 28.79 32.79 31.70 31.62 32.48 32.82 35.00 

ratio 1.018 .987 .961 .951 .988 .969 1.012 .998 1.074 ,979 1.013 1.015 1.025 1.014 .951 

actual 

1.0 estimated 

adj. est. 

ratio 

actual 

1.5 estimated 

adj. est. 

ratio 

actual 

1.7 estimated 

adj. est. 

ratio 1.095 1.051 .997 1.102 ,996 1.056 1.021 .984 1.034 1.060 .996 1.035 1.053 1.030 1.067 
Table 6c.-Actual water potentials (bars) of NaCl solutions with 60-second cool time, estimated water potentials by the model, the adjustedestimate of water potential, and the ratio of the actual to the adjusted-estimate for + 60, 0, and - 60 microvolt of zero-offset for eight 

new psychrometers 

Temperature 

NaCl Water 0 "C 7.5 "C 15°C 25 "C 35 "C 

molality potential +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 +60 0 -60 

actual 8.36 8.36 8.36 8.60 8.60 8.60 8.84 8.84 8.84 9.15 9.15 9.15 9.46 9.46 9.46 

0.2 estimated 8.51 9.36 8.77 9.88 9.22 8.78 8.64 9.22 9.41 7.92 8.86 8.51 9.88 8.67 10.14 

adj. est. 8.35 9.19 8.61 9.70 9.05 8.62 8.48 9.05 9.23 7.77 8.70 8.35 9.70 8.51 9.95 

ratio 1.001 .910 .971 .887 .950 .998 1.042 .977 .958 1.178 1.052 1.096 .975 1.112 .951 

actual 20.70 20.70 20.70 21.36 21.36 21.36 22.00 22.00 22.00 22.81 22.81 22.81 23.62 23.62 23.62 

.5 estimated 20.77 21.22 21.35 21.61 23.01 22.08 23.12 22.83 22.89 23.19 23.68 22.96 22.99 23.48 24.41 

adj. est. 20.38 20.83 20.95 21.21 22.58 21.67 22.69 22.41 22.47 22.76 23.24 22.53 22.56 23.04 23.96 

ratio 1.01 6 .994 .988 1 .007 .946 .986 .970 .982 .979 1.002 0.981 1.01 2 1 .047 1 .025 .986 

actual 29.01 29.01 29.01 29.98 29.98 29.98 30.91 30.91 30.91 32.10 32.10 32.10 33.28 33.28 33.28 

.7 estimated 29.83 30.40 31.31 30.27 29.94 30.35 32.34 32.08 27.72 32.43 33.36 33.97 32.26 33.75 32.99 

adj. est. 29.27 29.83 30.73 29.17 29.38 29.79 31.74 31.49 27.20 31.82 32.74 33.34 31.66 33.12 32.38 

ratio .991 .973 .944 1 .009 1.020 1 .006 .974 .982 1.1 36 1 .009 .980 .963 1 .051 1 .005 1 .028 

actual 41.69 41.69 41.69 43.18 43.18 43.18 44.59 44.59 44.59 46.40 46.40 46.40 48.15 48.15 48.15 

1.0 estimated 41.76 41.51 44.51 43.85 41.93 44.07 45.52 44.18 46.31 45.72 47.63 45.78 47.45 46.98 53.35 

adj.est. 40.99 40.74 43.68 43.03 41.15 43.25 44.67 43.36 45.45 44.87 46.74 44.92 46.57 46.11 52.35 

ratio 1 .017 1 .023 .954 1 .003 1 .049 .998 .998 1 .028 .981 1 .034 .993 1 .033 1 .034 1 .044 .920 

actual 63.59 63.59 63.59 66.06 66.06 66.06 68.37 68.37 68.37 71.34 71.34 71.34 74.11 74.11 74.11 

1.5 estimated 63.82 65.06 64.77 68.04 65.99 65.87 68.16 69.28 72.13 72.51 72.28 71.37 70.86 74.63 73.06 

adj. est. 62.63 63.85 63.57 66.77 64.77 64.64 66.89 67.99 70.78 71.16 70.94 70.04 69.54 73.24 71.70 

ratio 1.015 .996 1.000 .989 1.020 1.022 1.022 1.006 .966 1.003 1.006 1.019 1.066 1.012 1.034 

actual 72.60 72.60 72.60 75.50 75.50 75.50 78.20 78.20 78.20 81.70 81.70 81.70 84.90 84.90 84.90 

1.7 estimated 69.39 74.30 -* - * 76.52 74.51 78.13 80.07 78.92 77.90 84.19 80.38 73.39 84.96 76.71 

adj. est. 68.10 72.92 - - 75.10 73.12 76.68 78.58 77.45 76.45 82.63 78.88 72.02 83.38 75.28 

ratio 1.006 .996 - - 1.005 1.033 1.020 .995 1.010 1.069 .989 1.036 1.179 1.018 1.128 

*Beyond the range of the model 

GUI DES FOR USERS 

The following suggestions are provided to assist users 

in application of the calibration model when using 

screen-caged thermocouple psychrometers similar to 

those described here. We do not recommend application 

of the model to other psychrometer designs (such as 

ceramic cup and end-window designs) under irregular 

thermal environments until further research can verify 

their responses to temperature gradients. However, the 

model does apply to these and any other chromelconstantan psychrometer under the following restrictions: 

Used under isothermal conditions only, 

Constructed of 0.0025-cm (0.001-inch) diameter wire 

with welded junction, 

Peltier-cooling mode is used with 5 ma current, 

True temperature and vapor pressure equilibrium is 

achieved, and 

Used within the limits of temperature, cooling time 

duration, and water potential ranges pertinent to the 

model. 

The assumption IS that the user has access to computer 

facilities that will allow the model equations to be programed (appendix I). If this is not possible, the tables in 

appendix II could be used, but this is far more difficult, 

time consuming, and subject to interpolation error. 

Calibration 

1. It is recommended that each individual psychrometer be calibrated under isothermal conditions at three 

different water potentials and at one temperature within 

the range of anticipated need. For most general applications the 0.5, 1 .O, and 1.5 m NaCl solutions should be 

used at 25" C (77" F). Only one temperature is required 

since psychrometer response to this variable is far more 

predictable than to water potential. However, other solutions and temperatures can be used if the anticipated 

conditions for use are specifically known. In any case, 

three calibration solutions representing the nearextremes and middle range of water potentials are 

recommended. Outputs should be recorded to the 

nearest 0.1 microvolt. It is further recommended that 
calibration not be attempted under nonisothermal conditions to achieve zero-offset data points. This is an 

extremely complex process that may lead to more confusion than is warranted. The model adequately predicts 

water potentials under these conditions. 

2. For most general applications it is recommended 

that the 30-sec cool time duration be used throughout. 

Shorter cooling times may be justified in those cases 

where length of time between readings is crucial, but 

generally less precise estimates of water potential will 

result and the variability among psychrometers will likely 

be greater. Longer cooling times, up to 60 sec, generally 

do not appear to offer any strong advantages over the 30- 

sec cooling times, and also may unnecessarily prolong 

the length of time between readings. This is an important 

logistical problem when attempting to read large numbers of psychrometers during a specified time. 

3. Although calibration should ideally be conducted 

under carefully controlled temperatures in a water bath, 

suitable conditions can be achieved in a well-insulated 

water reservoir. For example, large picnic jugs, vacuum 

bottles, or insulated ice chests have all been used 

successfully with normal precautions to minimize rapid 

temperature fluctuations. Water temperature can be 

adjusted to that of the external environment to lessen the 

possibilities of temperature gradients. 

Model Application 

1. For the most accurate estimates of water potential, 

each psychrometer should be calibrated and its microvolt data be converted to water potential separately. 

Compute the ratio of actual to estimated water potential 

(equation 16) for each psychrometer. For example, the 

sum of the water potentials of the three NaCl solutions 

used divided by the sum of the water potentials predicted 

by the model for the microvolt outputs of that psychrometer provides the correction coefficient. 

2. Each psychrometer is now assigned a unique correction coefficient (or B value). Model estimates of water 

potential, whether obtained from the computer program 

(appendix I) or the tables (appendix II), made from data 

collected with that psychrometer are multiplied by this 

correction coefficient to obtain the adjusted estimate of 

water potential (equation 17). If the computer program is 

used, attention is called to step 61 in the BASIC program 

and step 8 in the FORTRAN program (where B = 1.0 

presently), which must be changed to the new correction 

coefficient. Also, insert the appropriate cooling time in 

seconds in step 9 of the FORTRAN program (where sec 

= 15, presently). 

3. For applications requiring large numbers of psychrometers, a single correction coefficient may be computed for the entire group. The principal advantage in this 

technique is that considerable time can be conserved 

during computation of data. The main disadvantage is 

that some loss in precision of water potential estimates 

results due to the variability in microvolt output characteristics among the psychrometers used. If this procedure is used, discard all psychrometers with calibration data that display a greater variability than 2 1 sd 

from the mean of the entire population. 

4. Occasionally a particular psychrometer may be 

more sensitive at low water potentials than those used to 

develop the model. In such cases its microvolt output 

may exceed the range of the model, and its water 

potential may not be calculated. This is most likely to 

occur at low water potentials near the lower limits of the 

model (about -75 to -85 bars). In such cases, which are 

anticipated to be very few, the data will have to be excluded from computation by the model and computed by 

hand from standard calibration curves. 

Data Acquisition 

1. For general laboratory use, psychrometers should 

be kept as clean and free of contaminants as possible to 

insure accurate data. The ultimate acquisition of reliable 

data depends more upon the user than the model. Precautionary measures to be followed are discussed in 

Brown and Van Haveren (1972), Brown (1970), and Wiebe 

and others (1971). 

2. During field use, efforts must be made to minimize temperature gradients. For in situ measurements of 

soil water potential, psychrometers should be buried in a 

horizontal position (Wiebe and others 1977; Wiebe and 

Brown 1979). The time when they are read during the day 

should be selected, if possible, to minimize temperature 

gradients. Season of the year may also affect the time of 

day selected. Samples collected and read in the field 

must also be protected from temperature gradients and 

other influences that may affect data. The meter or data 

gathering instrument must be shaded from direct solar 

insolution. 

3. Raw microvolt data, together with recorded temperatures, zero-offsets, and the appropriate cooling time 

duration are required for each computation of water 

potential by the model. The model estimate of water 

potential is then multiplied by the appropriate correction 

coefficient to obtain the adjusted estimate of water 

potential. If desired, water potentials expressed in bars 

by the model may be converted to the international term 

of MPa (mega Pascals) by multiplying bars times 0.1. 
CONCLUSIONS 

The outputs of Peltier thermocouple psychrometers are 

quite predictable at different cooling times, temperatures, temperature gradients, and water potentials. Responses to water potential are probably the weakest link 

in a modeling effort because of the variability among 

psychrometers in terms of construction techniques and 

the configuration of their components. Some of the contributing variables are the precise chemistry of the 

welded sensing junction, the length of chrome1 and 

constantan lead wires of the thermocouple, the geometric position of the sensing junction, and the freedom 

with which water vapor can be exchanged between the 

evaporating source and the psychrometer cavity. 

However, psychrometer responses to temperature, 

temperature gradients (within limits of unit size and 

materials used in construction), and cool times are all 

virtually fixed with far fewer possibilities for variation. 

Generally, the model predicts water potentials most 

precisely for so thermal conditions at the longer cool 

times (30 to 60 sec). The greatest bias occurs at the 

extreme water potentials, particularly near the lower 

limits of psychrometer sensitivity (about -80 bars), with 

the 15-sec cool time. Also, generally model bias is 

greater near the extreme zero-offsets (approaching k 60 

microvolts), although this is relatively small. Based on 

these limitations, it is recommended that psychrometers 

be calibrated at several water potentials under 

isothermal conditions at some intermediate temperature 

and cool time before use. Those units displaying a 

greater variability than a 1 sd from the mean of the entire 

population should be discarded. 

Absolute precision of water potential measurements 

with thermocouple psychrometers is probably not possible except under unusual circumstance. However, the 

model is designed to predict water potential precisely as 

described by psychrometer calibration data. Thus, it is 

more the care taken by the user during calibration and 

use of psychrometers that determines the precision of 

water potential values than it is the ability of the model 

to predict them. Hand-drawn calibration curves, as generally developed at present, do not provide the same 

levels of sensitivity and consistency for estimating water 

potentials as the model given here for the smoothed 

interactive effects of the four independent variables 

involved. Extensive calibration trials and data points for 

each psychrometer over a range of numerous temperatures and water potentials provide little or no assurance 

that water potential data will be any more accurate than 

that computed by the methods suggested. 

Comparisons of water potential estimates made by 

both the model and hand-drawn calibration curves 

suggest some advantages of the model. The model will 

consistently calculate water potentials for the entire 

range of conditions specified, and will do so for whatever 

level of fractional input is desired. Hand-drawn curves, on 

the other hand, yield water potential data that are subject to numerous additional errors. The physical process 

of plotting data points, fitting curves, and then interpreting data from them is contingent upon extreme care 

tempered with abundant quantities of expensive time. 

The very best hand-drawn curves yield only an approximate water potential, even if a set of curves is drawn for 

each individual psychrometer. We found that, not only 

can two different technicians read the same graph differently, but the same technician may make widely 

varying interpretations from the same graph at different 

times. 0n'e of the most common errors was interpreting 

data from the wrong graph -and, very often even these 

were read incorrectly. Thus, the magnitude of the error in 

data interpreted from hand-drawn curves was most often 

greater than that associated with the model. 

Since there is no simple factor that can be applied to 

water potential data to correct it for temperature 

gradients, the number of calibration curves that would be 

needed for each psychrometer to cover all specified 

conditions is beyond the limits of practicality. The magnitude of the effort just to interpret large numbers of 

observations from hand-drawn curves is overwhelming. 

Whether a study involves a few data points from one 

psychrometer, or numerous data points from hundreds of 

psychrometers, use of the calibration model promises to 

reduce the time and magnitude of the errors normally 

inherent in this kind of research. 

Based on the performance and verification of the predictive model, the hypotheses originally posed are all 

accepted. The responses of any given psychrometer of 

similar construction to those used here can be predicted 

for the conditions specified to at least within the limits of 

error normally expected with hand-drawn curves. The 

normal limits of error of predicted water potentials can 

be narrowed by adjusting the model based on only one or 

a few calibration points. The time and expense normally 

devoted to calibration can be significantly reduced with 

the assurance that normal limits of error are not 

jeopardized. Also, large quantities of either field or 

laboratory data can be analyzed more quickly and with 

fewer errors using the model than with conventional 

methods. 
PUBLICATIONS CITED 

Barrs, H. D. 

1968. Determination of water deficits in plant tissues. 

In Water deficits and plant growth, vol. I. Development, control, and measurement. p. 236-368. T. T. 

Kozlowski, ed. 

Brown, R. W. 

1970. Measurement of water potential with thermocouple psychrometers: construction and applications. USDA For. Serv. Res. Pap. INT-80, 27 p. 

Intermt. For. and Range Exp. Stn., Ogden, Utah. 

Brown, R. W., and J. M. Collins. 

1980. A screen-caged thermocouple psychrometer and 

calibration chamber for measurements of plant and 

soil water potential. Agron. J. 72:851-854. 

Brown, R. W., and R. S. Johnston. 

1976. Extended field use of screen-covered thermocouple psychrometers. Agron. J. 68:995-996. 

Brown, R. W., and B. P. Van Haveren, eds. 

1972. Psychrometry in water relations. 342 p. Utah 

Agric. Exp. Stn., Utah State Univ., Logan. 

Campbell, E. C. 

1972. Vapor sink and thermal gradient effects on 

psychrometer calibration. In Psychrometry in water 

relations research. p. 94-97. R. W. Brown and B. P. 

Van Haveren, eds. Utah Agric. Exp. Stn., Utah State 

Univ., Logan. 

Dalton, F. N., andS. L. Rawlins. 

1968. Design criteria for Peltier-effect thermocouple 

psychrometers. Soil Sci. IO5:12-17. 

Jensen, C. E. 

1973. Matchacurve - 3: multiple-component and multidimensional mathematical models for natural 

resource studies. USDA For. Serv. Res. Pap. INT-146, 

42 p. Intermt. For. and Range Exp. Stn., Ogden, Utah. 

Jensen, C. E. 

1976. Matchacurve - 4: segmented mathematical 

descriptors for asymmetric curve forms. USDA For. 

Serv. Res. Pap. INT-182, 16 p. Intermt. For. and 

Range Exp. Stn., Ogden, Utah. 

Jensen, C. E. 

1979. e-k, a function for the modeler. USDA For. Serv. 

Res. Pap. INT-240,9 p. Intermt. For. and Range Exp. 

Stn., Ogden, Utah. 

Jensen, C. E., and J. W. Homeyer. 

1970. Matchacurve - 1 for algebraic transform to 

describe sigmoid- or bell-shaped curves. 22 p. USDA 

For. Serv. Intermt. For. and Range Exp. Stn., Ogden, 

Utah. 

Jensen, C. E., and J. W. Homeyer. 

1971. Matchacurve - 2 for algebraic transforms to 

describe curves of the class Xn. USDA For. Serv. 

Res. Pap. INT-106, 39 p. Intermt. For. and Range Exp. 

Stn., Ogden, Utah. 

Lang, A. R. G. 

1967. Osmotic coefficients and water potentials of 

sodium chloride solutions from 0 to 40" C. Aust. J. 

Chem. 20:2017-2023. 

Merrill, S. D., and S. L. Rawlins. 

1972. Field measurement of soil water potential with 

thermocouple psychrometers. Soil Sci. 113:102-109. 

Meyn, R. L., and R. S. White. 

1972. Cali brat ion of thermocouple psychrometers: a 

suggested procedure for development of a reliable 

predictive model. In Psychrometry in water relations 

research. p. 56-64. R. W. Brown and B. P. Van 

Haveren, eds. Utah Agric. Exp. Stn., Utah State Univ., 

Logan. 

Michel, B. E. 

1979. Correction of thermal gradient errors in stem 

thermocouple hygrometers. Plant Physiol. 63:221- 

224. 

Omega Engineering, Inc. 

1976. Temperature measurement handbook. p. A-1 I. 

Stamford, Conn. 

Peck, A. J. 

1968. Theory of the Spanner psychrometer 1. The 

thermocouple. Agric. Meteorol. 5:433-447. 

Peck, A. J. 

1969. Theory of the Spanner psychrometer 2. Sample 

effects and equilibration. Agric. Meteorol. 6:111-124. 

Rawlins, S. L. 

1966. Theory for thermocouple psychrometers used to 

measure water potential in soil and plant samples. 

Agric. Meteorol. 3:293-310. 

Rawlins, S. L. 

1972. Theory of thermocouple psychrometers for 

measuring plant and soil water potential. In Psychrometry in water relations research. p. 43-50. R. W. 

Brown and B. P. Van Haveren, eds. Utah Agric. Exp. 

Stn., Utah State Univ., Logan. 

Rawlins, S. L., and F. N. Dalton. 

1967. Psychrometric measurement of soil water 

potential without precise temperature control. Soil 

Sci. Soc. Am. Proc. 31:297-301. 

Scotter, D. R. 

1972. The theoretical and experimental behaviour of a 

Spanner psychrometer. Agric. Meteorol. 10:125-136. 

Slavik, B. 

1974. Methods of studying plant water relations. 449 p. 

Springer - Verlag, Berlin. 

Spanner, D. C. 

1951. The Peltier effect and its use in the measurement 

of suction pressure. J. Exp. Bot. 2:145-168. 

Van Haveren, B. P., and R. W. Brown. 

1972. The properties and behavior of water in the soilplant-atmosphere continuum. In Psychrometry in 

water relations research. p. 1-27. R. W. Brown and 

B. P. Van Haveren, eds. Utah Agric. Exp. Stn., Utah 

State Univ., Logan. 

Wiebe, H. H., and R. W. Brown. 

1979. Temperature gradient effects on in situ 

hygrometer measurements of soil water potential. II. 

Water movement. Agron. J. 71 :397-401. 
Wiebe, H. H., R. W. Brown, and J. Barker. 

1977. Temperature gradient effects on in situ 

hygrometer measurements of water potential. Agron. 

J . 69:933-939. 

Wiebe, H. H., G. S. Campbell, W. H. Gardner, S. L. 

Rawlins, J. W. Cary, and R. W. Brown. 

1971. Measurement of plant and soil water status. Utah 

Agric. Stn. Bull. 484, 71 p. 
APPENDIX I 

COMPUTER PROGRAM IN BASIC AND 

FORTRAN 

Computer programs of the predictive calibration 

model; (A) in BASIC and (B) in FORTRAN. Text and 

related computer acronyms are defined in C for the 

FORTRAN program. 
APPENDIX I A 

Enhanced BASIC program for Hewlett-Packard 9845-B 
APPENDIX I B 

FORTRAN IV Program for water potential 

(Place system cards here) 

1 , DIHENSIQN TE)IIPX(5),oHVX(l3) ,L'rfIS{l(i,) ,UPS{lJ> 

2 REAL HV,HS,H15,IS,IlS,LNS,t.N15,NS,N15,HVS,HVl5 

3 DATA IBLWKP '/,bJPS/13:$OW/, 

*ONVX/-60. p-50~,-40*,-3Q.,-2Omt~tOo IOe,10m920* ,SO* ,40m ,50. ,60*/ 

0 = 1. 

SEC =: 15 

UPK = -22.5 

WAGE = O 

DO 99 J=1,5 

LNN = 1 

TEHP = TENPXfJl 

IPAGE = IPAGE + 1 

PRINT 101 ,IPAGE,SEC, TEMPX( 3) 

PRINT 102 

PRINT 103 

PRINT 104 

PRINT 103 

PRINT 105 

DO 99 1*(=1,;70 

NWPS= 0 

nu := I.: 

DO 15 L-1,13 

OMV = OMVHL) 

H15=3.2904052 

HS=2.!5+EXP( -(rlB!i( ( (60--SEC 1 /6O.-&I )/.405):##3) ) 

IS~,45+.000333*SEC+1.9846E-19*SEC*~10 

I1 5=. 4M?P5l 

LNS~&XP(-(ABS( (140-TEH13)/40--1 )/{!-IS) )*:*tiS) > 

LN15zEXP(- (ABS(((40-TElIPlf40-1 l/(l-IlS)):**HlS) 1 

RNS=EXP(-((l/(l-IS))**H?3) 1 

RNlScEXP(-((1/(1-115)):**M15)) 

DSEI - HNS 

Dl5=l-RN15 

NS=( (LNS-RNS )/DS *. l85+f,18 

Ni5=t (LN15-RU15)/DlS)*a185+1 =I8 

$1AS=12e1-~003475*(60-SEC)*:~1sb3 

$1A15=1 Q.3793553 

$1VS~39~2-.0004346*~6Q~8EC~**2~45 

$tY15=3L3195442 

UlS=$lASt.017288*%lYS*'TEHP*r1.1 

U115=%1A15+m017288*$1Y15*TEHP~~f 1.1 

$2AS=88-.0002579*(60-SEC~**2.7 

62A1S=8O04988970 

%2YS=8e4+2m734E~07~~6O~SEC~*f3.97 

$ZY15=9e4001202 

SPS~~$2h8-$2YS*.Q001 71 8S*( 4W-TEW) *162.35):*{ -1 

~P15~(%2A15-$2Y~5~e00017105*~40~TE~P~**2m35~*~~1~ 

20E=(,015*0HV+.00147l*OHV*TEHP~ 

HVS~~UIS-(UIS/(ABS(SPS)**NS~):~fABS(SP13-11PK~**NS~~ 
Appendix I B (con.) 

hV15=(UI15-(UX15/(4BS~SP1S)**N15))*~AB8(8P15-UPK)*:*H15)~ 

C=WS+ (liVS/HVlS)*ZOE)/HUS 

R=UIS*C 

IF(W,OT.R)OO TO 10 

UP=(t((ABS(SPS)**NS)*(UIS*C-HV))/(UI6;*C)~**~l/NS)+SP5)*B 

UP = WP*(=L) 

GO TO 12 

UP = 0. 

IF (UP.EQ. 0.) 60 TO 15 

NUPS = NUPS + 1 

UPS ( NUPS 1 =UP 

GONT XNIJE 

DO 18 XI=6,78,h 

IF (LNN .Ell. 11) GO TO 1Y 

CONTINUE 

GD TO 20 

PRINT 103 

LNN = LNN + 1 

LABL = 0 

DO 21 11=25,57,2 

LABL = LABL + 1 

IF (11 .EQ. LNN) 60 TO 22 

CONTINUE 

IHD1 = IBLNE 

GO TO 60 

GO TO (Xi,U,2Yp3l ,;33,35,IVt3Y,4l 143,45,47,4Y151 953,55,57) ,LAN. 

IHD1 = LTRS(1) 

60 TO 60 

IHD1 = LTRS(2) 

60 TO 60 

IHD1 @ CTRS(3) 

60 TO 60 

IHDl = LTRS(4) 

60 70 60 

IHDl = LTRSW 

80 To 60 

IHDl = LTRSW 

GO TO 40 

IHDi = LTRS(7) 

GO TO 60 

IHD1 = LTUSW 

00 TO 60 

IHDl = LTR6(9) 

60 TO 60 

IHD1 = IBLNK 

60 TO 40 

IHDl = LTRSOO) 

90 TO 60 

lHDl = LTRS(11) 

60 TO 60 

IHD1 = LTRSi02) 

60 TO 60 

IHDl r LTRS(13) 

60 70 60 

IHP1 = LTRSCl4) 
Appendix I B (con.) 

GO TO 60 

55 IHDl LTRS(15) 

GO TO 60 

57 IN01 = LTRSO6) 

60 IttD2 = K 

IF tNUPS,NE.O) 60 TO 62 

PRINT 10711HD1pIHD2 

60 TO 78 

62 60 TO (63,64,65,66,67,60,69,70,71,72,73,74,75),1(UPS 

63 PRIWT 1101fHD1,1HD2,(UPS(JJ),JJ=11NUPS) 

60 TO 78 

64 PRINT 11 1 , IHDl ,IH02, (UPS(JJ) ,JJ=:1 ,NUPSI 

GO TO 78 

65 PRINT 112,1HD1~IHD21(UPS(JJ)IJJ~lIHWP5') 

GO 'ro 78 

66 PRINT 113,1HD1pIHXS21(WPSIsJ,I),,JJ-l,NUY!~) 

GO TO 78 

67 PRINT 114,IliDl,Ill.D2,(UPS(J,J),JJ=1,NUPS) 

GD TO 78 

68 PRINT 11S,IHD1,1HD2,~UPS(JJ),JJ=111NWP5'~ 

GO TO 98 

69 PRINT 1 l6,IHDl JHII2, (UPS(JJ) ,J,JzI ,NUPS) 

60 TO 78 

70 PRINT 1 17,1HQ1 , IHD2, (UPS( JJ 1, JJ=1, WWPS) 

60 TO 78 

71 PRIWT 118pIHP1 ,IHPZI (UPS( JJ),JJ=l ,WUPS) 

60 TO 78 

72 PRIWT 119, IHDl, fHD2,(UP8(JJ)I JJ=1 ,WUP9) 

GO TO 78 

73 PRINT 120,THD1,1HP2,(UPS(JJ)IJJ=1pNUPS) 

GD TO 78 

74 PRINT 12t,IHD1,IHDZ,~UPS(JJ),JJ=1,NUPS) 

60 TQ 78 

75 PRINT 122vIHP1vIHD2, (UPS{JJ) ,JJ=l,NUPS) 

78 1WH = LNW + 1 

90 00 M=1, WUPS 

80 UPS(M) a 0. 

99 COWTINUE 

100 STOP 

10 1 FORHAT I "1 ", SSX, "PREDICTED UATER POTENTIAL' ,33X, IW'O-8 JBX, 

*'COOLING TIHE IN SECONDS ---------------- ',FS. 1/ *' ',28XI 'PSYCHRBHETER TEIIPEKbTIJRE, CERTTBRISIIE --- ' ,F5.1/" .' 1 

102 FORHAT ('0' ,53XIf OFFSET FROH ZERO IN HICROVOL'TS.' ) 

103 FORNAT (' ',28X,5('-----+'I,'----- * ------ * -....-.....- *"-----' 1 

104 FOHUAT (" ',28X,' -60 -50 -40 -30 -20 -10 0 t 

*10 +20 +30 +40 +50 +60') 

105 FORHAT ( ' " ,53X, 'WATER POTENTIAL, NEGATIVE BARS.'/.' -7 

110 FORHAT (' '119X,Alt2XI12,81X1Fl.t) 

111 FORNAT (' ',19X,A1,2X,12173X~Z(2XpF401)) 

112 FORHAT (' f119X,A1p2X,12,67X13(2X,F4m1)) 

113 FORHAT (' ',19XVA1,2X,IZlblX14(2X~F4w1 1) 

114 FORMI (' ',19~A1,2X,IZ,55X,5(2XIF4w1)) 

115 FORMT (" ",19X,A1,2X,12149X16~2XpF4.1 1) 

116 FORUAT (' ',19X,A1,2X,12,43X,fI.t,2Xpb(2X,F4.1)) 
Appendix I B (con.) 

FORBAT (' *'pl9X,AI12X,I2p35XpF4*l ,4Xpf4*1 ,2XSb(2X,F4m1 

FORMAT (' 'p19X,A192X,12p27X,2(2XpF4~1 ),4XpF4.1 p2Xp6(2X9F4m1 1) 

FORHAT 0 ',19X,A1,2X,X2,21X,3(2XpF4O1),4X,F4~1,2Xp6(2X,F4.1)~ 

FORnAT (' ',19X,A1,2X,I2p15X14(2XpF4m1)~4X,F4,1,2Xp6~2XpF4m1)) 

FORUAT (' 'p19XpA1,2X,I2~9X,S(2XIF4m1)p4X~F4a1~2XI,6~2X~F4m1~) 

FORHAT (' ',19X,A1,2X,I2,3XI6(2X,F4.1),4X9F4.1,2X,6(2X,F4.1)~ 

FORWAT (' ',1?X,Al92X,I2) 

LIHITS OF APPLICATION: 

14< SEC < 61 

-1 < TEHP, DEGREE CEN .:: 41 

HV < OR EQUAL TO VIS*B*C 

-61 < ow < 61 

DEBUG SUBCHK 

EWB 

Note that statements 1 through 176 comprise the program necessary to table output on 

any computer. Only systems cards and minor programming conventions peculiar to the 

computer to be used, need be altered. 
APPENDIX I C 

Text 

variable Related computer variables and explanation 

BIAS 

OMV 

SEC. SEC: 

TEMP TEMP: 

MV MV: 

MVS: 

MV15: 

WP W P: 

u I U IS: 

U115: 

SP S PS: 

SP15: 

N S: 

N 15: 

M S: 

M15: 

IS: 

115: 

LNS: 

LN15 

R N S: 

RN15: 

DS: 

Dl 5: 

$1 AS: 

$A15: 

$1 YS: 

$1Y15: 

$2AS; 

$2A15: 

$2YS: 

$2Y15: 

ZO E: 

0 M V: 

WPK: 

C: 

B: 

R: 

microvolt observation, time in seconds 

temperature in degrees centigrade, in soil medium 

actual microvolt reading 

estimated microvolt reading for variable seconds 

estimated microvolt reading for 15 sec 

estimated water potential for MV period of observation 

upper intercept for estimated MV curves, variable seconds 

as above, for 15 sec 

water potential at which the curve of estimated MV peaks, for 

variable seconds 

as above, for 15 sec 

power of the WP-effect for variable seconds 

as above, for 15 sec 

power of the sigmoid describing N, variable seconds 

as above, for 15 sec 

inflection point of the sigmoid describing N, variable seconds 

as above, for 15 sec 

left numerator of the sigmoid describing N, variable seconds 

as above, for 15 sec 

right numerator of the sigmoid describing N, variable seconds 

as above, for 15 sec 

denominator of the sigmoid describing N, variable seconds 

as above, for 15 sec 

intercept for UIS descriptor, at variable sec 

intercept for U115 descriptor, at 15 sec 

scaling height of TEMP-effect in UIS, at variable seconds 

scaling height of TEMP-effect in U115, at 15 sec 

intercept for SPS descriptor, at variable seconds 

intercept for SP15 descriptor, at 15 sec 

scaling height of TEMP-effect in SPS, at variable seconds 

scaling height of TEMP-effect in SP15, at 15 sec 

zero offset effect 

offset microvolts due to temperature differential at thermocouple 

points 

= WP of-22.5, a constant 

correction in MV estimate due to OMV 

least squares fitting coefficient for the MV model 

UIS*B*C 
APPENDIX II 

COMPUTER PRINTOUT OF MODEL 

Computer printout of predicted water potentials in 

bars for the temperature range of 0" to 40" C (32" to 

104" F), microvolt output, cool time in sec, and zerooffset in 10-microvolt intervals from -60 to + 60 microvolts. All water potential values are unadjusted. 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 0.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50. -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 1.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 2.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 3.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 4.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 5.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 6.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 7.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 8.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 9.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 10.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 11.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 12.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 13.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 14.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHRO1.1ETER TEMPERATURE, CENTIGRADE --- 15.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 16.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHRONETER TEPIPERATURE, CENTIGRADE --- 17.0 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTiGRADE --- 18.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TENPERATURE, CENTIGRADE --- 19.0 
PREDICTED WATER POTENTIAL 
PREDICTED WATER POTENTIAL 

COOLING TIIIE IN SECOIJDS ---------------- 15.0 

PSYCHROMETER TEIIPERATURE , CEIITIGRADE --- 21.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 22.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 23.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHRO@TER TEMPERATURE, CENTIGRADE --- 24. o 
PREDICTED WATER POTENTIAL 

COOLING TIFIE IN SECONDS ---------------- 15.0 

PSYCHRONETER TEIIPERATURE , CENTIGRADE --- 25.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 26.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 27.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 28.0 
PREDICTED WATER POTENTIAL 

COOLING TIIIE IN SECONDS ---------------- 15.0 

PSYCHROIIETER TEIIPERATURE, CEIJTIGRADE --- 29.0 
PREDICTED WATER POTEI'ITIAL 

COOLING TIIIE IN SECONDS ---------------- 15.0 

PSYCHROMETER TEI.IPERATURE , CEI'ITIGRADE --- 30.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 31.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 32.0 
PREDICTED WATER POTENTIdL 

COOLING TINE IN SECONDS ---------------- 15.0 

PSYCHROMETER TENPERATURE, CENTIGRADE --- 33.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 34.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 35.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEI.IPERATURE, CENTIGRADE --- 36.0 

OFFSET FROM ZERO IN MICROVOLTS 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 15.0 

PSYCHROMETER TENPERATURE, CENTIGRADE --- 37.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----f------+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL. NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 38.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 39.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 15.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 40.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEHPERATURE, CENTIGRADE --- 0.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 1.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 2.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 3.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 4.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 5.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 6.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 7.0 
PREDICTED WATER POTENTIAL 

COOLING TIIIE IN SECONDS ---------------- 30.0 

PSPCHROllETER TEMPERATURE, CENTIGRADE --- 8.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 9.0 

OFFSET FROPI ZERO IN MICROVOLTS -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 

-----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROIIETER TEMPERATURE, CENTIGRADE --- 10.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 11.0 

OFFSET FROM ZERO IN FIICROVOLTS -----+-----+-----+-----+---+--+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+---+--+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 12.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 13.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 14.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 15.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHRO!,IETER TENPERATURE , CENTIGRADE --- 16.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 17.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TENPERATURE, CENTIGRADE --- 18.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 19.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TENPERATURE, CENTIGRADE --- 20.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 21.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROITETER TEMPERATURE, CENTIGRADE --- 22.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 23.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIllE IN SECONDS ---------------- 30.0 

PSTCHROIIETER TEIIPERATURE, CENTIGRADE --- 24.0 
PREDICTED WATER POTENTIAL 

COOLING TIIlE IN SECONDS ---------------- 30.0 

PSYCHROIIETER TEMPERATURE, CENTIGRADE --- 25.0 
PREDICTED WATER POTENTIAL 

COOLING TIPIE IN SECONDS ---------------- 30.0 

PSYCHROIIETER TEMPERATURE, CENTIGRADE 26.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 27.0 
PREDICTED WATER FOTENTIAL 

COOLING TIIIE IN SECONDS ---------------- 30.0 

PSYCHROIIETER TErIPERATURE, CENTIGRADE --- 28.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 29.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSPCHROHETER TENPERATURE, CENTIGRADE --- 30.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 31.0 
PREDICTED NATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEHPERATURE, CENTIGRADE --- 32.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- k ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +GO -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 33.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 34.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 35.0 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 36.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHRONETER TEMPERATURE. CENTIGRADE --- 37.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 38.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 39.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 30.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 40.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 0.0 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 1.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 2.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 3.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 4.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 5.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 6.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +60 * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 7.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+----- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +lo +20 +30 +40 +50 +60 * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 8.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 9.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 10.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 11.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 12.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 13.0 

OFFSET FROM ZERO IN MICROVOLTS -----+-----+-----+-----+-----+--- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +lo +20 +30 +40 +50 +60 * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROllETER TEl4PERATURE , CENTIGRADE - - - 14.0 
PREDICTED WATER POTENTIAL 

COOLING TIIIE IPI SECONDS ---------------- 60.0 

PSYCHROIIETER TEIIPERATURE , CENTIGRADE --- 15.0 

OFFSET FROI-I ZERO IN IIICROVOLTS -----+-----+-----+-----+-----+----- n ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +10 +20 +30 +40 +50 +GO -----+-----+-----+-----+-----+----- * ----- -----+-----+-----+-----+-----+----- 

FJATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 60.0 

PSYCHROHETER TEMPERATURE, CENTIGRdDE --- 16.0 
PREDICTED WATER POTENTIAL 

COOLI1,IG TIIIE IIi SECOIdDS ---------------- 60.0 

PSI'CHROIIETER TEIIPERATURE. CENTIGRADE --- 17.0 
PREDICTED WATER POTENTIAL 

COOLING TII.IE IN SECONDS ---------------- 60.0 

PSYCHROIIETER TEPIPERATURE . CENTIGRADE --- 18.0 
PREDICTED WATER POTEI4TIAL 

COOLING TIIIE IN SECONDS ---------------- 60.0 

PSPCHROl.IETER TEIIFERATURE . CENTIGRADE --- 19.0 

OFFSET FROM ZERO IN IIICROVOLTS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHRONETER TEMPERATURE. CENTIGRADE --- 20.0 
PREDICTED WATER POTENTIAL 

COOLING TIHE 1L.J SECONDS ---------------- 60.0 

PS\'CHRO!lETER TEIIPERATURE , CENTIGRADE --- 21.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 22.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 23.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60 .O 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 24.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 25.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROHETER TEMPERATURE, CENTIGRADE --- 26.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 27.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 28.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSPCHRONETER TEIIPERATURE , CENTIGRADE --- 29.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60. 0 

PSPCHRO?.IETER TEf.IPERATURE , CENTIGRADE --- 30.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 31.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 32.0 
PREDICTED WATER POTENTIAL 

COOLING TItIE IN SECONDS ---------------- 60.0 

PSPCHROPIETER TEMPERATURE, CENTIGRADE --- 33.0 

OFFSET FROt.1 ZERO IN NICROVOLTS -----+-----+-----+-----+-----+---- * ----- * -----+-----+-----+-----+-----+----- 

-60 -50 -40 -30 -20 -10 0 +lo +20 +30 +40 +50 +60 * ----- * -----+-----+-----+-----+-----+----- 

WATER POTENTIAL, NEGATIVE BARS 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 34.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 35.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE. CENTIGRADE --- 36.0 
PREDICTED WATER POTENTIAL 

COOLING TINE IN SECONDS ---------------- 60.0 

PSPCHROllETER TEMPERATURE, CENTIGRADE --- 37.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEPIPERATURE. CENTIGRADE --- 38.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 39.0 
PREDICTED WATER POTENTIAL 

COOLING TIME IN SECONDS ---------------- 60.0 

PSYCHROMETER TEMPERATURE, CENTIGRADE --- 40.0 

1 55* U.S. GOVERNMENT PRINTING OFFICE: 1982-0-576-02616 

Brown, Ray W., and Dale L. Bartos. 

1982. A calibration model for screen-caged Peltier thermocouple 

psychrometers. USDA For. Serv. Res. Pap. INT-293,155 p. Intermt. 

For. and Range Exp. Stn., Ogden, Utah 84401. 

A calibration model for screen-caged Peltier thermocouple 

psychrometers was developed that applies to a water potential range 

of 0 to-80 bars, over a temperature range of 0" to 40" C, and for cooling 

times of 15 to 60 seconds. In addition, the model corrects for the effects 

of temperature gradients over zero-offsets from -60 to + 60 microvolts. 

Complete details of model development are discussed, together with the 

theory of thermocouple psychrometers, and techniques of calibration 

and cleaning. Also, information for computer programing and tabular 

summaries of model characteristics are provided. 

KEYWORDS: thermocouple psychrometers, calibration, modeling, 

water potential, temperature gradient effects, Peltier cooling, screen-caged psychrometers, psychrometer calibration model 
The Intermountain Station, headquartered in Ogden, 

Utah, is one of eight regional experiment stations charged 

with providing scientific knowledge to help resource 

managers meet human needs and protect forest and range 

ecosystems. 

The Intermountain Station includes the States of 

Montana, Idaho, Utah, Nevada, and western Wyoming. 

About 231 million acres, or 85 percent, of the land area in the 

Station territory are classified as forest and rangeland. These 

lands include grasslands, deserts, shru blands, alpine areas, 

and well-stocked forests. They supply fiber for forest industries; minerals for energy and industrial development; and 

water for domestic and industrial consumption. They also 

provide recreation opportunities for millions of visitors each 

year. 

Field programs and research work units of the Station 

are maintained in: 

Boise, Idaho 

Bozeman, Montana (in cooperation with Montana 

State University) 

Logan, Utah (in cooperation with Utah State 

University) 

Missoula, Montana (in cooperation with the 

University of Montana) 

Moscow, Idaho (in cooperation with the University of Idaho) 

Provo, Utah (in cooperation with Brigham Young 

University) 

Reno, Nevada (in cooperation with the University 

of Nevada)