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1. Early Warning and Croppo Condition Assessmentt

EW-21-04124NAS 9-16007

pjff5h-- Cep 1 (01 C)54A Joint Program forAgriculture andResources InventorySurveys ThroughAerospaceRemote Sensing

July 1981

REVIEW OF LITERATURE RELATING TO THE MODELING OFSOIL TEMPERATURES BASED ON METEOROLOGICAL FACTORS

Kent H. Sandefer, Richard E. Lund and Joseph M. CaprioMontana State UniversityBozeman, Montana E8?-10102

CT3 .i^, ^ohy

(E82-10102) REVIEW OF LITERATURE RELATINGTO THE MODELING OF SOIL TEMPERATURES EASEDoN METEOBOLOGSCAL FACTORS (Montana StateUniv.,) 94 p HC A05/MF A01 CSCL 02C

N82-22544

UnclasG3/43 00102

r.

U.S. Department of Agriculture1050 Bay Area BoulevardHouston, Texas

Lyndon B. Johnson Space CenterHouston, Texas 77058

1. Report No. 2, Government Accession No.EW-21-04124

4. Title and Subtitl e AgRISMSReview of literature Relating to the Modeling of SoilTemperatures Based on Meteorological Factors

7, Author(s)Sandefer, Kent H.Lund, Richard S. Caprio, Joseph M.

9, Performing Organization Name and Address Tech. MonitorMontana 'State University Frank Ravet

3. Recipient's Catalog No.

5. Report DateJuly 1981

6, Performing Organization Cade

8, Performing Organization Report No,

1U. work Unit No.

Plant and Soil Science Department 11, Contmot or Grant No.

I Bozeman, Montana 59717 NAS 9-1600713. Type of Report and Period Covered

12, Sponsoring Agency Name and Address Literature ReviewEarly Warning/Crop Condition Assessment Project, a ,joint USDA NASA, 10A 4 , USDI and AID AgRISTARS Program, 1050 Bay Area 14. Sponsoring Agr.^mcy CodeBlvd., Houston, TX 77058

15. supplementary Notes

16. Abstract

Literature review relating to the modeling of soil temperatures based on meteorologicalfactors. Included in this review are:

1. Brief abstract of paper2,, Facorable aspects of paper3. Limitations of paper4. Applicability of this paper to the overall. objectives for improvements to the

winterkill model

I 5. Comments, notes and referenceis

17, Key Words (Suggested by Author(s)) 18, Distribution StatementSoilsSoil temperatureMeteorological factors affecting soilSoil temperature modeling

19. Security ciassif. (of this report) 20. Security Classif. (of this page)

Unclassified IUnclassified

21. No of Psges 1 21, Price'

'For sale by the National Technical Information Service, Springfield, Virgi,.ia 22151

JSC Form 14241Rry Nov 75)i

NASA - JSC

4

REVIEW OF LITERATURE RELATING TO THE

MODELING OF SOIL TEMPERATURES

BASED ON METEOROLOGICAL FACTORS

PREPARED BY:

Kent H. SandeEerRichard E. LundJoseph M. Capri©

APPROVED BY:

rank Ravet, ec n,aT Non3torEarly Warning/Crop Condition Assessment Project

AgRISTARS Program

Altl^.114e,,-e

oatwr g ,it, augerEarly Warning/Crop Condition Assessment Project

AgRISTARS Program

AgRISTARSEARLY WARNING/CROP CONDITION ASSESSMENT PROJECT

1050 Bay Area BoulevardHoustony Texas

July 198x,

i1

y

REVIEW OF LITERATURE RELATING TO THE MODELING OF SOIL TEMPERATURESBASEL ON METEOROLOGICAL FACTORS

by

Kent H. Sandefer

Richard E. Lund

and

Joseph M. Caprio

April 20, 1981

li

Work Supported by National Aeronautics andSpace Administration Contract NAS 9-16007

Principal InvcgtiSator:Joseph M. CaprioPlant and Soil Science DepartmentMontana State UniversityBozeman, Montana 59717

111

.

In connection with the AgRISTARS Program, this review of literature

was conducted to fulfill a project objective of Task S untitled "Winter-

- kill Model Improvements" in the Early Warning Crop Condition Assessment

Project (EW/CCA). The title Lf this contributing project is "Study to

r Improve Winterkill Parameters for a Winter Wheat Model" and it has ther

following objectives:

1. To establish experimental sites at about five Agricultural

Research Centers in Montana for monitoring soil end air

temperature.

2. To make recordings at each site from about October 15

through April 15 of air temperature at the 2-meter height

and of soil temperature at the 3-cm depth (a) on bare

ground with snow cover removed, and (b) on bare ground

with natural snow cover.

3. To conduct analytical studies directed to the development

of a procedure(s) to estimete soil temperature at the 3-cm

depth using air temperature data.

Preliminary to conducting analytical studies of the field data, this

survey of the literature was undertaken, by Kent H. Sandefer, a graduate

student at Montana State University who has a Research Assistantship

Y supported by this research program. Dr. Joseph M. Caprio, Principal Inves-

tigator, and Dr. Richard E. Lund, M.S.U'. Mathematical Sciences Department,

supervised the wqrk.

iv

AUTHOR INDEX

I

Number

Arse, J. K. 36Ashcroft, G. L. 45Auctin, D. D. 20

Barton, I. J. 64Biggar, J. W. 57Bonham, C. D. 70Bresler, E. 63Brook, Do P. 7Brown, P. L. 51Budyko, M,. I. 5Burman, R. Do 2

Campbell, G. S. 46959Caprio, J. M. 3Carson, J. E. 49Cary, J. W. 25,32,33034,35

' 46047,48,58Cassel, D. K. 57Chahal, R. S. 53,54Chudnovskic, A. F. 30Cruse, R. M. 42

Deming, J. M. 23de Vries, D. A. 37,':9,40,56,.Dickey, D. D. 51'Jirksea, C. 44

Evans, D. D. 47,48

Ferguson, H. 51Fuchs, M. 59Fye, R. E. 70

Groenvelt, P. H. 60,61Gurr, C. G. 55

Hadas, A. 31Hagan, R. M. 62Hammel, J. E. 21Hanks, R. J. 20,45Hasfurther, V. R. 2Hutton, J. T. 55

Ingersoll, A. C. 27Ingersoll, L. R. 27Inhaber, H. 29

Number

Jackson, R. D, 47,48,50Jager, C. 28

Joni-Hu-Chang 9,10,11,12,13,14,

15016,17,18

Kastvow, P. I. 19Kay, B. D. 60,61Kijve, J,, W. 52Kuhaida,, A. J. 69Kulik, N. S. 41.

Larntz, K. 42Larson, W. E. 42Law, P. F. 23Lettau, HI, 71Linden, D. R. 42Loch, J. G. G, 63

Marshall, T. J. 55Mavland, H. F. 58McWhorter, J. P. 7Meikle, R. W. 68Miller, .R. D. 44,63Moses, H. 49Munn, L. C. 72

Munson, B. E. 69Munson, J. R. 69

National ResearchCouncil

26Nielsen, D, R. 47,48057,62Nowhall, F. 4

Ondrechen, W. To 20

Palagin, E. G. 67Papendick, R. I. 46,59Pessi, Y. 6Philip, J. R. 24,39

Radke, J. K. 42Rao, G. V. 43Revfein, K. J. 65Riemer, A. 66Robinson, L. 4Rosema, A. 38

V

L

I

AUTHOR INDEX (Continued)

Number

Shaykewich, C. F. 66Siddoway, F. H. 36Sinelshchikov, V. V. 41Smith, A. 1Smith, G. D. 4Staar, T. B. 19

Y Swanson, D. 4

Takagi, S. 2`2,Taylor, S. A. 33934935052Thompson, R. D. 8Toy, T. J. 69Treadway, T. R. 68

Wierenga, P. J. 62

Zobel, O. JH, 27

x

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i

a+

TI71E INDEX

Number Pam

Analysis of Sensible and Latent Heat Flow in a PartiallyFrozen Unsaturated Soil . . . . . • • • • , • . . . 59 70

Annual and Diurnal Heat-Exchange Cycles in Upper Layers of Soils 49 60

Climate and Permafrost in Canada r . . • 8 8

Climatological and Solar Radiation Relationships . . . . . . . . . 7 7

Closed-System Freezing of Unsaturated Soil . . . . . 44. 54

Criticism of a Viewpoint on "Thermodynamic and Soil Moisture" • • . 22 31

Crown-Depth Soil Temperature and Winter Protection . 36 45

Effect of ,,emperature and Trapped Air on the Energy Status ofWater in Porous Media . . . • . • • • • • • • • • • . • • . . 54 65

Effect of Temperature and Trapped Air on Matric Suction . . . . . . 53 64

Effect of Temperature on Unsaturated Soil Water Transport . . Y 48 59

Estimation of Manitoba Soil Temperatures from Atmospheric

Meteorological Measurements . 0 • . • • • • . . . • • • • • • . 66 77

Estimation'of Wintertime Soil Temperatures . 0 • . • • . • • . • . 70 81

Frost Action in Soils . . . Y Y • 26 35

Ground Temperature, Vol„ I, Chapters 1-9 . . . . 9-17 9-23

Ground 'Temperature, Vol. II . • . . ,0 , . , • . 18 24

Heat Conduction . . . . . . . . . • . . . . . . • . • 0 . . 27 36

Heat Conduction in Soils . . . . . c . . . . . o o 0 0 a 28 37

Heat Transfer in the Soil . . • • . . . o . . . . . • . • 30 39

Heat Transfer in Soils . • . . . . . . . . . . . . . . . • • . • 37 47

V11

TITLE INDEX (Continued)

Nu-. r

Improved Models of Thermal Diffusion in the Soil . . . . 71 82

Influences of Fields of Motion, Baroclit(icity and Latent HeatSourced on Frontogenesis . 43 53

Interaction of the Simultaneous Diffusions of Neat and WaterVapor ...a..........a .............. 33 42

Interaction of Water and Heat Transport in F,.-o--en and UnfrozenSoils: I. Basic Theory; the Liquid Phase . . . . . . . . . . . 61 72

Interaction of Water and Heat Transport in Frozen and UnfrozenSoils: I. Basic Theory; the Vapor Phase . . . . . 60 71

Lectures on Agricultural Meteorology . . o 41 51

Linear Equations for the Simultaneous Flow of Matter and Energyin a Continuous Soil System . . . . . . . . . . . . . . . . . . 35 44

Mathematical Method for Estimating Soil Temperatures . . a . . . . 68 79

Model to Predict Tillage Effec`it on Soil Tzmperaturg . . 42 62

Modeling Tillage Effects on Evaporation and Seedzone Water ContentDuring Fallow in Eastern Washington . . . . . a a 6 -. . . . 0 0 21 29

Moisture Movement in Porous Materials Under Temperature Gradients 39 49

Movement and Equilibrium of Water in Heterogeneous Systems withSpecial Reference to Soils . . . . . . . . . . . . . . . . . a 23 32

Movement of Water in Soil Due to a Temperature Gradient . . . .'. 55 66

Non-Stationary Method for Determining Thermal conductivity ofSoil in Situ . . . . . . . . . . . . . . . a . . . . . . . . 56 67

Parameterization of the Evaporation from Nonsaturated Surfaces . 64 75

Physics of the Environment . . . . . . . . . . . . . . . . . . . . 29 38

Predicting Soil Temperature Regimes of Mountain and Foothill. Sites 72 83

Prediction of Mean Monthly Soil Temperatures from Mean MonthlyAir Temperature . . . . . . . . . . . . . . . . . . . . . . . . 69 80

viii


r

f

Prediction of Soil Temperatures from Meteorological DataDuring the Winter period . r . • . . • . . . . . . . . • . • w

Relationships of Soils to Mountain and Foothill Range HabitatTypes . . . . . . . . . . • . • . . . / .. . ! . . . • .. . • i

Response of Spring Wheat Yield to Anomalous Climate Sequencesin the United States a . . . . . . . o . . . .

Salt and Water Movement in Unsaturated Frozen Soil . . . . . . . .

Seasonal Subsoil Temperature Variations . . , , . , , . . • . . . .

Simple Procedure for Estimating Global Daily Radiation on AnySurface . . . . . . . . . . . . . , . • . • . s . . . . . i .

Simulation of the Thermal Behavior of Bare Soils for RemoteSensing Purposes . . . . . . . . . . . • • . . . . . .

Simultaneous Flow of Water and Heat Under Periodic HeatFluctuations . . . . . i . i . • . . . . . . . . . . . . . . .

Simultaneous Transfer of Heat and Moisture in Potous Media . • . .

Soil Moisture Transport Due to Thermal Gradients; Practical.Aspects . . . O • Iq i • • . • • . • . Yr • . . . • . . i • • i

Soil Temperature EstivAtion by a Numerical Method . . . a , . . . •

Soil Temperature Modeling Using Air Temperature as a DrivingMechanism . . • . . . . . i . . . . . • . • . • . • . . . . ..

Soil-Temperature Regimes, Their Characteristics and Predictability

Soil-Water Movement in Response to Imposed Temperatures Gradients

Soil Water--Theoretical Analysis . . . • . . . . • . . . . . . 0 ,

Statistical Procedure For Determining the Assoeiation betweenWeather and Non-Measurement Biological Data . . . . . . • . . .

Numberp

67 78

72 83

19 25

58 69

1 1

65 76

38 48

31 40

40 50

32 41

20 27

2

4

68

58

3

3

61

63

Temperature and Soil-Water Diffusivity Relations . . . . . . i . . 50

Temperature Dependence of Soil Water Vapor Pressure . . , . . . . . 52

1x

X


Number Pa e

Temperature of the Active Surface and Its Bioqj$44, tic Significance 5 5

Theory of infiltration: 1, The Infiltration Equation and ItsSolution . . . . . . . . . . . . .0 a. 24 33

Thermal Conditions of Cultivated peat Soil,e in Pelsonsuo in1952-1955. « . . . . . . . . . . . . . . . 0 . . . . . . . 6 6

Thermal Properties of a Soil Based Upon Field and LaboratoryMeasurements . . . . . . . . . . . . . . . . . . . 0 . . . . 62 73

Thermally Driven Liquid and Vapor Phase Transfer of Water andEnergy in Soil . . . . . . . . . . . . . . . . . . . . . . . . 34 43

Transport of Water and'Heat in a Frozen Permeameter . . . . . . . . 63 74

Water and Salt Movement in Unsaturated Frozen Soil; Principlesand Field Oboarvationr, . . . . . . . . . . . . . » . . . . . . 46 57

Water Flux in Moist Soil: Thermal Versus Suction Gradients . . . . 25 34

Water Movement and Loss lender Frozen Soil Conditions . . . . . . . 51 62

Water Potentials . . . . . . . . . . . . . . . . . . . • . . . . . • 45 b5

E

r

The reviewer's comments are listed in sections according to

the following numerical system:

1) A brief abstract of the paper

2) Favorable aspects of the paper

3) Limitations of the paper

4') Applicability of the 'paper to this project

5) Other: comments, notes and references

XY

W

No. 1 File No. 2529

Title; Seasonal Subsoil Temperature Variations

P, ub, Journal. of Agricultural Research

Date; March 1, 1932 Vol; 44 No; 5 Pte; 421-428

Author; Smith, A

1. The paper presents data collected on subsoiltemperature for a two-year period betweenzecember 1925 and December 1930. The temperaturesat depths from one foot to 12 feet were recordedweekly. The data are presented in graphical,form and a qualitative agreement with theoryis shown.

2.

3. No model was included in the paper, buteference is made to a book by Keen (p. 308 (1) )for a discussion of theory. The relationshipof soil temperature and air temperature was notexplored, nor 'was the influence of soil moistureon soil temperature.

4. Since no model was presented and no quantitativerelationship discussed, the paper is of littleuse in the project.

5. (l) Keen, B. A.; The Physical Properties oft'he Soil: London, New York.

:4

1

No. 2 File No. 3400

Title: Soil Temperature Modeling Using Air Temperature As A DrivingMechanism

Pub: Transactions of thu ASAE

Date: Jan/Feb 1974 Vol: 17 No: 1 Pages; 78-81

Authors: Hasfurther, V. R.; Burman, R. D.

1. A mathematical model is used to predictsoil temperature at various depths, given thesoil temperature at a depth of one inch. Anempirical relationship is found to predict soiltemperature at one inch with the air temperatureof the same day and two previous days. Thenthe one dimensional heat equation is used topredict soil temperature at other depths usingthe predicted temperature at the one inch level.The accuracy of prediction was + 30F. Errors arelarger for greater depths.

2. Reasonable accuracy of prediction is demonstratedfor soil temperature at various depths, based onknowledge of soil temperature at the one inch level.The data show a near linear relationship ofair temperature and soil temperature at the oneinch depth.

3. The linear relationship of air temperatureand one inch level soil temperature is highlydependent on parameters unique to a particularsite. Two sites were used, but comparison betweenthe two sites are not made. No model is given torelate the parameters to soil properties orother influences.

4. Since the prediction is partially based onempirical equations and on a simple model ofbeat flow in the soil, ignoring moisture, etc.,this paper has limited interest in the project.

5. Addit ^.onal References:

Van Wizh, W. R., 1963Physics of Plant ".'avironmen tNorth-Holland PuzO,shing Co., Amsterdam 382 p.

Location of site for data collection wasArcher, Wyoming

F

No. 3 File No. 1446

Title: A Statistical Procedure for Determining the AssoctationBetween Weather and Non-Measurement Biological Z'A a

Pub: Agricultural Meteorology

Date: 1966 Vol: 5 No: 1-2

Pages: 55-72

Author: Caprio, J. M.

1. The paper gives a method of relating thegeneral nature of environment input such astemperature and moisture to crop yield. Forthree week periods of a year, a Frequency tableis constructed as follows. The years areclassified as good yield years, average yieldyears, or poor yield years. Then for each classof gear the number of times a temperature, forexample, was in excess of a preassigned valueis found and tabled. A Chi-Squared statisticis caluclated to compare years to each other.

2. Ms approach has good flexibility andgenerality. It explicitly relates when andhow long a high temperature condition can berelated to a poor yield or good yield, ratherthan an average temperature for the month. How

4 the temperature varies is as important or moreimportant than the average temperature.

3. The information given by this approach wouldbe hard to use to predict quantitatively, ghatare the effects of a 3-week cold period, Forexample, on winterkill or crop yield?

4. How the temperature varies with time wouldsurely affect the winterkill, since the durationof a cold spell is as important as the averagetemperature.

5.

3

No. 4 File No. 1220

Title: Soil-Temperature Regimes, Their Characteristics and Predictability

'Pub: U. S. Department of Agriculture

Date: April, 1964 Pages: 1-14

Authors: Smith, G. D.; Nowhall, F.; Robinson, L.; and Swanson, D.

1. The paper presents an extensive amount ofdata, in tables and in graphical form, aboutmonthly average temperatures in the air and atvarious depths in soil.

It discusses the effects of ground cover onsoil temperatures and moisture. It is concernedmainly with yearly and some monthly averages.

2. A source of data to compare with futuremodels about long term predictions. Also somedata on the effects of snow cover.

3. No quantitative model is given on heat flowchanges caused by ground cover, snow, etc.

4. Useful for some data to test the validityof future models. Data are available on monthlyaverages of air and soil temperatures.

5. Data presented have been collected fromaround the world.

A

9

I

No. 5 File No. 1760

Tile: Temperature of the Active Surface and its Bioclimatic SigniUcance.

Pub: Gidromesoezdat, (Translated by Weather Bureau)

Date: 1960 Pages: 201-211

Author: Budyko, M. I.

1. The papor is cor.cerned mainly with the effectsof temperature, humidity, etc., on the comfortof plants and animal. Data are presented to showthe difference in temperature between the air andthe active surface of the ground and possibleplant leaves, etc. It discusses the use of theheat balance equation.

2. It presents a fundamental equation of heat.balance, for a land area and gives approximatevalues of some of the constants involved.

3. No reference is made to soil temperatures.Only basic equations are used in the discussion.

4. A discussion of the basic heat balanceequation is presented. This is of littleadditional use in the project.

^: n 5

ti

No. 6 File No. 486

Title: On the Thermal Conditions of Cultivated Peat Soil in Pelsonsuoin the years.1952-1955.

Pub: Finnish State Agricultural Research Board. No. 154

Date: 1957 Not 154 Pages: 1-47

Author: Pessi, Yrjo

1. Presents data collected on a plot in Pelsonsuobetween 1952 and 1955 and a fairly completehistory of snowfall on the plot as well as soiltemperature at depth 5 cm, 10 cm, 20 cm, 50 cm,100 cm is given. The temperature is presentedin tabular form. The snow depth is provided ingraphical form only.

2. A good source of data on soil temperatureand snowfall.

3.

4. This paper demonstrates the importance ofconsidering ground moisture on temperature, sinceone year was particularly wetter than normal andthis shows up later in the temperature record.Also note evidence that the thermal conductivityincreases with increasing depth in approximatelya linear manner.

5. Thermal Conductivity in dry soil .00022 cal/cm sec Co

Thermal Conductivity in wet soil .00107 cal/cm sec Co

Additional References

Bouyoucas, Q. J., 1913"An investigation of soil temperature andsome of the most important factors influencing it."Michigan Agr. Coll. Exp. Sta. Techn. Bul. 17: 1-196

Smith, W. 0., 1939"Soil temperature, thermal conductivitiesin moist soils."Proc. Soil Sci. Soc. Amer. 4: 32-40.

et. al., 1938"The thermal conductivity of dry soils ofcertain of the great soil groups."Proc. Soil Sci. Soc. Amer. 3: 13-19

i'

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No. 7 File No. 1348

Title: Climatological and Solar Radiation Relationships

Pub: Agr. Exp. Station, State College, Mississippi

Date: August 1965 No% 715 Pages: 1-35

Authors: McWhorter, J.P.; Brook, B. P.

1. Uses empirical relationships of solarradiation, evaporation rate, air temperature andsoil temperature to predict solar radiation. Alarge amount of data is presented.

2. The data are given mainly in weekly averagesof the above variables, but some daily averages,collected every six days, are also available forsoil depths at four and eight inch intervals.

3.

4. Useful as a source of data to test models.

5. Most of the relationships are closely linearbetween the variables, in this paper.

3

No. 8 File No. 3486

Title: Climate and Permafrost in Canada

Pub: Weather

Date: August 1974 Vol: 29 No: 8 Pages: 298-305

Author: Thompson, R. D.

i 1. The paper presents a qualitative discussion ofpermafrost and the factors influencing permafrost.Microclimate is shown to be very important in

' the formation, etc., of permafrost.

Y.

2'. A good qualitative discussion of the variousfactors influencing permafrost.

3. No models, no data.

4. Of little use in the project.

d

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No. 9

Title: Ground Temperature Vol. I

Pub: Blue Hill Meteorological Observatory, Harvard University

Date: June 21, 1958 Vol: I Pages: 1-11 (Chapter 1)

Author: Jen-Hu-Chang

1. Chapter One is an introduction to theproblems and needs of accurate quantitativeinformation. It shows the importance ofunderstanding ground temperature and relatedareas.

2. Good introduction to the need for understandingground temperature.

3.

4.

9k "

No. 10


Pub: Blue Hill Meteorological Observatory, Harvard university'

Date: 1950 Vol: I Pages: 12-20 (Chapter 2)


1. The title of this chapter is "Measurement ofGround Temperature". It discusses the errors ofmeasurement involved in the collection of data.Also it discusses the different types ofthermometers in use, end gives advantages anddisadvantages of each. Also discusses measurementerrors due to the time of observation.

2. Gives a numerical example of the differencesin the way thf daily average is estimated. Thisis Table One in the text. It shows differencesof + HOC in the different methods commonly usedto estimate daily averages.

3.

4. Useful in designing the data collecting phaseof this project.

5. Of the three thermometers in use; mercury,resistance and thermocouple, the easiest andmost rugged one is the resistance thermometerwhich has fairly small measurement errors.

10

i

7

No. 11

Title: Ground Temperature

Pub: Blue Hill Meteo. Obser.

Ante: 1953, Vol: I Pages: 21 Y-42 (Chapter 3)


1. This chapter discusses the various thermalproperties of soil and soil cover, giving afair amount of information about conductivity,reflectivity, transmissivity, etc. It alsodiscusses the influence of moisture and temperatureon these properties.

For example, thermal diffusivity dependson soil moisture in a very important way, asmoisture varies from 10% to 30% water by weightthe diffusivity varies from .0015 to .0030.Also, at freezing, the diffusivity is alsodependent on temperature.

2: A good discussion of the thermal propertiesof soil and what factors influence these propertiesand by how. much.

3.

4. Will be of use to determine vhat factors shouldbe included in a model, giving information abouthow the properties depend on the factors, etc.Clearly any model is an oversimplification ofthe problem. This chapter shows the need to trymany different models, each being progressively morecomplex, until a reasonable agreement with datais found.

5. A list of factors that influence variousproperties.

A. Ref(a)(b)(c)

k (e)

(f)

(g)

1

lectivity.Wavelength (important)Angle of incident (important)Soil color (albedo) (important)Type of minerals in soil (less important)Organic material, influence color (importanMoisture influence on color (importantfor a short time after rain)Snow cover (important)

1

No. 11Page 2

B. Transmissivity.(a) Snow cover, age, compactness,presence of layer or not, allinfluence transmissivity. (important)

C« Emissivity.(a) Wavelength (important)(b) Absolute temperature (important)(c) Character of surface (smooth orrough, etc.)(d) Kirchoff's Law (good absorber +^good emitter)(e) Stefan-Boltzman Law (rate ofradiation s (Tl4 T24), 8.i3 x 10-11cal cm-2 min-1 deg-4

D. Specific Heat and Heat Capacity.(a) Moisture (important)(b) Soil ComposiU on (less important)

E. Thermal Conductivity.(a) Porosity (important)(b) Moisture (important)(c) Organic content (less important)(d) Temperature (minor)(e) Soil minerals (minor)

F. Thermal Diffusivity(same as Thermal Conductivity)

r

12

No. 12

Title; Ground Temperature Vol. I

Pub: Blue Hill Mateo, Obser.

Dater 195$ Vol I Pages: 4357 (Chapter 4)

Author; Jen-Hu-Chang

1. This chapter is about heat flux in the ground.It discusses the sources of energy and the dispositionof energy as well as the factors influencing theflow of heat in the soil. It also shows theimportance, of considering soil moisture and othermodes of transfer of heat in the soil.

2. Good overview of the factors and the importanceof each factor that influence heat transfer in thesoil and to the soil.

3. Most all of the 4quations used in this chapterare based on the assumption that the soil ishomogenous througbou.. It is not completely anaccurate model since data are presented that showthat near the surface, within 30 cm, this modeldoes not agree well with the observations,

4. This serves as a starting point to select themajor sources of energy and major disposition factorsfor a model.

5, 1. Sources of Energy.A. Earths interior heat (minor)B. Radioactivity of rock (minor)C. Decomposition of organic matter (minor)D. Chemical Reactions (generally minor)E. Radiation, from moon, stars, etc. (very minor)F. Direct solar radiation, not reflected

from moon, etc. (major)

II. Disposition of Energy received at theground surface.A. Evaporation of soil moisture (important)B. Transfer to atmosphere (important)C. Transfer into ground

1. By conduction (major mode at lower depths)s 2. Heat transfer to water in soil.4

3. Convection of air in the soil(negligible if soil particles aresmaller than .1 cm and pores are small)

13

No. 12Page 2

4. Diffusion of water vaporin soil,(may account for as muchas 45% of total transfer,generally x 1% or 2%)

5. Movement of water in soil.

14

No. 13

Title; Ground Temperature Vol, T

Pub: Blue Hill Meteo, Obser,

Date: 1958 Vol: 1 Pages 58-127 (Chapter 5)

Author; .Ten-Hu-Chang

1. This chapter presents, in graphical form,the annual trends of soil temperature at variousdepths over the world, if data are available,The discussion is generally qualitative andsummarizes the data collected,

2. it combines the data and knowledge of thefield about soil temperatures.

3. Very little is said about a detailed modelof the soil, temperature problem, but the informationpresented will be very useful, in forming the model.

4. This is useful because the chapter discussespractically all of the factors involved with soiltemperatures and gives information about therelative importance of each factor. This chaptershould help in choosing the variables to includein ":e model.

5. This shows that the conduction process in theground is dominant at lower depths, but not nearthe r Mace.

15

Ai;m

No . 14


Pub.: Blue Hill Meteo. 4bser.

Date: 195$ .Vol: I Pages: 128--193 (Chapter 6)

Author: ,den-Hu-Chang

1. This chapter summarizes the factors thatinfluence ground temperatures and presentsliterature to support the claims and also toestimate the relative importance of the variousfactors. The main conclusion is that microclimaticproperties have a sizable effect on .soil temperature.Most important are ground cover, moisture ir, theground and on or near the surface, color of ground,whether the ground is cultivated or not, latitude,slope and altitude.

2. This chapter shows the importance of thevarious factors influencing soil temperature.

3.

4. This chapter should be useful to help selectvariables, factors, etc.,, to include in a model,but gives little help in determining quantitativerelationships of the various effects. A largesupply of graphs. No equations.

5. A Meteorological Elements.1. Solar Radiation2. Radiation, related to clouds

(a) keep heat in at night(b) keep heat out by day

3. Rain(a) source of heat energy, due totemperature difference, generallycooling the soil(b) changes the thermal properties(c) temporarily increases at lowerdepth due to forcing soil air down(very minor)(d) changes reflectivity as well

4. Snow cover.(a) low thermal conductivity(b) high reflectivity(c) excellent long wave radiator

16

r

No. 14Page 2

(d) large heat of fusion(e) density changes, depending onage of snow, degree of melting, etc.(f) the insulating effect is notproportional to depth of snow(g) affects the temperature ofsoil depending on the initialcondition of soil(h) shows heat exchange betweensoil and air. Shows lag andamplitude reduction

5. Air temperature6. Humidity (latent heat)7. Heat transfer by wind

(a) more important in daylight

B. Properties of Soil1. Soil texture

(a) sand(b) loams(c) clays

2. Moisture content• (a) varies 'heat capacity

I, (b) surface evaporation(c) increases conductivity(d) percolation

3. Organic matter(a) reduce heat capacity(b) reduces thermal conductivity(c) increases water holding capacity(d) increase absorptivity due to adarker color

4. Color (changes absorptivity)5. Structure, cultivation and compaction

(a) cultivation loosens soil andacts as a mulch to reduce heat exchangewith lower depths, acts as a protectivelayer to keep moisture in the lowerdepths(b) diurnal wave at surface ofcultivated soil is larger thanuncultivated soil(c) compaction increases thermalconductivity

C. Topography1. Aspect

(a) direct insolation is influenceby aspect and slope(b) diffuse sky radiation isinfluenced by slope only

17

No. 14.Page 3

7. Slope(a) southward slopes are warmerthan northward slopes, in theNorthern Hemisphere

3. Altitude.(a) less air, more radiation(b) greater loss at night also,but gain is generally greaterthan loss(c) higher altitudes have largervariations in temperature

4. Concavity and convexity(a) at night the ground coolsfaster than the air, thereforethe cool air near the surfaceflows downslope in the valleysthus transporting energy fromthe high slope into the air inthe valleys

D. Vegetation Cover1. Forest

(a) low albedo(b) most insolation is used byplants(c) slows the losses by radiation

w at night(d) trees, etc., impede air flownear the ground(e) very little runoff of rainin forest(f) evaporation is less, due toground cover of leaves, etc.(g) changes the nature of thesnow fall

2. Grass(a) increases evaporation losses(b) interferes with heat exchangebetween ground and atmosphere,depends on height and density of grass

3. Crops(much the same as grasses)

E. Urban Environment(a) generally warmer air andprobably warmer soil temperature{b) less wind(c) shading, etc.

F. Fires

418

No. 15



Date: 1958 Vol: I Pages:

Author: ,den-Hu-Chang

4

194-229 (Chapter 7)

1. The subject of this chapter is formation offrost and thawing properties. Some equationsfor predicting frost depth are discussed. Eachrequires a knowledge of detailed measurementsof soil properties. There is also a purelyempirical equation given. During the formationstage, the temperature of subsoil is constantat OoC, due to the release of the latent heatof fusion of ice.

2. A fairly complete discussion of the factorsinfluencing the formation of frost, with mathematicalmodels and empirical equations. It also brieflydiscusses thawing processes.

3.

4. Since we are to predict temperatures inthe soil during the winter, the freezing processwill be very much a part of the whole model.

5. A. Freezing Point, Latent Heat, and Zero Curtain.(a) freezes at x 1.OoC, due to saltsin the soil, etc.(b) the release of latent heat duringfreezing warms the layer below andmaintains a fairly constant OoC(c) :once frozen the thermal conductivityis increased and normal temperaturevariation continues

B. Factors Determining Frost Penetration(a) air temperature(b) snow cover(c) vegetation cover (minor)

C. Thawing(a) influenced mainly by rain andconduction of heat from above, representsabout 70% of the heat to thaw

D. Permafrost(a) near and under flowing riversthere is no permafrost

19

10

No. 15Page 2

E. Map of Frost DistributionF. Prediction of Frost Penetration into

the ground.(1) Use the freezing index

(a) cumulative total of degree - daysbelow freezing point

(2) Mathematical Approach(a) assumes homogeneous material

in models(b) Bergeron's equation

7.X ?Bwhere z=thickness of frozen layerB - growth coeff. of frozenlayer (need table)t - duration of subfreezingsurface temperature in hoursKh = thermal diffusivity of thesoil (relative error reportsas 50%)

(c) Franklin's equationK4 -t.

rW volume percentage of waterTo temperature of the surface

(3) Analog Computer(a) used to solve the differential

equations of the heat problem(b) direct physical analog is used

like hydraulics(4) Heat Balance (little use)

20

No. 16

Title: Ground Temperature Vol I

Pub: Blue Hi l l Meteo. Obser.

7



1. This chapter discusses the influence ofground temperature on air temperature. Theprincipal processes are molecular conduction,convection, terrestrial. radiation, and evaporation.

2. It refers to works that have used models andgives some of the equations available. However,many of the processes involved are very complexand no models have been used.

3.

4. In order to show how much heat is conductedinto the soil, we need to know the incomingenergy and out going energy not in the soilthis involves transfer into the air. So someparts of the model must include the influenceof ground temperature on the air.

5. A. Temperature gradient in the air layernear the ground.

B. Processes of heat transfer from groundto the air.(1) molecular conduction(2) convection

(a) thermal convection(b) dynamic convection(c) roughness of surface reduceslosses due to convective exchange

(3) Terrestrial radiation(a) the direct effect of longwaveradiation from the ground is confinedto an air layer of several metersnear the ground(b) the high air layer at night,cool by radiating to lower airlayers, not directly to the ground(c) gives a formula for determiningback radiation on cloudless nights

21

Ye' ..!`^ .., _ _:..s

-° iIR11^n1M++^wartre+.wwi1

No. 16Page 2

(4) Evaporation(a) influenced by

(i) temperature(ii) salinity(iii) wind velocity(iv) air pressure(v) difference in vapor

pressure between watersurface and the air

(b) very complex mathematicalproblem

C. Variation in Ground Surface, ThermalAdmittance.

(a) thermal admittance

where K = thermal conductivityC.- specific heat of soilp - soil densitythe fraction of heat enteringthe soil is roughly proportionalto the Jn_4'—KGp and increaseswith :increased moisture

(b) ideally, in the absence ofturbulence, the air adjacent to theground at night is colder and denserthan the air above

Brunt's Equationcooling of the ground surface in thours from sunset, of soil withconductivity K, heat capacity, C is

a h.twhere Rt = net rate of heat lossfrom ground

Rt;:-,U- (T + 273) 4 (.48 - . 06Wvewhere T is temperature in oCa is vapor pressure in mm

22w

No. 17

Title: Ground Temperature Vol I




1. The chapter outlines methods used to modifyground temperature mainly to retard frost andto warm soil by adding sand to the top layerto increase insolation.

2.

3.

4.

5. A. Arti£ica.l Ground Cover(1) paper mulch(2) straw mulch(3) polyethylene

» (4) screen and capB. Carbon BlackC. Heating and SmudgingD. Wind MachineE. Irrigation and SprinklingF. Sanding

k

23

No. 18

Title: Ground Temperature Vol II

Pub: Blue gill Meteorological Observatory, Harvard University

Date: 1958 Vol: II Pages: 1-196


1. This is a summary of data on ground temperaturesfrom around the world. The data are generallymonthly averages at variouP depths. Additionalinformation is generally latitude, longitude,and altitude with remarks on method of datacollection, if possible.

2.

3.

4.

5.

24

No, 19 Pile No. 4849

Title: The Response of Spring Wheat Yield to Anomalous ClimateSequences in the United States

Pub: Journal of Applied Meteorology

Date: August 1,978 Vol: 17 .No: 8 Pages: 1101-1115

Author: Staar, T. B.; Kastrow, P. I.

1. The authors have used monthly temperatureand precipitation averages, after detrendingwheat yields, to predict residual wheat yields.The detrending was done to compensate forchanges in farming methods over the periodfrom 1932 to 1975.

The independent variables were firststandardized to have mean zero and varianceone and then were transformed into principalvariates by a principal component analysis_Each eigenvector was used to identify adifferent type of anomaly in the distributionof temperature and precipitation.

2. The approach shown in this paper has givena deeper insight into the type of anomalythat influences wheat yields than multiple

„ regression can. Also this approach has beenproposed by others to deal with the problem ofhighly interdependent explanatory variables.A variation of this: approach has been proposedfor time seriep analysis, so the method usedhas great generality.

3. The method is based on linear relationshipsbut extension to some non-linearity relationshipis possible, particularly for interaction termsbetween temperature and precipitation thatwould be most interesting.

4. The approach of the paper would be usefulin reducing the number of independent variablesto explain winter kill of wheat. The paperconsiders independent variables includingtemperature of various time periods throughout

• the winter. Each time period temperature oraverage temperature would be an independentvariable, by reducing the consideration to thelinear conbinations most variable that are mostlikely to explain the differences in the winter kill.

25

No, 19Page 2

if a Particular linear combination of temperaturesis constant or near constant for all casesthen it is not useful to explain differencesin winter kill percentages.

S. The eigenvector coefficients actuallydescribe patterns of temperature and moistureconditions.

»

No. 20 File No, 4523

Title: Soil Temperature Estimation by a Numerical Method

Pub: Proceedings of Soil Science Society of America

Date: September-October 1971 Vol 35 Nos S Pages: 665-667 =i

Author: Hanks, R, J.; Austin, D. D.; Ondrechen, W T.

1. The authors use a numerical method tosolve the one-dimensional heat equation withvariable thermal diffusivity and make comparisonswith actual data for accuracy. Generallyerrors increase with the time period and withincreased intervals of depth, An error of10C - 1.70C plus or minus was reported. Alsocomparisons assuming uniform thermal diffusivitywere made and increases in errors of .1 - 1.40Cwere reported. It appears that an assumptionof uniform diffusivity would be in error byabout + 3.5 0C at most.

2. This paper gives some insight into thesize of error likely to be made by ignoringthe variation of diffusivity with depth.

,. 3.

4. Outlines a numerical method of solutionof the heat equation that may be useful forthe :omplex equations that we will need to solve.

5. Additional References

1. de Vries, D. A., 1963Thermal properties of soils.p. 210-235 In W. R. van WijkPhysics of plant environmentJohn Wiley and Sons, Inc. New York

2. Hanks, R. J. and S. A. Bowers, 1962Numerical solution of the moistureflow equation for infiltration inlayered soils.Soil Science Society of America Proceedings26: 530-534

No. 20Page 2

3. Hanks, R. J. Klute, A. andE. Bresler, 1969A numerical method for esttmatinginfiltration, redistribution, drainageand evaporation of water from soil.Water Resources Research 5s 1064-1069

fi

4. Hanks, R. J. Jacobs, H. S.;Schimmelpfennig, H. and M. Nimah 1971Evapotranspiration estimated fromoats by the energy budget, aerodynamicsand combination methods.Utah ARr. Exp. Sta. Utah Resources Report 54

5. Wierenga, R. I. and C. T. de Wit, 1970Simulation of heat Flow in soilsSoil Science Society of America Proceedings34: 845-848

28

r,

f

No. 21 File No. 4855

Title: Modeling Tillage Effects on Evaporation and seedzone WaterContent During Fallow in Eastern Washington

Nib: Doc Thesis from Washington State University, Department ofAgronomy and Soils

Date: 1979 Pages: 1-65

Author: Hammel, J. E.

1. Develops a mathematical model of soilmoisture and soil temperature allowing forthe interaction of moisture on temperatureand temperature on moisture by using numericalmethods to solve the equations. It teststhe model with experimental data and usesthe model to explore the effect of tillageon soil moisture and temperature at seed level.

2. The model developed here considers theinfluence of changing moisture on temperatureflow as well as the influence of temperaturegradients on moisture flow. Most other modelsconsider the moisture constant when discussingtemperature changes or consider the flow ofwater with temperature constant. Hammel'smodel shows the importance of consideringjointly moisture distribution and temperaturedistribution.

3.

4. This model appears to be one of the mostcomprehensive models for predicting soiltemperatures and soil moisture. Since moisturehas a large influence on temperature bath factorsshould be included in a model of soil temperatures.If this model or a more complex model can beshown to accurately predict soil temperature

I. with experimental data, then when using themodel one could evaluate, the accuracy of othermethods of predicting soil temperature basedon less information than this model.

5. The two main equations of the model are:

29

30

No. 21Page 2

and

:: --;L ( ^- ,a) V4 D,

The model considers both liquid and vapormovement in the soil and influences on heattransport by movement of liquid and vapor.

No. 22

Title: Criticism of a Viewpoint on "Thermodynamic and Soil Moisture."

a Pub: Soil Science

Date: 1954 Vol: 77 No: 4 Pages: 303-312

Author: Takagi, Shunsuke

1. The author comments on misconceptionsof early workers. The discussion is on Gibb'sTheory and discusses energy considerationslike Helmholtz free energy enthalpy, Gibbsianfree energy and entropy.

h

2.

3.

4. No direct use in project.

31

No. 23

Title: Movement and Equilibrium of Water in Heterogeneous Systemswith Special Reference to Soils

Pub: Soil Science

Date: 1953 Vol: 75 No: 1 Pte: 187-202

Author: Law, P. F.; Deming, J. M.

1. The approach of the pager is basicallythermodynamic using free energy, etc. Littleis said about the distribution, of moisturein the soil. The discussion is very micro-detailed considering electrostatic effects, etc.

2.

3.

4. The paper does not help to predict moisturein the soil and its relationship to the soiltemperature, since the discussion was limitedto constant temperature processes.

f

:i

32

No. 24

Title: The Theory of Infiltration: 1. Tht Infiltration Equationand its Solution

Pub: Soil Science

Date: 1957 Vol: 83 No: 4 Pages: 345-357

Author: Philip, J. R.

1. Considers infiltration in soil underconstant temperature conditions. It usesthe equationK

The K is a potential function generally usedfor gravitational potential.

2. The author applies a numerical method hedeveloped, since the Crank-Nicholson Methoddidn't give accurate results. This methodis developed in a separate paper by the authorgiven in item 5 of this report. 4

3.

4. Since accsrate prediction of soil temperaturerequires knowledge of the moisture distributionin the soil, some part of the model will needto predict the moisture content. However thispaper considers only isothermal movement ofmoisture, but the methods of approximationused in the paper should be investigated forpossible use in the project.

5. Philip, J. R., 1955"Numerical solution of equations of thediffusion type with diffusivityconcentration-dependent."Trans, Faraday Soc. 51: 885-892

s

33

34

No. 25

Title: Water Flux in Moist Soil; Thermal Versus Suction Gradients

Pub: Soil Science

Date: 1965 Vol: 100 No: 3 Pages: 168-175

Author: Cary, J. W.

1. Flows of heat and moisture were measuredexperimentally through a loam soil and theresults presented. The conclusion was thatlarge amounts of heat are transported bymovement of water vapor and liquid. Moreover,temperature gradients are important in themovement of water as well.

2. Presents experimental evidence of theimportance of temperature gradients to movewater.

3.

4. Shows that simultaneous consideration ofmoisture and temperature will be needed topredict temperature accurately.

5. Important equation from text.

PC T

r.•^t

ti

No. 26

Title: Frost action in soils

Pub: National Research Council Highway Research Board

Date: 1952 No: 1 & 2

1. Volume one is a survey of the literatureon frost action. Volume two presents empiricalinformation on frost action. This is ofinterest mainly to engineering.

2. Used an unusual method of approximation.(see 5)

3.

4. Of little use to developing a model of'soil temperature. Very little data areavailable in the book.

5. One novel idea in volume two was the useof an unusual analog computer to caluclatetemperatures in the soil, based on an approximationthe details of which are given below.

Basic Heat Equation:

1Approximate Equation:

at ZS x

This is found by subsituting the differenceapproximation for , but not changingThis system of equations can now be solved byusing anjelectrical c- went of the-OEorm.

The approximate equation may also be solved

t analytically as well and this can easily be modifiedto consider nonhomogenous diffusivity, etc.

x

t L

35

No. 27

Title: Heat Conduction

Pub:

Date: 1954

Authors: Ingersoll, L. R., Zobel, 0. J., and Ingersoll, A. C.

1. An introductory text on basic heat flowtheory. No examples related to soils.

2.

3.

4.

3E

i<

No. 28

Title: Heat Conduction in Soils

Pub:

Date:

Authors: Jager, C.

Not in library. Found in No. 26.

37

No. 29

Title: Physics of the Environment

Pub:

Author: Inhaber, H.

1. Discusses how physics can be applied toenvironmental problems, mainly pollution.

2.

3.

4. No discussion of soil temperatures at all.

.t.

38

No. 30

I

Title: Heat Transfer in the Soil. ^(r

itPub: 'by Israel Program for Scientific Translations for National

Science Foundation and Department of Agriculture

Date: 1948 Pages: 1-164 f

Author: Chudnovskic, A. F.

1. Discusses the processes of heat transferin the soil and between air and soil. Usesmathematical models of the heat transfer insoil and between soil and air. The approachdoes not develop a single complete model.

Detailed discussion is made of themeasurement problems and various instrumentsare analyzed mathematically and many newinstruments are presented.

2. Good discussion of instruments andmeasurement errors. New methods are presented.

3. The models are mainly of the one-dimensionalheat equation type assuming homogenous diffusivity,and linearly variating idff usivity.

4. Not much insight into the modeling problemis given by this work. However, the methodsof measurement of diffusivity, conductivity,and heat content could be useful.

39

No. 31

Title: Simultaneous Flow of Water and Heat Under Periodic HeatFluctuations

Pub: Soil Science Society of America Proceedings

Date: 1968 Vol: 32 No: 3 Pages: 297-301

Author: Hadas, A.

1. An experiment was conducted to tent theaccuracy of a mathemetical model for smu-ltaneousflow of moisture and heat. The results showedsizable errors with relative errors of 700%being the largest.

2. The work shows the need to consider a morecomplete model than that used in the paper.

3. Assumes that temperature flow is notinfluenced by moisture changes. Used a constantthermal diffusivity, in time and space. Inshort, the model is too simple to reasonablyrepresent the experimental data.

4. Shows the need for a more complex modelthan they used in this paper.

5. Details of the model assumptions:1. Relative humidity of soil is 100%2. Moisture: changes are small3. Temperature is sinosoidal in time4. Thermal diffusivity is constant intime and space and there is negligibletransfer of sensible heat and latent heatof vapor transport.

Equations:

lb . 'D

t 0 is moit-s%-ure contentT is ti mperatureL is tortuisity factor .67S is air porosity (cm3/cm3)P(T) is saturated water vapor as a function of

temperatureD(T) is vapor diffusion coeff - temp dependent (cm 2/sec)

40

a

41

,_ k

No. 32

1

Title: Soil Moisture Transport Due To Thermal Gradients:Practical Aspects

Pub: 1966 Vol: 30 No: 4 Pages; 428-433

Author: Cary, J. W.

1. The author discusses four proposedmechanisms of thermally induced moisture,vapor and liquid flow, The mechanism forvapor transport appears satisfactory, but the„mechanisms proposed for liquid don't completelyexplain all the f4cts satisfactorily.

2. A good qualitative discussion of thermallyinduced moisture flow.

3. No discussion of moisture movement onheat flow.

4. Since no model is proposed for theinteraction of heat flow and moisture flow,the paper is of no interest for the project.

5. Jd T (Vapor flux)yap ,Ii nl z

Jliq = C ` P) ^ -r (Liquid flux)

CX 1 c4

Note: ( ) coeff, depend on T.

No,, 3

Title: The Interaction of the Simultaneous Diffusions of Heat andWater Vapor


Date: 1962 Vol: 26 No: 5 Pages: 413-416

Authors: Cary, J. W. and S A. Taylor

1. Discusses some predictions of the theoryof irreversible thermodyamic processes aboutsteady-state flux of vapor due to temperaturegradients and energy flue: due to temperaturegradients. In general good agreement was foundbetween experimental results and the theory.

2. Good agreement was found between experimentaldata and theoretical predictions.

3. Only the steady-state conditions werestudied, assua%.d content moisture distribution

Y and constant temperature distribution.

4. The assumptions made in this paper are-veryrestricted in nature, Le. steady-state conditionsand only vapor flow was considered.

42

0

No. 34 E

Title: Thermally Driven Liquid and Vapor Phase Transfer of Wgterand S^tergy in Soil


Date: 1962 Vol: 26 No: 5 Pages: 417-420

Authors: Cary, J. W.; Taylor, S. A.

1. A comparison of experimental results withpredictions from the general theory ofir;:eversible thermodynamic process was made.Thin agreement wars good.

2. A good test of general theory was made.

3. The assumptions are steady-state conditionsand constant moisture distribution. Theseassumptions limit application of equation tofield conditions which are very rarelysteady-state conditions.

4. Very strong assumptions of steady-stateconditions limit application of results and

" equations of this paper to the project.

43

M

No. 35

Title: Linear Equati.ona for the Simultaneous Flow of Matter andEnergy in a Continuous Soil System

t;

r'Pub: Soil Science Society of America Proceedings

Date: 1564 Vol: 28 No: 2 Press 167-171

Authors: Taylor, S. A.; Cary, J. W.

1. This paper derives general equations formass and energy transfer and applies them tothe soil s',, em. This work shows that olderequati^:.. ijr moisture flow are special casesof this general approach, namely Darcy's Lawand the diffusion equation, if we assumeisothermal conditions and no hysteresis. Theevation of Philip and de Vries is also aspacial case which assumes that water is theonly mass that can move.

2. A general equation is developed thatextends previous work to possible applicationwhere older theories give poor fit to experiment.

3. No experimental'-evidence is given toshow this approach works where older methodsdo not.

4. Could be explored if older and simplerequations break down.

5. Basic Theory Used.

I. Conservation of Mass

II. " .,.s;,,:Q.^ation of Energy

III. Law of Thermodynamics

IV. Result from the Theory of IffeversibleProcesses.

. 44

No. 36 rile No. 4762

Title: Crown-Depth Soil Temperature and Winter Protection

Pub: Submitted to Soil Science Society of America

sags: 1580 Sages: 1-23

Authors: Asse t J. K.; Siddoway, F. H.

Location: Sidney, Montana

1. In order to study the blanketing effectof snow cover, an experiment was performed.On various plots of soil, barriers wereerected of various heights, 8, 15, 23, and30 cm, in order to maintain snow at roughlythe same heights. Soil and air temperaturewere recorded at 15 minute intervals, againat various depths in the soil, namely 0, 3,10 cm, and at the 150 cm height for airtemperatures. The authors conclude that7 cm of snow appear sufficient to protectwinter wheat from occasional, air temperaturesof -40oC.

2. Certainly valuable information has beenfound in this study on what conditions are

u most favorable to survival of winter wheat.

3. What does "occasional air temperaturesapproac'tAing 400 C "' mean exactly, a largenumber ::f possible air temperature plot meetthat requirement, greater precision is neededon that point.

The statistical analysis in this paperhas a number of problems. First there is abasic set of assumptions for reasonableapplication of regression analysis. One inparticular is "reasonable" independence forcases. In, the data of this paper, it isunlikely this type of data calls for timeseries analysis and most frequently does notmeet the requirement of standard regressionanalysis. However, with suitable modifications,regression-like methods can be used, but thiswas not done in this paper.

Secondly, due to the objection above, thesignificance levels could be very misleading.

Lastly, a large amount of data was notused since daily minimums were the only dataanalyzed and 96 observations per day werecollected. Hourly observations may be enough.

3

45

46

maims

No. 36Page 2

A. First of all, the data collected is verymuch like the data that this project is tocollect. Consequently this data could beuseful in comparing with models of soiltemperature although soil moisture was notrecorded which also affects soil temperaturedistribution. But the data would be usefulin designing the data collection for thisproject and for checking the assumptions usedin this paper for the purpose of analyzingour own data.


Kulik, M. S.; Sinelshchikov, V. V., 1966M

Lectures onAgricultural Meteorology.Indian National Scientific DocumentationCentre, New Delhi, India. Availablefrom National Technical InformationService, United States Department ofCommerce, Springfield, VA 22151(Translated from Russian, 1978) 402 p,Chapter 10 was file number 4573.

Let Y = Min soil temp at 3 cm (oC)

at 115 cm (oC)

Bare soil

6-7 cm of snow

15-17 cm of snow

^at5cm

at 115 cm

Let X = Min air temp

Y = 2.39 + .826X

Y = -1.84 + .383X

Y = -1.17 + .27)X

Let Y = min soil tem,

Let X = min air temp

in absence of snow

Y = 1.54 + .773X

Bare soil

Y = 1.33 + .637X

19 cm Stubble

r Y = 1.54 + .627X

35 cm StubbleY

No. 37

Title: Heat Transfer in Soils

Pub: Heat and Mass Transfer in the Biosphere

Date: 1975 Pages: 5-28

Author: de Vries, D. A.

Presents a survey of models and state ofthe knowledge on heat transfer in soils.The author is very active in this area andhas contributed much to the subject.

2. An excellent summary on heat transfer insoils.

3

4. The model developed by Philip and de Vriesis the most advanced model on this subjectto date.


Lefur, B.; Balaille, J.; Aguirre-Picente, J.C. R. Acad. Sc. B. 259, 1483-1485, 1964(Ref. no. 10)

Jury, W. A. "Simultaneous transportof heat and moisture through a mediumsand." PHP Thesis Univ. of Wisconsin,1973 (Ref. no. 19)

Philip, J. R.; de Vries, D. A.Trans. Amer. Geophys. Union 38.222-232., 594. (1957) (Ref. no. 24)

de Vries, D. A.Trans. Amer. Geophys. Union 39.909-916, 1958 (Ref. no. 25)

Van der Kooi, "Moisture transport incellular concrete roofs." PHD ThesisEindhoven, Univ. of Technology;Waltman, Delft, 1971

Cary, J. W.Soil Science Society of America Proceedings30, 428-433, 1966.

ti 47

E

No. 38

Title: Simulation of the Thermal Behavior of Bare Soils forRemote Sensing Purposes

Pub: Heat and Mass Transfer in the Biosphere

Date: 1975 Pages: 109-123

Author: Rosema, A.

I. This paper gives the results of a simulationof soil temperature of bare ground. Theequations of Philip and de Vries were used forthe soil temperature and soil moisture partof the model. The paper concludes that nearthe surface the equation of soil moisturedoes not describe moisture movement well.

2. Presents a mathematical model for soiltemperatures that could serve as a startingpoint for this project.

3. Presents no experimental data.

4. The approach of this paper appears to bethe standard model for this problem and representsa likely starting point for modeling of thisproblem.

48

jr

No. 39

Title: Moisture Movement in Porous Materials Under TemperatureGradients

Pub: Tran. Amer. Geophy, Union

Date: 1957 Vol: 38 No: 2 Pa es: 222-232

Authors: Philip, J. R.; de Vries, D. A.

1. The authors discuss some of the shortcomingsof previous models and develop a more detailedmodel which is compared with existing data.However, most of the available data does notinclude all of the required variables for acomplete comparison with the theory.' Whatcould be checked agreed with observed databetter than previous work.

2. Improves the theory of heat and moistureflow in soils.

3. A complete and total comparison withexperimental data is needed to further supportthis model.

4. A mathematical model for heat and moistureflow is presented that appears to be the bestto date. This is a good starting point formodel heat flow in the soil.

49

No, 40

Title: Simultaneous Transfer of Heat and Moisture in Porous Media

Pub: Trans. Amer, Geophy. Union

Date: 1958 Vol: 39 No: 5 Pages: 909-916


t1. In this paVav the author extends the model E

given by Philip and de Vries by ,separatingtransport by water vapor and water liquid.Only steady-state experiments were used tocompare with theory.

2. This should be a better morel, since vaporand liquid transports are very different innature and also heat transport is considerablyaffected by evaporation and condensation inthe soil.

3. More extensive testing of the model isneeded.

4. The model of Philip and de Vries and modifiedby de Vries in this paper is the most frequentlyreferred to model of heat and moisture flow inthe soil.

50


Title: Lectures on Agricultural Meteorology

Pub: Indian National Scientific Documentation Centre, Hillside Road,New Delhi, for U. S. D. A. Soil Conservation Service and theNational Science Foundation, Washington, D. C. (translatedfrom Russian)

Date: 1966 Pages: 217-220

Authors: Kulik, M. S.; Sinelshchikov, V. V. (editors)

1. Gives an empirical relationship betweenminimum soil temperature at the 3 cm depth,minimum air temperature, depth of freezing,and depth of snow.

2.

3.

4. Gives empirical relationships that maybe useful for comparison.

5. 'Let y = Min soil temp at 3 cm depth ( o C)

t = Min air temp. (o C)

x = Depth of .soil freezing (cm)

.76t + 2.88 if no snow cover and x < 30 cm

.81t + .26 if no snow cover and x > 30 cm

y =.64t - . 07x + 5.2 if snow depth = 5 cm

.15t .06x + .43 if snow depth 10 cm

51

5'?


Title.: A Model to Predict Tillage Effects on Soil Temperature

Pub: Soil Sciattce Society of America Journal

Date: 1980 'Vol: 44 Imo: 2 Pages,: 378-383

Authors: Cruse, R. M. Linden, D. R., Radke, J K, Larson, W. E.;and K. Larntz

1. Presents a model of soil temperatures inI order to study the effects of tillage on

modifying soil temperatures. A number offactors are included in the model - solarradiation, wind speed, soil water content atS cm depth and stage of evaporation.

.1

2. The analysis of the data used to formthe simulation model is good using timeseries methods of Box and Jenkins.

3. Beat flow is assumed to be by condui.tiononly and the "simple" theory of heat flowis used.

4. Many empirical relationships useful forheat flow modeling are given in this paper,such as soil roughness effects oa solar radiation,absorption, water-content effect on reflectivityand surface residue effects. All of theseand more will be needed.

sm


Title: On the Influences of Fields of Motion, Baroclinji,city andLatent Heat Sources on Frontogenesis,


Dater 1966 Vol: S No: 4 Pages: 377-387

Author: Rao, G. V.

1, Discusses some effects of the release oflatent heat of evaporation on frontal weather.

2. .

3.

4. In the soil, consideration of the releaseof latent heat of evaporation and freezing willbe an important consideration but, since theair in the Boil, is different in nature thanfree air, little in this paper could be usedexcept the qualitative similarity of the twoproblems.

50 3


T, ice: Closed-System Freezing of Unsaturated Soil

P, ub: Soil Science Society of Americo Proceedings

Dater 1966 Vo.' 30 No; 2 Pages: 168-173

Authors: Dirksen, C.; Miller, R. D.

1. Presents laboratory experiments to studyfreezing and heaving in unsaturated soil.In general, as soil freezes water is drawnto the freezing zone and into the freezing zone,but 'thermal gradients alone appear to accountfor only 20% of the. total flow to the OoCregion. The rest appears to be due to ahydraulic gradient that is formed in thefreezing region.

The authors rejected the models of Caryand Taylor because the equations are largelyfor steady-state conditions and this processis not steady-state. In general, no model gavea satisfactory explanation For the observedprocess.

2. This shows that the model of moisture andheat transfer does not apply well to anunsaturated freezing soil - a likely conditionin the field.

3. No complete explanation is given for allof the results of the experiments.

4. Since the period of most interest to thisproject includes the period of freezing andafter, this paper suggests that the model ofCary and `Saylor as well as other models generallyused do not reasonably predict the eventsduring freezing.

54

I +

No, 45

Titles Water Potentials Unit 2

Pubs Applied Soil 'Physics

Dates 1980 pages: 20-61

Authors: Hanks, R. J.; Ashcroft, G. L.

1. This chapter presents an introduction tothe various potentials acting on water inthe soil, It also discusses how to measurethe various potentials.

2. This is easy to read'and presents a numberof examples.

3. Considers isothermal water flow and potentials.

4. This gives a background on the potentialsacting on soil, water, but since the projectinvolves temperature changes the discussion 1

in this chapter needs to be modified to includetemperature effects.

5. Notes on the various potentials.

Yz - Gravitational potential

Ywater = Ypressure + Ysolute + Ymatrix

Yhydraulic - Yz + Ym + Yp

Ytotal - Ywater + Yz

Ymatrix i4 related to moisture content butis not strictly a single-valued functionof moisture content, but depends also onthe history of moisture, ie) drying vs.wetting, two different curves. Alsostrongly depends on soil type.

Ypressure applies mainly to saturated soils..Zero at and above water level in the soil.

Yhydraulic Yz + Ym + Y.p

Soil Water Characteristic Curves relationship» of Ym to Ov (volume water, content).

a

55

No. 45Page 2

Ysolute is present mainly in a systemwith a semipermeable membrane. Air isa good membrane.

Ys w -RTCx

R w Gas content

T . absolute temperature

Cs - moles/cm3 of solute

P

{ q

it

56


Title:: Water and Salt Movement in Unsaturated Frozen Soil:Principles and Field Observations

Pub: Soil. Science Society of America Journal

Date; 1979 Vol: 43 No: 1 Pte: 3-8

Authors: Cagy, J. W.; Papendick, R. T.; Campbell, G. S.

k Soil Type Palouse silt loam. One site was bare, another coveredwith wheat stubble.

Location: Pullman, Washington

Solute was of a low concentration.

1. The paper presents a comparison of fielddata to an equation for liquid water flux infrozen soil. The equation is based on theassumption that hydraulic conductivity infrozen soil is similar to that in unfrozensoil. The factors required are soil, temperature,solute concentration, soil water releasecurve and saturated hydraulic conductivity.The authors report general agreement of theequation and field data.

The solute proved to be an important" factor in the movement of water to the freezing

zone. Heat flux is also an important factor,

2. The data, unlike most, are field data.The authors state that few, if any, fielddata are known that would be able to testthe equation.

3.

4. The period of most interest to this projectis when the ground is frozen and water movementdoes transport a sizable amount of heat, so ajoint model of moisture and heat flux isnecessary to accurately model soil temperature.

0

No. 47

Title: Chapter 3 Theoretical Analysis

Pub: Soil eater

Date: 1972 Peres: 21 -63

Authors: Edited by Nielsen, D. D., Jackson, R. D., Cary, J. W., andEvans, D. D.

1. This chapter presents a summary of thevarious mathematical models used to studysoil water flow and related problems, suchas heat transfer and dispersion of solutes.

2. This is an introduction to the Field,but not as basic as Hanks and Ashcroft.

3.

4. Useful as a partial list of the mathematical,models for heat and moisture.

53

No. 48

Title; Chapter 5 Effect of Temperature on Unsaturated SoilWater Transport

Pub; Soil Water

Date; 3,972 Pages: 96-120

Authors: Edited by Nielsen, D. D., Jackson, R. D., Cary, J. W., andEvans, D. D.

1. This chapter presents, with more detailsthan Chapter 3, the joint modeling of soilwater and soil temperature. It discusses thediffusion equation model, the model of Caryand Taylor and the model of Philip and de Vries.It makes comparisons of each with experimeaitaldata.

Generally the model of Cary and Taylorgives better fit, but is not as general asthe model of Philip and de Vries.

2.

3.

4. Useful as a summary of the most ,popularmoisture and heat models.

519

No. 49 File No. 348

Title: The Annual and Diurnal Heat-Exchange Cycles in Upper Layersof Soils


Date; 1963 Vol: 2 No; 3 Pages: 397-x, , ; G

Authors Carson, J. E.; Moses, H.

Location; Argonne, Illinois

Soil Type: Yellow clay of glacial origin.

Z_. This paper discusses the yearly and dailyvariation of temperature. The model usedfor most of the calculations assumes a homogenoussoil. The results agree qualitatively withconclusions of other investigators.

2. Some thermal property information is givenin the paper. Various graphs of soil temperatureversus depth are presented.

3. Generally the authors ignored the importanceof moisture and its effect on temperaturedistribution.

4. This paper could be useful to compare theresults of this project to the results in thispaper.

f

60

Q

n

No. 50

Title: Temperature and Soil-Water Diffusivity Relations


Date: 1963 Vol: 27 No: 4 Pages: 363-366

Authors: Jackson, R. D.

1. This paper discusses the relationshipof diffusivity and temperature to soil.-waterflow based on the capillary analogy. Theexperimental work presented shows reasonablepredictions based on the theory.

E

2. This gives a laboratory test of thetemperature effect on soil-water diffusivity.

3.

4. It gives a qualitative relation between thesoil-water diffusivity and temperature sincethe complete model of temperature requiressimultaneous consideration of moisture movementand diffusivity is very important in moisture

„ movement.

51

am

No. 51

Title: Water Movement and boas Under Frozen Soil Conditions


Date: 1964 .17ol: 28 No: 5 Pa es: 700-703

Authors: Ferguson, H.; Brown, P. L.; Dickey, D. D.

1. Presents data of soil temperature and soilmoisture at depths 3 inches, 12 inches, 24 inches,36 inches, 48 inches, 60 inches, and 72 inchesduring a period of time when the soil was frozen.The authors concluded that water movement inthe unfrozen part is sizable where the matr',xpotential is less than 2 atm, but if tensionis 5 atm or greater no flow to the freezingzone is observed.

2. Gives data on soil temperature and soilmoisture at various depths.

3. No comparison to a model.

4. Some small amount o g data is availablein the paper.

62

isNo. 52

a

Title: The Temperature Dependence of Soil Water Vapor Pressure


Date: 1964 Vol: 28 No: 5 Pages: 595-599

Authors: Kijne, J. W.; Taylor, S. A.

1. The relationship of soil water vaporpressure and temperature are explored usinga psychrometric method for .96 to 1.00relative vapor pressures and gravimetricand calorimetric heat of immersion below.96. The authors conclude that in theliquid state soil water is more randomthan free water and soil water vapor isless random than over free water.

2. It relates that a tensiometer measuresonly the matrix potential where as psychrometricmeasures include solute effects and soil matrixpotential.

3.

4. Useful as a background on the soil waterand its relationship with temperature. Nonew equations are developed.

63#.

No. 53

Title: Effect of Temperature and Trapped Air on Matric Suction

Pub: Soil Science

Bate_ 1965 Vol: 100 No: 4 Pages: 262-266

Author: Chahal, R. S.

1. The author proposes that the differencebetween observation and the classical theoryof surface-tension and temperature effectsis due to the entrapped air in the water.Indirect evidence is presented showingqualitative agreement with the authorshypothesis.

2. This represents a step toward a betterexplanation of the relationship of matrixpotential and temperature.

3. No direct experimental evidence is givenand no complete quantitative theory was developed.

4. During the freezing process water flowstoward the freezing zone and estimates of the

Uamount based on temperature alone underestimatethe amount of flow. Perhaps the "true effectof temperature" is on the matrix potential.This is not the only mechanism for temperatureeffects.

O;n

No. 54

Title: Effect of Temperature and Trapped Air on the Energy Statusof Water in Porous Media

Pub: Soil Science

Date: 1964 Viol,: 98 No: 2 Pages: 107-112

Author: Chahal, R. S.

1. This paper derives an equation that relatesthe energy status of the water and that considers

k the effect of entrapped air.

2. Extends the work of Wilkinson and Kluteto a more complete theory.

3. The distribution of bubble radios isimplicitly assumed to be uniform.

4. Useful as a detailed model that considersthe effect of temperature on matrix potentials.

55

No. 55

T_itl : Movement of Water in Soil Due to a Temperature Gradient

Pub: Soil Science

Date: 1952 Vol: 74 N, o: 5 Pages: 335-345

Authors: Gurr, C, G.; Marshall, T. J.; Hutton, J. T.

1. The authors performed an experiment todetail the movement of water in the liquidand vapor state. Chloride concentration wasused as a "tag" for liquid water and changesin chloride concentration were used to measureliquid flow. The general conclusion is thatliquid and vapor flow results from temperaturegradients--liquid from cold to hot and vaporflow from hot to cold.

2. They conducted an experiment to detailthe mechanism better than previous work.

3.

4. General background on the interactionof moisture and temperature.

Lil

^ h

oil

No. 56

Title: A Non-Stationary Method for Determining Thermal Conductivityof Soil in Situ

Pub: Soil Science

Date: 1952 Vol: 73 No: 2 Pa es: 83-89


1, This paper describes a method for measuringthermal conductivity and in place gives somedata collected by this method.

2. One of the .few methods usable in the .field.

3.

4. Useful as a background on measuring techniques,since thermal conductivity is a very importantproperty and must be known in order to usethe various theories since estimation based ontemperatures do not provide a test for the theory.

67

No. 57

Ti, tle: Soil-Water Movement in Response to Imposed Temperature Gradients


Date; 1969 Vol: 33 N`. 4 Pages: 493-500

Authors:hors,: Cassel, D, K.; Nielsen, D. R.; Biggar, J. W,

1. The authors conducted an experiment totest three different theories of soil.-watermovement, simple diffusion, the Philip-de 'Vriestheory, and the Cary-Taylor, equations. Theconclusion was that the Philip-:de Vries wasthe closest and that the assumptions in theCary-Taylor equation are too strong.

2. Some limited data is present in this paper.

3.

4. By providing a comparison of the threemain theories of soil-water movement, thispaper should help in selecting the mostuseful theory to use in this project.

5^

N

No. 58

Title: Salt and Water Movement in Unsaturated Frozen Soil


Date: 1972 Vol: 36 No: 4 Pages: 549.555

Authors: Cary, J. W.; Mayland, H. F.

1. This presents a qualitative theory for themovement of water and salt in frozen soiland compares theory with laboratory experimentaldata. The agreement is reasonable.

The movement of liquid water toward thefreesing zone transports salt but the returningvapor flow doesn't move salt, so salt becomesconcentrated near the freezing edge.

2.

3.

4. The apparent influence of salt concentrationseems very small and probably can be Ignored,

69

^i

No. 59

Tim: An Analysis of Sotnoi .ble and Latent Heat Flow in a PartiallyFrozen Unsaturated Soil

Pub: Soil. Science Society of America Proceedings

Date: 1978 V 1: 42 No: 3 Panes: 379-385

Authors: Fuchs, M,; Campbell, G, S,; Papendi.ck, R, 1.

1. This paper presents a quantitative systemof equations that consider solutes and latentheat into the heat equation. Some comparisonsare made with laboratory experiments withreasonable results. The use of the equation,like most other theories, involves a largenumber of very microclimate variables.

2. This paper presents a theory for heatflow in partially frozen soil. Prior to this,most theories applied to unfrozen soils only

3.

4. Most of this project concerns :Frozen soil,so models of the type presented hove shouldbe useful in this project.

70

No. 60

2 t̂le; On the lnteracti,on of Water and Heat Transport in Frozen andUnfrozen Soils; T. Basis Theory; The Vapor. Phase


Date: 1974 Vol: 38 2:. 3 beess,: 395-404

Autos Kay, B. D.; Groenvelt, P. H.

1. By using energy methods, the authorsdevelop transport equations for vapor phasetransport of water and heat. The equations

r are of the same form as Cary and 'Taylor'sequations, but use equilibrium equations indeveloping the theory.

2. By deriving the same basic equations fromdifferent points of view, we can believe thatmaybe the equation will work.

3. The; make a number of simplifying assumptionsmainly ignoring sloute and streaming potentials.

4. Serves as a supplement to the equation ofCary and Taylor, et al., but the form of theequations are all about the same.

71

a

72

No. 61

Title: On the Interaction of Water and Heat Transport in Frozenand Unfrozen Soils: The Liquid Phase

Pub: Soil Science Society of America proceedings

Date: 1974 Vol: 38 No: 3 Pages: 400-404

Authors: Groenvelt, P. H.; Kay, B. D.

1. This is an extension of a previous paperby the authors to include liquid phase trnnspoutof water. (See K. S. No. 60)

2.

3.

4. (See K. S. No. 60)

No. 62

Title: Thermal Properties of a Soil Based Upon Field and LaboratoryMeasurements


Date: 1969 Vol: , 33 No: 3 Pages: 354-360

Authors: Wierenga, P. J.; Neilsen, D. R.; Hagan, R. M.

1. They measured thermal conductivity inIm situ and soil temperature at various depths

in dry soil and under irrigated soil conditions.The usual method of measuring soil temperatureand computing thermal conductivity was comparedwith the direct measurement end they foundthat the direct method is far better. Also,the wetter the soil the more homogenous thethermal conductivity.

2. This paper presents a comparison of thedirect measurement of thermal conductivityand the usual calculation of the conductivityfrom temperature measurements.

3.

4. It shows that if thermal conductivitiesare needed the best way to find them is bydirect measuroien+t or secondly by many closelyspaced temperature probes.

73

OWN Whow lMI.11^Wi^o ^

fi

f

Y 7".

Zie

No. 63

Title: Transport of Water and heat in a Frozen Permeameter

Pub: Soil Se ence Society of America Proceedings

Date: 1975 Vol: 39 No: 6 Pages: 1029-1036

Authors: Miller, R. D.; Loch, J. G. G.; Bresler, E.

1. This extends the models of'tiay and Groenvelt,et al, to include so ild phase movement. Detailedequations are given in the paper.

2. ,

3. This movement of soil water is probablysmall and relatively unimportant,

4. The model presented is extremely complex.Simplification is needed if the movement ofice is to be included in the model.

7No. 64

i Title: A Parameterization of the Evaporation from Nonsaturated Surfaces


Date: 1979 Vol: 18 No: 1 Pa es; 43-47

Author: Barton, 1. J.

1. The author presents a modification of aformula developed by Priestley and Taylor

w for evaporation by including a term to representthe water availability,

y 2. A More complete model is developed forevaporation than the Priestley and Taylorequation.

3. A fairly limited test of the formula isdeveloped.

4. Evapor ition ^, t the foil-air interfacerequires heat and is an important effect toconsider in modeling the amount of heatabsorbed by the soil.

An

No. 65

Title: A Simple Procedure for Estimating Global Daily Radiationon Any Surface

Pubs: Journal of Applied Meteorology

Date: 1978 Vol: 17 No: 8 Pages: 1126-1131

Author: Revfein, K. J.

1. The author presents a method estimatingthe solar radiation on a sloped site fromdata on a flat site. The method uses a Fourierseries in the estimation.

2.

3.

4. To accurately estimate the temperaturedistribution in the soil we need informationon the solar radiation at the surface.

7^

No. 66

Title: Estimation of Manitoba Soil Temperatures from AtmosphericMeteorological Measurements

Pub: Canadian Journal of Soil Science

Date: 1960 Vol: 60 No 2 Pages: 299-309

Authors ,: Riemer, A.; Shaykewich, C. F.

1. They discuss the analysis of data obtainedfrom a five-year study that measured soiltemperatures at various depths along withvarious atmospheric measurements at hourlyintervals. The approach is a partial empiricaland partly simple diffusion theory. The aimwas to ,develop a prediction method based onatmospheric measurements only. The approachworked fairly well.

2. The amount of data is extraordinarily largefor this type of work. Most other studies are ibased on one or two years and more frequentlya matter of months.

k

3. The data analysis in this paper is Fairlysimple and possible could be improved can byuse of time series techniques. Also, theauthors did a good deal of smoothing priorto analysis which tends to inflate thegoodest-of-fit, R2.

4. This paper presents what appears to bethe first method for predicting subsoil temperaturebased on atmospheric measurements and it is basedon the largest amount of data.

5. More complete results are given in:

Reimer, A., 1978Soil temperature estimation.Thesis, University of Manitoba, 84 p.

T!

77

C.•

No. 67

Title: On the Prediction of Soil Temperatures from Meteorological

iData During the Winter Period

2&: Boundary-Layer Meteorology

Date: 1976 Vol: 10 No: 3 Pages: 331-336

Author: Palagin, E. G.

1. The author proposes a physical model thatconsiders the changing snow depth and themoving freezing front in the soil. The authorreports reasonable agreement with real data.

2. The model is simple enough to be usefulin applications and appears accurate enough.Since the snow layers can change depths inthis model it is an extension of a previousmodel.

3. This requires many nicroclimate variablesto be used, but not ae many as most physicalmodels.

4. The model presented needs more completetesting, but should not be overlooked forthis project.

5. The mathematical model presented is atemperature-only type of model that considersvarying parameters with time only and considersspatial differences very small.

78

No. 68

Title: A Mathematical Method for Estimating Soil Temperatures

Pub: Soil Science

Date: 1979 Vol,: 128 No: 4 Pages,: 226-242

Authors: Meikle, R. W.; Treadway, T. R.

1. The authors give a simple regression methodto predict soil temperature at various pointsin the United States using the day of the yearas the independent variable.

2. A very simple method to predict max and mintemperatures at a depth of 10 cm.

3. A periodic analysis of the data in termsof cosine and sine functions may have fittedbetter, but in any case would have been ona more physical basis since the process isa large peric.,dic function.

4 This would be useful in examining thevariates of lattitude and elevation on soiltemperatures, both max and minx.

i4A

719

No. 69

Title: The Prediction of Mean Monthly Soil Temperatures From MeanMonthly Air Temperature

Pub: Soil Science

Y

Date: 1978 Vol: 126 No: 3 Pages: 181-189

Authors: Toy, T. J.; Kuhaida, A. J.; Munson, J. R.; Munson, B. E.

1. The authors provide a simple regressionequation to predict soil temperature at2 inches based on air temperature. Regressionsare based on monthly averages for each variable.

2.

3. The method gives only monthly averagepredictions based on monthly average airtemperature. Many other important variablesare not included in this method.

4. The results of this paper are based ona limited number of locations (six), and arebased on the data in the Annual Summary,Climatological Data for the United Statesby Section for the years 1962-1971. Thissource should be referred to instead of thispaper.

No, 70

r

Title: Estimation of Wintertime Soil Temperatures

Pub: Journal of Economic Entomology

Date; 1970 Vol: 63 No,: 4 Pa es: 1051-1053

Authors:hors: Bonham, C. D.; Fye, R. E.

1. The authors provide a simple linear vegressionequation to predict the soil temperature atvarious depths based on air temperature. R 2 valuesravage from .96 to .77.

2.

3.

4. This is one of the earliest papers topredict soil temperature with air temperatures,empirically using simple linear regression.

r

0

i

lK

R7

No. 71

Title: Improved Models of Thermal Diffusion in the Soil

Pub: Transactions, American Geophysical Union

Date:, 1954 Vol: 35 No: 1 Pastes: 121 -132

Author: Lettau, H.

1. The paper discusses the problems in usingthe homogenous simple heat equation to estimatethermal diffusivity based on temperature dataonly and uses an improved method that allowsfor non-homogenous soil.

2. This improves on the typical method ofestimating thermal diffusivity to allow fornon-homogenous soil with depth and/or time.

3.

4. This method of estimating thermal diffusivityshould be used since it does not depend on ahomogemous soil profile.

32

No. 72

Title; I. Relationships of soils to .mountain and foothill rangehabitat types . .

II, Predicting soil temperature regimes of mountain andfoothill sites . . .

Pub: PHD Thesis, Montana State University

Date: 1977 Pages: 1-126

Author: Munn, L. C.

1. In the second part of this thesis, thoauthor develops a predictive equation foraverage yearly soil temperature based onmLtltiple regression using as independentvariables, site latitude, aspect, slope,elevation and thickness of an 0 horizon, ifpresent. The R for various regressions rangesfrom .69 to ,97.

2.

3

4. The independent variables used in thiswork most certainly will be used in anycomplete ,physical model to predict soiltemperature.

It

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