Preliminary Assessment of Soil Moisture Over Vegetation

Final Report

to

NASA

Goddard Space Flight Center

Greenbelt MD

Grant # NAG 5184

March 1, 1985 - February 28, 1986

by

Toby N. Carlson

Department of Meteorology

The Pennsylvania State University

University Park, PA 16802

(NASA-CB-177226) PBEIIMINAEY ASSESSMENT OF N86-27704

SOIL MOISTURE OVEB VEGE1ATIGN Final Report,

1 Mar. 1985 - 28 Feb. 1986 {Eennsylvania

State Univ.) UO p HC A03/MF A01 CSCL 08M Unclas

G3/43 U3322

July 1986
1. Introduction

The previous year saw a change in emphasis from purely modeling to

combining modeling of surface energy fluxes with in situ measurement of

surface parameters, specifically the surface sensible heat flux and the

substrate soil moisture. In France we were able to incorporate a vegetation

component into our atmospheric/substrate model and subsequently to show that

the fluxes over vegetation can be very much different than those over bare

soil for a given surface-air temperature difference. Results of this work are

summarized in an article by Taconet et al. (1986b).

Because of my interaction with members of the CRPE/CNET group in France

we feel that a high priority must be given to interpreting the temperature

signatures measured by a satellite or airbourne radiometer in conjunction with

surface measurements of modelled parameters, e.g., surface sensible or latent

heat fluxes and soil moisture. Paradoxically, our analyses of the large-scale

distribution of soil moisture availability show that there is a very high

correlation between antecedent precipitation and inferred surface moisture

availability, even when no specific vegetation parameterization is used in the

boundary layer model (Carlson, 1985; Flores and Carlson, 1985; Flores and

Carlson, 1987). A similar result was obtained by Wetzel and Woodward (1986).

Accordingly, we have continued to maintain an effort in modeling the

surface canopy but with a greater emphasis on verification. One weak link in

the theory pertains to the transfer of radiant and heat fluxes in vegetation

canopies. The amounts of radiant energy incident on the vegetation and on the

soil beneath depend on the density of vegetation, normally parameterized using

the leaf area index or similar quantity. We have also begun to test simple

models based on the full boundary layer model but which require a minimum of

observations. We have begun to look closely at observations, including
I

3. Conclusion

Our major scientific findings are summarized in three publications

attached to this report: the long-awaited review article in Remote Sensing

Reviews, a discussion of preliminary results by E. Perry of our infrared/

microwave measurement comparisons from the Beauce experiment and a summary of

the results of modelling experiments done in France by the PI in conjunction

with the CRPE/CNET boundary layer model. The latter paper is merely an

extended abstract of a fourth publication, which is soon to appear in the

Journal of Climate and Applied Meteorology (Taconet et al., 1986b), concerning

the modelling done in France. Much of the time spent during the last year

involved preparatory work in streamlining the present boundary layer model,

developing better algorithms for relating surface temperatures to substrate

moisture, preparing for participation in the French HAPEX experiment, and

analyzing aircraft microwave and radiometric surface temperature data for the

1983 French Beauce experiments.
References

Carlson, T.N., 1986: Regional-scale estimates availability and thermal

inertia using remote thermal measurements. Remote Sensing Reviews, ^_,

197-247.

Choudbury, B.J. and S. Idso, 1984: Simulating sunflower canopy temperatures

to infer root-zonal soal water potential. Agric. Forest Meteor., 31,

69-78.

Deardorff, J.W., 1978: Efficient prediction of ground surface temperature and

moisture, with inclusion of a layer of vegetation. J. Geophys. Res., 83,

1889-1904.

Dwyer, L.M. and D.W. Stewart, 1984: Indicators of water stress in corn.

Can. J. Plant Sci.. j>4_, 537-546.

Flores, A.L. and T.N. Carlson, 1985: Acercade la estimacion de la

disponibilidad de humedad en el suela a partir de mediciones remotas.

GEOACTA, 13 (Argentina).

Flores, A.L. and T.N. Carlson, 1987: On the estimation of antecedent

precipitation from remote surface temperature measurements. Submitted

to J. Geophys. Research.

Hicks, B.B., D.D. Baldocche, R.P. Hosker, Jr., B.A. Hutchison, D.R. Matt,

R.T. McMillen, L.C. Satterfield, 1985: On the use of monitored air

concentrations to infer dry deposition. NOAA Tech. Memo SRL ARL-141,

Silver Spring, MD, 65 pp.

Holben, B.N., C.J. Tucker and C.-J. Fan, 1980: Spectral assessment of soybean

leaf area and leaf biomass. Photogrammetric Engineering and Remote

Sensing, 46, 651-656.

Jackson, R.D., R.J. Reginato and S.B. Idso, 1977. Weat canopy temperature:

a practical tool for evaluating water requirements. Water Res.

Management, 13, 651-656. .

Rambal, S., 1984: Water valance and pattern of root water uptake by a Quercus

conifera L. evergreen scrub. Oecoligia, 62, 18-25.

Ritchie, J.T., 1981: Water dynamics in the soil-plant atmosphere system.

Plant and Soil, _58, 81-96.

Seguin, B. and Itier, 1983: Using midday surface temperature to estimate

daily evaporation from satellite thermal IR data. Int. J. Remote

Sensing, 4_, 371-383.

Taconet, 0., R. Bernard and D. Vidal-Madjar, 1986a: Evapotranspiration over

an agricultural region using a surface flux/temperature model based on

NOAA-AVHRR data. J. Glim. Meteor., 25, 284-307.
Taconet, 0., T.N. Carlson, R.Vemard, D. Vidal-Madjar, 1986b: Evaluation of a

surface/vegetation model using satellite infrared surface temperatures.

J. dim. Appl. Meteor., 25 (in press).

Wetzel, P.J. and R.H. Woodward, 1987: Soil moisture estimates using

GOES-VISSR infrared data: A case study with a simple statistical method,

submitted, to J. Glim, and Appl. Meteor.
S.9

SOIL MOISTURE ESTIMATES FROM SATELLITE INFRARED TEMPERATURES

AND THEIR RELATION TO SURFACE MEASUREMENTS

Toby N. Carlson

The Pennsylvania StaCe University

University Park, PA 16802

1. INTRODUCTION

Spatial and temporal variations in soil moisture are reflected by variations in the surface

temperature. Exact measurements of the soil moisture using remote measurements of thermal infrared

temperatures of the surface are possible, in theory, but very difficult to make in practice because of

the enormous complexity of the ground surface, especially in the presence of vegetation. Our approach

is to Invert a time-dependent, initial-valued, one-dimensional boundary layer model in conjunction with

measured surface temperatures to obtain the surface energy balance, a soil moisture parameter, called

the moisture availability, and the thermal inertia. For the theory behind the model, the reader is

referred to papers by Carlson and Boland (1978) and Carlson et al. (1981; henceforth referred to as

CM). Similar models have been used to obtain soil moisture values from satellite infrared measurements

by Wetzel et al. (1984) and Price (1982) in the United States and by Taconet et al. (1986a,b; henceforth referred to as OT) and Abdellaoui et al. (1985) in France and by Nieuwenhuls et al. (1985) in

Holland. Recently, modelers have begun to treat vegetated surfaces by including parameters that govern

the fluxes between the soil/plant/atmosphere system. The vegetation component in both the CM and OT

are nearly Identical, being based on an earlier version by Deardorff (1978), but simplified and

streamlined by Bernard et al. (1986) using data for sorghum.

The purpose of this paper Is to report some of the recent results showing agreement between

moisture values calculated with the model using satellite infrared temperatures as input and groundbased measurements of related parameters.

2. RESULTS

2.1 Soil Moisture Versus Antecedent Precipitation as Measured by COBS

Twenty days of satellite Images were analyzed for a period during the summers of 1978 and 1980

over Kansas. The region and dates were chosen because of the extreme drought conditions that were

affecting a wide region of the midwest extending from Kansas to Texas.. We reasoned that if the Infrared method was viable it should prove so under conditions of great horizontal variation in soil moisture and rainfall. Accordingly, the parameter called moisture availability (M) was determined over a

region a few hundred kilometers on a side using GOES daytime and nighttime infrared temperature

.measurements (Carlson et al., 1984). The vegetation model was not used for this study.

Moisture availability is defined as the ratio of evaporation to potential evaporation and Is

also equal in the model to the ratio of soil water content (9) over a layer near the surface to the

value of soil water at field saturation (8fs). Thus, M varies from 0 (for perfectly dry surfaces) to

1.0 for saturated surfaces. In the example shown in Fig. 1, the vegetation model was not used to

derive the results. Consequently, the prairie surface is treated as bare soil. Contours of M in Fig.

1 closely reflect the surface temperature over the region of Kansas on the afternoon of the 14th of

July, 1980. There is an overall similarity on all the days between the M field and antecedent precipitation, which is effectively a running mean of the rainfall. Low values of M (0.12-0.25) in the

south correspond roughly to low rainfall and high values in the north to higher rainfall totals. The

correlation between the log of M and the antecedent precipitation is about 0.7 for all cases. A

similar relation was found by Flores and Carlson (1985) for scenes over Texas on three days during the

same month of July, 1980.

2.2. AVHRR Images and Surface Measurements Made Over France

During a field measurement program conducted over the Beauce .region of France (near the town of

Voves) by scientists at two French national laboratories (INRA, CRPE), there occurred a remarkable

Increase in the surface sensible heat flux during a period of drying. Although the drying trend had

been continuing a couple of weeks, the Increase (measured by both the SAMER method of Itier (1981) and

by sodar) began Just after the 6th of July and was most abrupt between the llth and 14th (Fig. 2).

313
Heat flux values derived from the CM and OT models (using the same set of Initial conditions) using

afternoon temperatures (approximately 1400 sun time) from NOAA AVHRR as input also show a similar

trend, although the version of CM with bare soil was less able to capture the Increase in sensible heat

flux with time.

Fig. 1. Moisture availability (M) analysis over a portion of eastern Kansas and

Nebraska for 14 July 1980 based on surface

temperature measurements for a pair of GOES

images (left). Dark, irregular shapes are

bodies of water, Including the Missouri

River near upper right. Scalloping denotes

regions obscured by cloud. Antecedent

precipitation for 14 July 1980 is shown on

the right. Dots Indicate location of rainfall measurement stations.

ORIGINAL PAGE'IS

POOR QUALITY

\

BVOIUTIOM or MAXIMUM 3UKFACI FLUXES »T VOVtS. JULT 19«3

10 II 13

-3

14 ,3

Fig. 2. Evolution of maximum net radiation (top curve dashed) and maximum surface sensible heat flux

(bottom curve; in wm~2) for Voves during during a period in July 1983. The last rainfall before the

end of the record occurred on the 6th of July. Symbols refer to maximum heat flux values determined

froa the models using AVHRR data as surface temperature Input: the CM for bare soil (X), the CM for

vegetation (•) and OT for vegetation (A).

Soil water content (8) measured with a neturon probe near the Voves site continued only up

until the 12th of July. Averages of 0 over four depths (Fig. 3) show a decreas at all levels down to

about 40 cm below the ground; the most rapid drying, of course, occurred in the top 30 cm, where levels

of water content were approaching the wilting point of the soil (approximately 0.15 cm3/cm3; field

saturation was about 0.35 cm3/cm3).

Model results also show a corresponding decline with time In soil water content, although more

preclpltiously than the measurements made earlier in the period suggest. Curiously, although the model
water concents pertain to the vegetation parameterization, Che bare soil valued for CM were virtually

Identical to Chose shown In Fig. 3. These values correspond Co very low moisture availability

(approximately 0.2 on Che 15th), which are comparable Co chose in Che dryer pares of the Kansas Image

of Fig. 1. The puzzling face here is that the surface measurements seem unassailable and are supported

by the model results. At the same time it is to be noted that Che wheat crop over which chese

measurements were made did not appear to be highly water stressed.

e

020H

awan-

.asORIGINAL PAGE IS

Of POOR QUALITY

— a* • «. is

t §ov»r top-15 cm

X " 30 uw

0 » I. C cm

, u so t«

• a, «.«oi<»vj «• OT

«i

. C«

Fig. 3. Measured (solid lines) soil water concent (cm3/cm3) versus time for averages over four

vertical soil depths as given In the key. Soil water content (6) determined from the model using the

1346 GMT AVURR surface temperature measurement is shown by the dashed and dot-dashed lines,

respectively, for the OT and CM. The vertical arrow denotes the last rainfall during the period.

3. CONCLUSION

Infrared temperatures measured with Che aid of satellite can reflect large spatial and temporal

changes in soil moisture but not enough Is known and the parameterization sufficiently undeveloped to

arrive at a completely consistent measure of the real soil water content or the soil depth over which

it applies.

4. REFERENCES

Abdellaoui, A., F. Becker and E. Orlory-Hechinger, 1985: Use of metwosat for mapping thermal Inertia

and evapocranspiraclon over a limited region of Mall. Submitted to J. Clim. and Appl. Meteor.

Bernard, R., J.L. Hatfleld and M. Vauclin, 1986: Test of an evapotranspiration model for diurnal and

seasonal behavior of sorghum fields under various water availability conditions. Submitted to

Boundary Layer Meteo.

Carlson, T.N., J.K. Dodd, S.G. Benjamin, J.N. Cooper, 1981: Remote estimation of surface- energy

balance, moisture availability and thermal Inertia. J. Appl. Meteor.. 20, 67-87.

Carlson, T.N., F.C. Rose, E.M. Perry, 1984: Regional-scale estimates of surface moisture availability

from GOES satellite. J. Agronomy. 76, 972-979.

Carlson, T.N. and F.G. Boland, 1978: Analysis of urban-rural canopy using a surface heat flux/

temperature model. J. Appl. Meteor.. 17. 998-1013.

Deardorff, J.W., 1978: Efficient prediction of ground surface temperature and moisture with inclusion

of a layer of vegetation. J. Geophys. Res.. 83. 1889-1904.

315
Flores, A.L. and T.N. Carlson, 1985: Esclmaclon de parametlos del suelo domblnado 1magenes dlglcales

de GOES en un taodelo de copa limite. Meteorologlca (Argentina) (In press).

Icier, B., 1981: Une methode simple pour la measure de 1'evapotransplration reelle a 1'echelle de la

parcelle. Agronomic, 10, 869-876.

Nieuwenhuls, G.J.A., E.H. Snldt and H.A.M. Thunmlssen, 1985: Estimation of regional evapotransplration

of arable crops from thermal infrared Images. J. Remote Sensing. £, 1319-1334.

Price,-J.C., 1982: Estimation of regional scale evapotransplration through analysis of satellite

thermal-Infrared data. IEEE Transactions on Ceosclence and Remote Sensing, GE-20, 286-292.

Taconet, 0., R. Bernard and D. Vldal-Madjar, 1985: Evapotransplration over an agricultural region

using a surface flux/temperature model based on NOAA-AVHRR data. J. dim. Appl. Meteor, (in

press).

Taconet, 0., T.N. Carlson, R. Bernard, D. Vldal-Madjar, 1986: Evaluation of a surface/vegetation model

using satellite Infrared surface temperatures. Submitted to J. Clim. Appl. Meteor.

Wetzel, P.J., P. Atlas and R. Woodward, 1984: Determining soil moisture from geosynchronous

satellite infrared data: A feasibility study. J. Appl. Meteor.. 23, 375-391.

316
ORIGINAL PAGE IS

10 OF POOR QUALITY

CORRELATIONS BETWEEN REMOTELY MEASURED SOIL WATER CONTENT AND

SURFACE TEMPERATURES FOR THE BEAUCE REGION, FRANCE

Eileen M. Perry

The Pennsylvania'State University

University Park, PA 16802

1. INTRODUCTION

Soil water content has been shown to be highly correlated with radlometrlc surface temperatures, and a number of studies have demonstrated that the surface temperature increases as the

substrate soil water content decreases. (See Hatfield et al. (1983) and Carlson (1984) for a summary

of articles on this research.) As part of a study to model the available water in the unsaturated zone

using thermal Infrared data, this paper is a first look at some aircraft measurements that show a

correlation between microwave measured soil water content and radiometrlc surface temperatures.

During an experiment held in the summer of 1983 near Voves, France, active microwave and

thermal infrared measuraments were made during the early afternoon aboard a French aircraft flying a

grid pattern over a flat, agricultural region south of Paris called the Beauce. The vegetation consisted mainly of wheat and corn, with some stands of trees. The Infrared sensor was a Barnes PRT-5

radiometer which has a measurement accuracy to within .5 degrees Celsius. The active microwave

measurements were taken with the ERASME scatterometer (5.35 CBz (FM-CW) with an incidence angle of

eleven degrees for minimizing the effects of roughness and therefore maximizing the accuracy of soil

water, measurement. Calibration missions of the microwave measurements were performed with reference to

in-situ measurements of soil water content; the correlation coefficient was .89 between the microwave

back scatter coefficients and the ground measurements of the soil water content In the first ten

centimeters. Accordingly, soil water content was converted directly from backscattering cross section

to soil water content. The scatterometer and radiometer were nounted so that the two instraments were

taking measurements of the same ground area simultaneously, five measurements per second, with each

having a surface sampling area of approximately 40 meters squared. The average flight altitude was

about 400 meters.

Data was collected during July and September of 1983; the dates in July were 8 and 12 July

during a period of drying following a 6 July rainfall episode; the September dates were the 20, 23, 26,

28-and 29 September following a 19 September rainfall episode. Data segments along two of the aircraft

legs were selected to discuss because they represent alternately the poorest and best correlation of

surface temperatures with microwave-derived soil water content measurements, respectively on 8 July

(1:45 LT) and 26 September (3:45 LT).

To examine the data through time and perform some descriptive statistics, a statistics/graphics

package (SAS) was used to plot the microwave and thermal IR data, and to perform correlations between

them. Figure 1 shows a plot of the temperature resonse as the sensor was flown over a west to east

transect near the town of Voves on 8 July. Figure 2 shows a plot of the soil moisture values measured

along the same transect. In order to gain a simple visual comparison between the temperature and

microwave measurements, the two lines are overlain on the same plot, using a cubic spline to fit the

points (see figure 3). Note the inverse relation between the microwave backscatter and the surface

temperature at the points where the sensor was flown over road surfaces (A, B, D, L, M, N on figure 3)

which are very dry and have a high surface temperature. Figure 4 is a transect flown on 26 September,

over approximately the same area as In figure 3. Note that for the same roads (points B, D, L, M), the

data again show that a low soil water content correlates with a high surface temperature. However, for

the 26 September case, this Inverse relation is demonstrated over the entire transect. For both of the

cases, the subset area labelled on figures 3 and 4 were plotted to show the variations of the microwave

and thermal Infrared response on a field basis (see figures 5 and 6).

2. RESULTS AND DISCUSSION

The first and most important observation Is the poor correlation between the microwave

backscatter coefficients and the thermal Infrared measured temperatures for the 8 July case (shown In

figure 3). The correlation coefficient for the entire data segment is .3459. The correlation between

these same data types is -.7795 for the 26 September case, which is what would be expected given

previous research. Possible explanations (not yet confirmed) for this lack of correlation of the

vegetated 8 July case are:

317
ORIGINAL PME- IS

OF POOR QUAUTV

i) For the July case, the plants may be In effect "Integrating" the available water because

they are using the water at depth (in the root zone). If the surface temperature was being Influenced

by the amount of water available at a depth of perhaps 45 cm or more, and the variability of this soil

water content is not as great as that at 0-10 cm (being measured by the microwave), there would be a

difference in the variability of the surface temperature and the microwave measurements. This

difference in variability could decrease the correlation between the remotely measured temperature and

soil moisture for any given point.

11) There could be a difference In the "measurement depths" between the July and September

cases. For the July case, the thermal Infrared sensor is measuring temperatures that are largely

Influenced by the water available to the plants in the root zone (much deeper than 10 cm), while the

microwave backscatter coefficients are most highly correlated with the top ten centimeters. For the

September case, with nearly bare soil conditions, the thermal Infrared temperatures are more Influenced

by the soil water content near the surface, and the microwave backscatter coefficients are again most

correlated with the soil water content in the first ten centimeters.

ill) If the stomates were closed for some reason other than lack of available water, the plant

temperatures measured by the thermal Infrared sensor could be much higher that what would be expected

for a given soil water content.

Another observation is the possible lack of a significant correlation between remotely measured

soil water content and surface temperatures within an individual field. For one corn field (field 10)

there is a correlation coeffient of -.326 for 3 July and -.484 for 26 September. For the forest stand

(field 7), the correlations are +.403 for 8 July and -.18 for 26 September (see Table I).

Finally, it can be seen from figures 5 and 6 that there is a greater variation of microwave

backscatter coefficients than surface temperature . This would tend to support the. idea that the

variability of soil moisture is greater in the surface layers of the soil.

Table 1.

DATE

8 July

CORRELATION COEFFICIENTS BETWEEN TEMPERATURE AND SOIL MOISTURE

26 Sept.

FIELD COVER

all data (mixed cover)

segment 3 (mixed)

segment 3

subset (mixed cover)

field 10 (corn)

field 7 (woods)

all data (mixed cover)

segment 3 (mixed)

segment 3 subset

(mixed cover)

field 10 (stubble)

field 7 (woods)

SURFACE TEMPERATURE

29.7

30.1

31.3

31.4

+/- 1.98

+/- 1.98

30.4 +/- 1.15

29.1 •+/- .308

29.2 +/- 1.07

+/- 2.79

+/- 3.02

30.8 +/- 2.92

26.8 +/- .537

32.4 +/- .538

MICROWAVE

-2.10

-1.87

+/- 2.26

+/- 1.77

-.660 +/- 1.52

-.051 +/- .984

-2.80 +/- 1.23"

-3.98 */- 2.82

-3.15 +/- 2.82

-2.94 +/- 2.69

.258 +/- .755

-4.61 +/- .642

9165

1004

218

68

29

7556

926

232

73

24

CORREL.

-.004

.346

-.170

-.326

.403

-.712

-.780

-.722

-.484

-.181

Temperature (degrees celsiua)

VOVES 8 JULY 1883 DATA SBCMENT 3

. : •

> - ..-/• , •• * ••• » •*- ' ? *i **• : ; **

•\:*t . •/• *.^v>; -^>*L- " «• >-r •-<#$

' • \ v ».v.

field 10 field ^

subset 1 km

./.

Time (seconds)

Figure 1. West to east tranvorsa showing the thermal Infrared response.

Time of day approximately 1:45 LT Note locations of fields 10 and

7, and the* location of th» mub**t to b« axaainvd latar.

318
Temperature (degrees Celsius) - - - - -

Soil water content (cm»»3/cm»»3 x 10»»2)

ORIGINAL

OF POOR QUALITY

0 A " B

VOVES 8 JULY 1983 SEGMENT 3

Tine (seconds)

Figure 3. Combined plot for soil water content and temperature.

inverse relation of the responses for roads (points A,B,

Note the

D, L,M,N) .

Soil water content (cm*»3/cm«*3)

'

VOVES JULY S 1983 DiTA S2CUKNT 3

.

-. ;» • ,*. --. . /;•

 %?

. v

,' ' \ <!:. ••' "'.•*'

•- ••

field 7

Time (seconds)

Figure 2^ Soil^water^content measured with active microwave,

same transverse

319
Temperature (degrees Celsius) ------ -

Soil water content (cm*»3/cm*»3 x 10»»2)

I VOVES 26 SEPTEMBER 1983 SEGMENT 3

ORIGINAL PAGE IB

OF POOR QUALITY

B

u • iv iig in IB

Time in seconds

Figure 4. Combined remoteI/ measured soil water content and surface

temperature for approximately the same transect as in figure 3, '

data taken on 28 September at approximately 3:45. Note the inverse

relation of the microwave and temperature responses. The road

locations are the sane as in figure 3.

Temperature (degrees Celsius) - - - -

Soil water content (cm**3/cm*»3)

VOVES 8 JULY 1983 SEGMENT 3 SUBSET

1 ! 1 1 ! J 1 ', i ; I J I I J I 5 ? 5 5 I ! M I ! 1 ? M J 5 1 3 51 M 1 J I

Time (seconds)

Figure 5. Combined temperature and soil water content responses for the

subset of data segment 3. Mote that the variation for soil water

content within a field is much greater than the variation of

temperature.

320
Temperature (degress Celsius) .....

Soil water content (cm*»3/cm*»3) -

OUALiT •c«"^un yv

VOVES 28 SEPTEMBER 1983 SEGMENT 3 SUBSET

mm, TOD comviT in IIMIJIII u •• iaa

H m M M m i; i m < 2 M ii i i ? m ;;;::: M :>

Time in seconds

Figure 6. Combined temperature and soil water content for the subset of

data segment 3, for the 26 September case. Note again the greater

variability of the soil water content measured by the microwave.

3. CONCLUSION

The data analyzed so far has Indicated a strong negative correlation between remotely sensed

soil water content and surface temperatures for the near bare soil conditions of 26 September, while

for the same area on 8 July there is little correlation between the remotely sensed soil water content

and surface temperature.

4. REFERENCES

Barnes Engineering Company (no date): Bulletin 14-3150, product description of the Model PRT-5

radiation thermometer.

Bernard, R. and D. Vldal-Hadjar, 1983: ERASME: Dlffuslometre heliportable en bande C. Application a

la mesure de 1'humldlte des sols. Proceedings of EARSeL/ESA Symposium on remote sensing

applications for environmental studies, ESA SP-188, July 1983, pp. 59-64.

Carlson, T.N., 1984: Regional scale estimates of soil moisture availability and thermal Inertia using

remote thermal measurements, In Interpretation of thermal Infrared data. J. Price (ed.), Harwood

Academic Press, Remote Sensing Rev., pp. 197-247.

Hatfield, J.L., A. Perrler and R.D. Jackson, 1983: Estimation of evapotransplratlon at one time of day

using remotely sensed surface temperatures. Agricultural Water Management. _7, 341-350.

321
Rfiniae Sensinn Reviews. 1986. Vol. I. pp. 197-247

0275-7257 86 OI02-OI97S12.1X) 0

i' I9H6 hurwood academic publishers GmbH

Primed in Creal Britain

/ Regional-Scale Estimates of Surface

Moisture Availability and Thermal

Inertia Using Remote Thermal

Measurements

TOBY N. CARLSON

The Pennsylvania State University, Department of Meteorology. University Park.

Pennsylvania 16802

1 INTRODUCTION

Thermal infrared measurements (10-12 um) made by satellites reveal

temperature patterns which are closely related to surface properties,

especially soil moisture and thermal inertia. In this paper, a variety of

models are reviewed which have been developed to interpret thermal IR

measurements and to determine these governing parameters. These

models fall into four general classes: analytic, predictive, diagnostic and

empirical, of which, the diagnostic models of Price (1982a, 1982b) and

the predictive models of Carlson (Carlson et al., 1981), and Wetzel and

Atlas (1981, 1983) already have been used to obtain regional-scale soil

moisture or evaporation patterns from satellite infrared measurements.

The purpose of this paper is to (1) present a brief summary of the

various theoretical approaches (i.e. models) which have been developed

specifically for determining the surface energy fluxes and governing

surface parameters using remote thermal IR measurements. (2) present

J some recent results from one of these methods, that of Carlson et al.

(1981; henceforth referred to as CM), (3) discuss limitations and uses in

applying such methods by listing the various sources of errors and

constraints inherent in theory and measurement and (4) conclude with

an assessment of present capabilities of the thermal infrared method

and its future potential.

197
198 T. N. CARLSON

2 FACTORS INFLUENCING SURFACE TEMPERATURE

The basis for determining surface parameters remotely is a variety of

observations which show, for example, that evaporating surfaces are

cooler than dry surfaces, and that as the soil moisture content

decreases, the amplitude of the surface temperature wave becomes

larger (Jackson, 1982). At an idealized surface, the surface temperature

response is governed by a variety of surface, substrate, and atmospheric

variables, most notably the ground moisture and thermal inertia (which

will be shortly defined) and albedo (Carlson and Boland, 1978). The

greatest temperature variation occurs at the ground-air interface but

with increasing distance from the surface, in the ground or in the

atmosphere, the diurnal temperature wave decreases. Well above the

surface advection plays such an important role that the air temperature

variation becomes responsive to surface heating over a relatively large

area and may no longer reflect the local character of the substrate.

Over bare soils the temperature is known to vary rather sensitively

with both the thermal inertia! and volumetric moisture content (Myers

and Heilman, 1969; Idso et al., 1975d; Idso et at., 1976; Idso eta/.,

1977c). This sensitivity is reflected in both the ground surface and

screen-level (1.3m) air temperatures (Idso et al., 1976), especially the

day-night differences.

Over plant canopies the temperature of the leaf is known to rise in

response to a reduction of available water in the root zone (Byrne et al.,

1979; Jackson, 1982). Severe reduction in available water to the plant

canopy can lead to what is called "plant water stress", which has been

shown by various workers (Cihlar, 1976; Idso et a/., 1977a; Ehrler et al.,

1978) to be related to crop yield. The extent of plant stress is highly

correlated with moisture in the root layer of the soil, especially the top

few centimeters. Radiometric measurements show that the leaf temperature can vary from one crop to another under identical meteorological

conditions (Blad and Rosenberg, 1976; Heilman eta!., 1976) and that

such temperature variations partially reflect differences in evapotranspiration between the canopies (Wiegand et al., 1968; Wiegand,

1971; Schmugge, 1978; Heilman and Moore, 1980).

The observation that leaf temperature becomes elevated when

evaporation diminishes has led to the development of methods for

remotely determining soil moisture from radiometric surface temperature measurements. Empirical results by Idso et al. (I975a, 1976, 1977a)

MODELING SURFACE ENERGY BALANCE 199

relating radiant energy available from the sun to soil moisture clearly

demonstrate that algorithms can be formulated for the purpose of

calculating plant moisture availability from canopy temperatures. The

development of a reliable method for interpreting satellite blackbody

temperature measurements within the framework of a soil-atmosphere

model was accelerated by the advent of meteorological

satellites such as TIROS-N (currently NOAA-7), the Heat Capacity

Mapping Mission (HCMM) satellite, and GOES, all of which are

capable of making surface temperature measurements close to the

optimum times.

The value of being able to determine surface evaporation patterns is

obvious in agriculture and hydrology. Techniques for combining a

numerical or analytical surface layer or boundary layer model with

satellite IR measurements for the purpose of determining the governing

surface parameters and surface energy fluxes originated with geologists,

who were interested in mapping the thermal inertia of mineral butcroppings and other geological structures (Watson, 1971: Pohn et al.,

1974; Watson, 1975; Kahle, 1977; Price, 1977; Watson and Miller, 1981).

Price (1977) and Kahle (1975) both refer to the techniques as thermal

inertia mapping, following an idea previously suggested by Pohn et al.

(1974) and Blanchard et al. (1974). Indeed, the latter article plainly

addresses the idea of soil moisture measurement by satellite.

Recent efforts to use thermal inertia mapping to determine moisture

availability and the surface energy fluxes from satellite IR measurements have been made by Carlson et al. (1981, 1984), Wetzel and Atlas

(1981, 1983) and by Price (1982a, I982b) in the United States and by

Rosema eta/. (1978) and Soer (1980; see also Dejace et al., 1979;

Reiniger and Seguin, 1985—this issue RSR) in Europe. Although

Carlson et al. (1981) restricted their investigation to an analysis of the

urban heat island, they showed that thermal inertia mapping affords the

opportunity to determine the surface moisture availability over regionscale areas including both urban and vegetated types of surfaces. The

fact that moisture availability may be the single most important

parameter governing the partition between sensible and latent heat flux

at the surface (Carlson and Boland, 1978; McCumberand Pielke, 1981),

suggests that thermal inertia mapping may contribute to improved

initialization of atmospheric prediction models.

The relatively large fluctuation in the surface temperature, compared

with that in the atmosphere, and the strong sensitivity of that surface
:oo T. N. CARLSON

temperature to surface and substrate parameters, such as soil moisture

and thermal inertia, suggests that remote measurements can be used in

conjunction with an atmosphere-substrate model to infer values for the

surface fluxes and the substrate and surface parameters. In the case of

remote measurements, such as those derived from satellite, the information available is a blackbody temperature measurement integrated

over the area of one pixel.

Models of differing complexity have been developed for the purpose

of calculating surface fluxes of heat and moisture and deriving the

surface and substrate parameters using remote surface temperature

measurements. While complexity in a model is advantageous in

research for studying the sensitivity of surface temperature to atmos-

>pheric and surface conditions, the lack of knowledge of initial or in-situ

atmospheric and substrate conditions and the errors of measurement

produce uncertainties in the results which effectively limit the value of

any model and thereby lessen the advantages of complex

parameterizations,

A strong impetus for current research into remote determination of

the surface parameters was the Heat Capacity Mapping Mission

(HCMM) satellite which was launched in early 1978. The relatively high

resolution (500 m) of the HCMM radiometers and its favorable orbital

period, which allowed measurements to be made near 2 AM and 2 PM

local times, afforded an opportunity to study the surface properties on a

scale small enough to resolve details of the land use pattern but broad

enough to permit relatively large areas to be examined. Essentially, the

problem was to derive information about the surface from a pair of

temperatures, one made during the early afternoon (local sun time) and

the other at night. Day-night pairs of temperatures were obtained by

HCMM 12 hours apart every 16 days and 36 hour pairs about every

five days. HCMM made it necessary to develop models relating the

surface temperature response to the surface parameters as measured at

two times during the daily temperature cycle, via the use of

atmospheric-substrate models.

MODELING SURFACE ENERGY BALANCE 101

3 MATHEMATICAL PROCEDURES FOR INTERPRETATION OF

THERMAL INFRARED DATA

(a) Analytic approximations

The familiar daily variation of surface temperature T0 results from the

balance between incoming and outgoing energy fluxes at the earth's

surface. This balance is expressed through the equation

Ra = Ga + H0 + Lt£0 = (1)

where the net radiant energy (Rn), consisting of the absorbed solar flux

(Rj), the downward longwave flux (RL), and the outgoing longwave flux

(/?,), is balanced by the upward fluxes of sensible heat (H0) and latent

heat (LfE0) into the atmosphere and the flux of sensible heat into the

ground (G0). The simplest solution to the surface energy balance

equation is to consider a time-dependent energy flux Fcos (at incident

on a uniform homogeneous material satisfying the heat flow equation

,cT S{.dT\ —= — A — ct cz\ cz J (2)

where p' is the density, c' the heat capacity, and /. the thermal

conductivity; /./p'c' is the thermal diffusivity of the substrate, referred to

as K'.

Classical solutions to the heat transfer Eq. (2), as presented by Jaeger

(1953) and by Carslaw and Jaeger (1959), inevitably led to adaption of

the simple cases to which the solutions are appropriate for application

to boundary meteorology (Sellers, 1965) and subsequently to their use

in remote sensing of surface temperature and surface characteristics. In

regard to the latter, the earliest theoretical developments were made

with geological applications in mind, the thermal inertia being a

measurable property of soils and rock. Watson (1973) recognized the

uses of the thermal inertia method in identifying minerals and his

theoretical papers (1973, 1975; see also Watson and Miller (1981) and

Watson, 1982) were soon followed by those of Price (1977, 1980, I982a,

1982b) and Pratt and Ellyett (1979; see also Pratt (1980) and Pratt et al.

(1980) in which thermal inertia was related directly through analytic

expressions to the maximum and minimum surface temperatures, which

could be measured by a satellite. Fourier models have also ;been
202

T. N. CARLSON

Re'

formulated in Europe (Viellefosse and Favard, 1979; Hechinger et a/.,

1982).

Equations (1) and (2) can be analyzed in order to derive formulas

pertaining to the 24-hour mean surface temperature and the amplitude

of the diurnal temperature cycle, the latter being obtainable from a

day-night pair of satellite temperature measurements. These quantities

are shown to be closely associated with the evaporative flux at the

surface and with the diurnal heat capacity (or thermal inertia), which is

also closely related to the soil moisture in the near-surface layer (Pratt

and Ellyet, 1979; Dejace et ai, 1979; Idso et ai, 1975a, 1975b, 1975c,

1977a, 1977b, 1977c).

By time averaging Eq. (1), a simple result may be obtained. Assuming

that no net heating or cooling of the earth occurs over a 24-hour period,

so that the average of G0 vanishes over a complete solar cycle, one finds

< R m > = <tf0> + <Le£0> (3)

where the brackets < ) represent a 24-hour average.

Now, using simple expressions for the solar and longwave fluxes,

'. (4a)

(4b)

RL = £a£g<7Ta

4

 (4c)

the net available radiant energy RB can be calculated from available

measurements of temperature and humidity and a knowledge of the

solar geometry and atmospheric transmission. Here, V represents the

effective atmospheric transmission for direct and diffuse solar radiation,

A0 is the surface albedo and Z is the solar zenith angle. For longwave

radiation a is the Boltzmann constant, Ta the near-surface air temperature, et

 the emissivity of the ground (usually taken as 1.0)* and ea is the

emissivity of the atmosphere, usually calculated as a function of surface

specific humidity (Brunt, 1932) or as a function of precipitable water

(Monteith, 1961). Similarly, simple expressions for surface heat and

moisture fluxes can be written in the following form (Sellers, 1965)

T.l (5a)

MODELING SURFACE ENERGY BALANCE

LeE0=LJ e (u)(q0-qa )

203

(5b)

where cp is the specific heat of air at constant pressure, L, is the latent

heat of evaporation, q0 and qa are specific humidity of the surface and

air, and for the sake of brevity, we write the atmospheric transfer

coefficients for heat and water vapor, respectively, as fh(u) and f e (u) to

signify the dependence of these coefficients on the ambient wind speed

it', in general, /e(u) =/i,(u). Accordingly, it is possible to write an explicit

expression for LeE0 by averaging the various quantities over a 24-hour

day, by making use of the constant term in the Fourier expansion of the

angle of solar incidence (C0), and by imposing some additional

simplifications concerning the averaging procedure such as in the

linearization of Eqs. (4) and (5). Thus, Price (1980) obtains

<Le£0> = SV(\ - A0)C0

(6)

where a and b are constants in Brunt's ( 1 932) equation for the emissivity

of the atmosphere, k is the Von Karman's constant, and p is the air

density (see also Sellers, 1965). The roughness length and height of the

atmospheric measurements (nominally 1.3m) are expressed, respectively by za and za. The daily maximum and minimum temperatures are

indicated by the appropriate subscripts. The result is that the mean

daily evaporation can be calculated from mean daily values of ground

temperature (T0), the near-surface temperature |7]|. specific humidity

(qa) and wind speed (ii), which can be obtained from conventional

meteorological measurements. Solar geometry is used to provide

estimates of S for clear skies. Surface roughness, albedo and emissivity

are determined from a knowledge of the surface characteristics.

Because of the linearization and averaging of the long wave fluxes,

which contain a Ta dependence, the maximum and minimum ground

temperatures also appear in the equation for LeE0. These temperatures

can be measured by satellite, although the mean daily evaporation in

this formulation is not very sensitive to the diurnal temperature

amplitude at the ground. Similar equations for the mean daily evaporation fluxes have been presented by Pratt et al. (1980).
204

T. N. CARLSON

MODELING SURFACE ENERGY BALANCE 205

Both Price (1980) and Pratt et al. (1980) explicitly treal surface

evaporation although only Price considers moisture flux explicitly as a

variable to be determined from the temperature wave. Pratt et al. (1980)

solve for two surface parameters simultaneously, thermal inertia a.nd

albedo, following the graphical models. So far, only Price (1980) has

derived patterns of a surface parameter (evapotranspiration) from

satellite data using an analytical model.

An approximate description of the diurnal temperature cycle may be

obtained through consideration of a periodic energy flux incident on a

uniform material. The analytic solution for the temperature is readily

obtained: its value at the surface T0(t) = T(z = 0, t) is given by

T0(t) = F cos (o>t - K/4)/(«p'c'A)

1/2 (7)

Further, the heat flux across the ground-air interface (C) can be

represented by the equation

(8)

where T., is the temperature of the first substrate level, a distance

AZ_ , below the surface in the finite-difference notation on the righthand side of Eq. (8).

The quantity (p'c'A)"2 is frequently referred to as the thermal inertia

(P) or sometimes the conductive capacity, thermal property or thermal

admittance, having a value of approximately 500 TIU (joules m '2 C "'

s~ "2) or 0.0125 (cat cm"2 C"' s" 1/2 ) for dry sand and about 4000 TIU

for solid quartz. Because these units are somewhat clumsy to work with

it is sometimes convenient to incorporate the earth's rotation rate

(oj = 2>t/24 hours) and define the diurnal heat capacity

I

1

'

2

 (9)

The factor o> brings D to the typical range of values 4-35 W m" * C~l,

which are simpler units. The advantage in using the thermal inertia is

that it contains two surface parameters, conductivity and diffusivity (or

heat capacity) in one parameter. As Carlson and Boland (1978),

Blackadar (1978a) and Price (1982a, 1982b) have shown, most of the

variance in the surface temperature wave is contained in the first

Fourier harmonic and, consequently, differing values of /.|and K' will

yield almost identical results in a model for a fixed value of P or D.

Using Eq. (7) as the thermal forcing at the ground-air interface yields

a very rough estimate of the temperature variation at the earth's

surface:

(10)

For typical values of the solar amplitude, atmospheric transmission,

albedo and diurnal heat capacity, one finds that the diurnal temperature range (T0mmf

 — T0rnla) is rather too large. It is evident, therefore, that

energy exchanges at the earth's surface must be considered, although

Eq. (10) properly identifies the solar forcing, surface albedo and thermal

inertia (D) as important factors influencing the variations in surface

temperature. Both Pratt et al. (1980) and Price (1982a, 1982b) consider

more realistic boundary conditions which require additional simplifying assumptions (Watson, 1975; Price, 1977). Price represents the solar

flux as an explicit function of time, while the diurnal variation of all

other fluxes exchanged with the atmosphere is regarded as linear in the

surface temperature. Thus the surface boundary condition Eq. (1)

Rs= Rs( t) = A + BT0 + G0 (II )

The constants A and B are evaluated by averaging over 24 hours and

by averaging the appropriate partial derivative with respect to surface

temperature. Realizing that <G0> = 0,

and

(12)

(13)

where the averages are readily computed from the expressions for the

solar and surface heat and evaporation fluxes (Price, 1980). The first

equation is simply the linearized version for the expanded form of

Eq. (1). The second equation defines a quantity which is significant

through its effect on the day-night temperature variation. Because H0

and R, depend on air temperature, it is appropriate to recognize that
206 T. N. CARLSON

air temperature is strongly affected by surface temperature. For these

terms the approximation

d dTa = d |T.(day)-T.(night)] d =

cT0 cT0 dTa [T0(day)-T0(night)]

(14)

is used.

Given these assumptions, it was shown by Price (1980) that the 11-

hour surface temperature variation, which was to be measured by

HCMM, could be approximated by the expression.

T0( 1330LST) - T0(0230LST) =

2SK(l-/t.)C,

(15)

where C, is the first Fourier coefficient in the expansion of the

insolation. In Eq. (15) the times of measurement represent the northern

hemisphere mid-latitude (45°N) overpass times for the HCMM.

However, it is possible to adjust the theory by changing the phase

differences between the two temperatures in order to accommodate

surface temperatures measured at two different times; here it is assumed

that those temperatures represent the maximum and minimum values.

Price (1980) obtained a simple approximation for the thermal inertia.

Defining a parameter Q which is equal to

2SV(l-A.)Cl

[T0(1330LST) - T0(0230LST)]

he obtained the result that

(16a)

(16b)

With B set equal to zero Eq. (16) reduces to an expression for

"apparent" thermal inertia which is a parameter provided by the

HCMM program (HCMM Data Users Handbook, 1978).

Price (I982a, 1982b) used the results of a prognostic model (the

European TELL-US predictive model referred to in the next section) to

tune his own model results, specifically by adjusting his expressions for

LeE0 and D. In this manner Price was able to eliminate what he felt was

internal bias resulting from the limiting assumptions and simplifiMODELING SURFACE ENERGY BALANCE 207

cations specific to the analytic model. Pratt et al. (1980) have suggested a

similar direct approach for determining the parameter B from ground

measurements, a procedure necessitated by the uncertainty in evaluating this parameter theoretically.

A primary virtue of the analytic models is their simplicity, which

allows for a high computational efficiency without seriously degrading

the results. They are somewhat limited, however, by the approximations involved in obtaining and expression for the thermal forcing at

the surface and by the time averaging of meteorological quantities.

Perhaps the most serious limitation is the simplified manner in which

atmospheric processes are treated, particularly those changes in temperature, wind, and moisture which are occurring in the surface and

mixing layers. In the following section we treat a physically more

elaborate model in which some of these simplifications are addressed.

(b) Combined ground/atmosphere simulation models

Time-dependent, initial value prediction models are widely used in

meteorology and a variety of boundary layer models exist as separate

one-dimensional components for diagnostic purposes (e.g. Myrup,

1969; Sasamori, 1970) or as integrated routines in two- and threedimensional numerical atmospheric models (Blackadar, 1978a, 1978b).

The function of such sub-components in atmospheric models is of

course, to predict changes in the substrate temperature and in the

atmospheric temperature, wind speed and moisture as a function of

time. Carlson and Boland (1978) and Rosema (1978; see also Dejace

et al., 1979) proposed similar methods in which a predictive model can

be inverted, given the measured surface temperatures, to yield unique

values of two surface parameters, either thermal inertia moisture

availability (or surface relative humidity) or thermal inertia and albedo.

Sensitivity tests by Saltzman and Pollack (1977) and by Carlson and

Boland (1978) demonstrate that the three most important surface

parameters which govern the surface temperature response are the

moisture availability, thermal inertia and albedo. However, within the

normal range of satellite pixel brightnesses encountered over heterogeneous terrain, such as a city or a vegetation canopy, the horizontal

variations in surface albedo are relatively small. The relative importance of the moisture availability and thermal inertia, as opposed to

surface roughness or albedo, can be seen by inspection of Figure !.
T. N. CARLSON

MODELING SURFACE ENERGY BALANCE 209

TIME ILSTI

6PM 12AM SAM 6AM

THE (LST)

6PM 12AM 6AM

i SOO

i

290

i

1

 200

I

270

MOISTURE AVAILABILITY (Ml

A 001

B 01

C 03

0 05

WIND SPEED (U0I

A IO on/MC

B IOO cm/MC

C SOO on/MC

A

 0 1OOO cm/MC

THERMAL INEWtlA IP) ,

A Oil col-tm2 KMC^

8 009frX€E RUNS

c 006J wrra

E 002 coUDn2-Ki«c2

PRECIPITA8LE «»TEH(.I

A 50o8 20<B»

C I Oc*i

0 05c«

I2PU 6PM 12AM

TIME (LSTI

6AM BAM 12PM 6PM 12 »M

TIME (LST)

FIGURE I Model sensitivity tests varying moisture availability, thermal inertia, wind

speed at :,, roughness length, precipilable water and albedo.

Moisture availability exerts a large influence on the temperature

variation during the heated portion of the day whereas thermal inertia

variations produce their greatest effect on the night-time temperatures.

The remaining parameters not only exert a smaller effect on the surface

temperature wave but such properties of the ground as albedo or

roughness can be estimated from an approximate knowledge of the

terrain to within an acceptable accuracy. Initial wind speeds al the top

MI1ING

sumcc

(TURBULENT KIR UHR)

SUBSTIITE

= 50 II

= 0 I

FIGURE 2 Basic model framework of the CM.

and above the atmospheric surface layer (Figure 2) can be provided by

conventional large-scale weather observations and thereafter predicted

internally in the model.
210 T. N. CARLSON MODELING SURFACE ENERGY BALANCE :n

The Carlson simulation method

The underlying constraint in virtually all predictive models is the

surface radiation balance, as expressed by Eq. (1). The basic structure of

the Carlson model (Figure 2) consists of four layers, an atmospheric

mixing layer, a surface layer, a shallow transition layer between the

surface air layer and the substrate. Fluxes in the atmosphere are

specified by equations similar to those used by Price (1982a, 1982b)and

by Pratt el al (1980). To clarify the definition of the important

parameters, moisture availability and thermal inertia, and in order to

discuss the predicted variables, the flux equations are presented, using

the resistance notation of Monteith (1975), as

pcp(T0-Ta) _ »"•/>'

L,Ea = Rcv

M

(17a)

(17b)

where T0 — Ta and qos — qa, respectively refer to the vertical temperature

and specific humidity differences between a saturated surface (subscript

zero) and the fop of the surface layer (subscript a), nominally chosen to

be 50 m above the ground. The resistance for eddy conduction Ra refers

to that in the atmospheric surface layer for heat and moisture fluxes

between the top of the transition layer at height z, and at the top of the

surface layer at za. The subscripts ch and cc refer, respectively, to

resistances for heat and moisture fluxes through the transition layer,

which is envisioned to be a narrow region over which a combination of

eddy, molecular and radiative fluxes coexist in some fashion. Le is the

heat of vaporization for water.

The above flux equations are more elaborate versions of those used

by Price (1982a, 1982b) and Pratt el al. (1980) in their analytic models

and referred to in Eqs. (5) and (6). The factor M in Eq. (17b) is called the

moisture availability and is defined as

= E/E0(T0) = (»7c)

tation functions as a bulk stomatal resistance parameter, accounting for

the resistance for water vapor between the canopy and the atmosphere.

Generally, M represents the fraction of potential evaporation (E/E0(Ta))

at the temperature of the surface (7^). Under saturated conditions R, is

essentially zero and evaporation is equal to the potential value. For a

completely dry surface M is zero. Below some low value of M soil or

plant wilting occurs (Tanner and Pelton, 1960), the vegetation may begin

to suffer physiological stress (Monteith, 1975) and the soil approaches a

limiting dryness (Jackson, 1973; Idso el «/., 1974).

Moisture availability can be expressed in various other forms than that

of Eq. (17b). Nappo (1975), for example, explored an alternate parameterization in which the moisture parameter is expressed as a surface

relative humidity (ha), a form which both Price (I982a, 1982b) and Pratt

el al. (1980) prefer (i.e., in Eq. I7b the quantity (qM(Tt) - qa)M is replaced

by (hqm — qa). Both M and /»„ vary between 0 and 1.0 and can be

expressed as mathematical transforms of one another. In most cases Lc£0

depends on saturation specific humidity at the surface, and must vary

with surface temperature and, consequently, its value may change rapidly

with time for a constant value of M. The virtue in using M is that it

represents an intrinsic property of the soil such as the ratio of volumetric

water content to that at field saturation for bare soil. If so, it must vary

over a small fraction of its maximum range during the day when

averaged over a typical rooting depth (Jackson, 1973). Horizontal

variations in M or temporal changes over a period of several days should,

therefore, reflect real changes in the near-surface or vegetation moisture

content.

The resistance terms are calculated as follows. For heat

where Rb = Ra 4- Rcv and Rs is a surface resistance, which over vegeR,. + R a = \ dzl(Kh(z) + Ck) (18a)

Jo

r-°

R +Rt t=\ dz}(Kh(z) + Cr) (18b)

Jo

where Kh is the eddy diffusivity for both heat and moisture fluxes in the

surface layer. These integrals depend upon the wind speed, roughness

length, and static stability (surface heat flux) and thus require interation

to achieve solution. The integrals in Eq. (18) are obtained in two parts, by

considering that molecular and radiative processes are unimportant
212 T. N. CARLSON MODELING SURFACE ENERGY BALANCE 213

above the transition layer and that stability corrections to the logarithmic profile (Panofsky, 1974) are negligible in the transition layer.

Solutions are obtained for both heat and moisture conduction by

insertion of the appropriate constants for Ch and Cu; Rch and Rcu are

assumed to be equal. For want of better values, the molecular conduction

coefficients were used for Ch and Ctt. Analogous expressions for the

momentum eddy conduction Km, evaluated between the limits of the

roughness height and za are also determined. The eddy conduction

integrals such as Eq. (18) are solved by using analytic expressions for Kh

and Km (Panofsky, 1974) based on solutions presented by Paulson (1970)

and Benoit (1977) for the case of an unstable temperature profile.

Tests with the Carlson model show that the results are somewhat

sensitive to the values of the transition layer depth. Large vertical

gradients are generated by the inclusion of small values of the transition

layer coefficients and for that reason the molcular values may be rather

too small, at least over rough terrain where surface elements may

protrude into the airstream.

Solution Equations (1), (2), (4), (8), (17) and (18) form a complete set

which can be solved to obtain the variables Ta, LeE0, H0, G0 and T_, in

the atmospheric surface layer and substrate given the measured temperature, specific humidity and wind speed at two levels (e.g. the surface and

at zj. In the Carlson model, the temperature, specific humidity and wind

speed at za and in the mixing layer are predicted from a set of initial

conditions, as is the temperature in the ground. The diffusion Eq. (2) is

used to predict the temperature variation below the ground. In the

mixing layer, temperature and specific humidity are calculated from a

model originally formulated by Tennekes (1973) for conditions of free

convection during the day. Wind speed is calculated from the timedependent momentum equations, including the effects of coriolis force

and vertical mixing, the latter being determined by specifying the vertical

distribution of the mixing coefficient (KJ in the mixing layer as a function

ofz(Obrien, 1970).

At night the critical Richardson number formulation of Blackadar

(I978a) is used to calculate the temperature and wind speed tendencies in

the surface and turbulence layers with an additional equation for

temperature tendency imposed near the surface. The surface temperature is determined as a quasi-equilibrium value at each time step from the

forementioned set of equations. Solutions quickly approach radiative equilibrium after sunset with the vanishing of turbulence, except

under windy conditions when turbulence episodes may still occur. Under

radiative equilibrium the equations closely resemble those of Outcalt's

(1972) model. Advection is completely neglected.

An advantage in using a predictive model is that it permits a fuller use

of the governing equations than does a simpler model. In allowing

solutions to proceed from a single set of initial conditions, which may be

determined from large-scale meteorological data, the results do not

depend upon continuous in-situ measurements of air temperature,

humidity and wind speed. Moreover, the vertical profiles of the atmospheric variables in the surface layer are internally consistent with the

surface fluxes and with the surface energy balance. The Carlson Model

(CM) treats the surface and mixing layers in detail, accounting for the

temperature, wind and moisture variations throughout the lower

atmosphere.

As an example, consider the daily temperature wave generated by the

CM in Figure 3. The figure suggests that the temperature wave is highly

sensitive to the moisture availability during the day and to the thermal

330

320

a.

2

290

280

M = 0.05

z0=IOcm

(

z0=IOOcm

P=0.05 calcm-2K''sec""2

M = 0.55

I I I I I I I I I I I I I I

9 10 II 12 13 14 15 16 17 18 1920 21 22232401 O2 03 04 05

TIME (LST)

FIGURE 3 Simulated surface temperatures Tor different values of moisture availability (M) thermal inertia (/>). and surface roughness (:„( starting al 0600 l.ST. The

vertical dashed lines refer to the limes of IICMM satellite data measurement.
214 T. N. CARLSON

inertia at night, as is also indicated in Figure 1. It is not obvious, however,

that unique values for the surface parameters can be determined from an

inversion of the temperature information contained in Figure 3. Carlson

and Boland (1978) and Rosema (1978) suggested a method whereby two

ground parameters, thermal inertia and moisture availability (or surface

relative humidity), can be determined uniquely in most cases from two or

more measurements of surface temperature. Other parameters are held

fixed at their assumed values during the calculations.

To illustrate the inversion method for recovering the two governing

surface parameters, thermal inertia and moisture availability, consider

the values of temperature at 1400 and 0200 local time in Figure 3,

approximately the times corresponding to those of a day-night HCMM

image pair. If the temperatures are then replotted for both the day and

night-time values in a graph of M — P space, one obtains a pair of

intersecting contours, as is shown in Figure 4 for the data used to

construct Figure 3. It is evident from inspection of Figure 4 that unique

values of M and P are obtainable for this case within the range of

temperatures shown in the figure. Provided that the measured ground

temperatures fall into the range of temperatures shown in Figure 4 a map

of thermal inertia and moisture availability (and also the surface heat

fluxes) can be generated from two satellite temperature images, one at

0200 and the other at 1400 local time. Bi-valued solutions for the surface

parameters are possible under certain conditions but these situations

appear to be rare and occur when extraordinary initial conditions are

chosen. Ambiguous solutions for M and P may occur, however, if the

temperature pairs do not differ from each other by a large amount. A

more complete discussion of the uncertainties in this method, including

alternate combinations of satellite imagery, other than those at 1400 and

0200 local time, is presented in Section 5.

In practice, images of the transformed quantities, M, P, H0, LeE0 and

G0, are not obtained graphically but by means of regression equations

fitted to the model output from a succession of model runs with differing

values of the parameters M and P. Unlike the energy fluxes, which

correspond to the time of the afternoon image, the intrinsic terrain

parameters, M and P, are considered averages for the entire day.

Recently,-Polansky (1982), Wetzel (1983) and Wetzel and Atlas (1981,

1983) have shown that image pairs, other than those for the day and

night, and image triplets can be used effectively to derive unique values

for the governing surface parameters.

MODELING SURFACE ENERGY BALANCE 215

0 1.0 I.I 1.2 1.3

FIGURE 4 Variation of surface temperature as a function of Al and P for daytime

temperatures at limes of HCMM measurements (- 1400 LST solid lines and 0200 LST

dashed lines labeled in 'C above 200 K). Initial conditions for model same as those for

Figure 3. The lead digit has been deleted from the temperature values.

Other models In Europe a parallel effort has been made in developing

predictive models for the remote determination of the governing surface

parameters. Such models, as reported by Rosema et al. (1978), Nieuwenhuis and Klaassen (1978) and Soer (1977), are variants of the TELL-US

model (Reiniger et al., 1982) which is similar to that of CM, except the

former does not account for a turbulent interaction between the surface

layer and the free atmosphere above, nor does it possess a detailed

predictive capability except in the substrate. It also requires meteorolog-
216 T. N. CARLSON

ical observations at 2 m as hourly input. The TELL-US model does,

however, attempt to describe some detailed aspects of the cropatmosphere exchange in a manner more closely tailored to the character

of the crop canopy than does the model of CM. The models resemble

each other with regard to the formulation of a crop-atmospheric

resistance parameter (i.e. Rc a in Eq. 18), which is specified by Soer(1980)

as a generalized canopy resistance which may depend upon the canopy

geometry (Klaassen, 1979). A further discussion of the need for an

improved vegetation parameterization is contained in Section 7.

Wetzel and Atlas (1981) and Wetzel el al. (1984) describe the use of a

predictive boundary layer model of Wetzel (1978) for obtaining the

governing surface parameters from measurements made from geostationary satellites such as GOES. Soil moisture is included in their

model explicitly as a fraction of soil saturation, a similar parameter to

M in Eq. (3); the model is otherwise very similar to that of CM.

Application of the model to satellite measurements is made not using

the full model but, instead, the morning rise in temperature in the model

is fitted to a simple polynominal, which relates wind speed and

normalized rate of rise of morning temperature to the soil moisture

parameter; the relationship is assumed to be applicable to a wide range

of meteorological conditions, latitudes and seasons. This method

requires only two temperatures made about two to four hours apart

during the morning but explicitly uses only one temperature difference.

The predictive model of Kahle (1977; see also Kahle et al., 1975) also

employs similar equations to those referred to above and has been used

to infer the thermal inertia of geological formations. This model does

not account for an exchange with the free atmosphere above the surface

layer, nor does it specifically deal with latent heat flux.

(c) Diagnostic models

A class of models which can be referred to as diagnostic are the socalled combination models which make use of the flux relationships,

such as Eqs. (17) and (18), combined with the surface energy balance

Eq. (1). An example of a combination model is the Penman-Monteith

equation (Monteith, 1975), which, as formulated does not lend itself to

direct satellite measurement of surface temperature since it is expressed

in terms of air temperatures. In using a combination model to derive

surface moisture availability, concurrent surface and air temperature,

MODELING SURFACE ENERGY BALANCE 217

wind speed and humidity are required, the surface temperature to be

provided by remote observations. In effect, Price (1982a, 1982b) uses a

form of combination equation in Eq. (6) to determine the evaporation.

Various combination models have been derived for agricultural purposes, such as those by Black et al. (1970), Brun et al. (1972), Ritchie

(1972), Brown and Rosenberg (1973), Stone and Morton (1974), Heilman and Kanemasu (1976), Verma et al. (1976), and Byrne et al. (1979).

These authors discuss various forms of combination equations as

applied to vegetated canopies where detailed measurements of air

temperature and humidity may be available.

Combination models are, in principle, easy to apply but they require

a knowledge of the atmospheric parameters immediately above the

surface. Consequently, there is a danger that the measured air temperature and that for the ground derived from satellite may be incompatible,

yielding an erroneous or inconsistent result when vertical differences

are formed between values at the canopy surface and in the atmosphere.

In this respect, the prediction methods avoid the problem by determining internally consistent vertical profiles of temperature, wind, and

humidity.

(d) Empirical models

A fourth class of model can be called empirical because the physical

relationships are replaced by empirical equations which are based

either on direct measurements or on the results of more complicated

models. Underlying the empirical approach is the observation that

leaf-air temperature differences (or soil-air temperature differences) are

dependent upon soil moisture. Such models have been developed

largely by the Arizona group (Idso et al., 1975a, 1975b, 1975c; Idso

etai, 1976; Idso and Ehrler, 1976; Idso et al., 1977a, 1977b, 1977c;

Jackson et al., 1977; Millard et al., 1977; Ehrler et al., 1978). Daily sums

of leaf-air temperature differences, called the "accumulated stress", are

shown to be related not only to soil moisture but to crop yield. Based

on simple formulae, the measured canopy temperature during the

afternoon or the measured day-night canopy temperature difference

are related to measurements of soil moisture, evapotranspiration, or

crop yield. For example, Jackson et al. (1977) gives the following

equation which is based on an expansion of the surface energy budget

Eq. (I) but with measurements used to determine values for the
218

coefficient B

T. N. CARLSON

(19)

where Tc is the canopy temperature, analogous to 7^.

Fdso and his group at Arizona have endeavored to utilize the

empirical relationships between the temperature response, as measured

by a radiometer, to derive expressions for evaporation and crop yield.

These formulae, while of practical significance, surfer from being

sensitive to ambient meteorological conditions and are appropriate for

use only over the region and type of surface for which the expressions

were derived.

So far, empirical models have not been applied directly to satellite

measurements, although Heilman and Moore (1980) derive their

empirical equations from an analysis of in-situ soil moisture data and

corresponding HCMM satellite infrared surface temperature measurements. Though not universally applicable to satellite measurements,

such empirical expressions provide further evidence thai the satellite

may be capable of determining soil moisture patterns (Seguin and Itier,

1983).

4 RESULTS

(a) The urban heat island

One of the most notable meteorological anomalies produced by human

activity is the urban heat island. This phenomenon is readily distinguishable on satellite imagery (Rao, 1972; Carlson and Augustine, 1977;

Matson et ai, 1978) and is indisputably linked to human alterations of

the surface, specifically the removal of vegetation and its replacement

with non-evaporating and non-porous materials.

Recent studies by Landsberg (1979) for Washington, D.C. and by

Changnon (1978) for St. Louis show that the precipitation patterns

downwind of urban areas are significantly influenced by the heat island.

The cause of this weather change in the urban areas appears to be due

to differential heating at the surface and its effects on the boundary

layer (Kropfli and Kohn, 1978; Wong and Dirks, 1978)1. Significant

inflow of surface-level air into the warmer parts of the city and the

subsequent lifting of the converging warm air leads to the formation of

an elevated warm plume downwind of the urban centers.

MODELING SURFACE ENERGY BALANCE 219

In Figure 5, taken from Carlson et al. (1981). the warmest temperatures appear over downtown St. Louis (the location marked D), East St.

Louis (E) and over Granite City (G). The temperature pattern in Figure

5 is very similar to those obtained for other HCMM scenes (CM) and

for TIROS-N measurements (unpublished data) over this city.

Moreover, the overall character of the urban temperature anomaly also

resembles those for other urban centers, such as Los Angeles (Carlson

and Augustine, 1977; CM), Houston, TX and Washington, D.C.

(unpublished analyses).

A close relationship is evident between the afternoon temperature

and moisture availability upon inspection of Figures 5 and 6. Temperatures exceeding 40°C over the downtown portion of the city correspond

to relatively low values of M (less than 0.2) in Figure 5 and to relatively

high surface heat fluxes (in excess of 200 Wm" 2) in Figure 7. Interestingly, despite the pronounced urbanization over these cities, the Bowen

ratio (H0/LeE0) is near 1.0 on a scale of a satellite pixel, a situation

which attests to the importance of existing trees and grass in the

evapotranspiration process over cities. A similar conclusion was

reached by Oke (1982) for Vancouver, B.C.

Another curious result obtained by CM was that the distribution of

thermal inertia, once thought to be the important parameter in forming

the nocturnal urban heat island, exhibits a rather flat pattern with no

pronounced maximum over the city. It appears that the daytime heat

island, in summer at least, is the driving mechanism behind the

nocturnal temperature anomaly, rather than the distribution of absorbing materials in the substrate. The city remains relatively warm at night

because the surface is hotter during the day and more heat is transferred

into the substrate because of the greater surface-substrate temperature

difference. The urban summertime nocturnal temperature maximum

therefore is ultimately the result of vegetation removal in the urbanization process. A similar conclusion regarding the genesis of urban heat

islands was reached by Oke (1982) except that he regards canopy

geometry to be as important as moisture.

(b) Soil moisture over vegetated areas

It is obvious from examination of Figure 6 that HCMM satellite

imagery is capable of detecting significant variations in ground moisture over urban areas. Over vegetation the response of the thermal
220 T. N. CARLSON MODELING SURFACE ENERGY BALANCE 221

SS

si

G °9

lg'-•••".•;~~ "— -•-

ST. LOUIS, MO

1O km

FIGURE 5 Surface lemperalure analysis in °C over St. Louis, MO, at apgn-oximaiely

1330LST, 23 August I978. Bold-faced capital letters refer to surface types or sites

(C: croplands; D: downtown St. Louis; E: east St. Louis; G: Granite City; fit Horshore

Lake; P: park).

ST. LOUIS, MO I1O km •i

FIGURE 6 Surface moisture availability analysis over St. Louis. MO, 23 August I978

based on a day-night HCMM image pair.
T. N. CARLSON MODELING SURFACE ENERGY BALANCE 223

O O

"" &

O

ST. LOUIS, MO 1O km

FIGURE 7 Surface heal flux analyses (W nr2) for 1330 LST 23 August I9<78 based on

day-night HCMM image pair.

pattern to soil moisture is much more complex than over bare soil or

urban areas. While temperature variations between crops cam reveal

significant differences in evapotranspiration or soil moisfunre, such

differences may be no greater than a few degrees or less (under identical

meteorological conditions) between extremes of dryness. Because vegetation type and geometry play such an important role in plant response

to thermal stress, it is still not clear to what degree quantitative

measurements of soil moisture can be made over vegetated surfaces.

Indeed, Monteith (1981) has voiced reservations concerning the capability of satellites to measure soil moisture over vegetated surfaces.

In the face of such pessimistic evaluations, recent evidence cited in

this paper suggests that the satellite possesses a modest capability of

measuring a soil moisture parameter with some degree of definition

over short vegetation such as grass. Evidence for this positive assessment is provided by earlier studies over vegetated regions by Kocin

(1979), Heilman and Moore (1980) and Harlan et al. (1980).t In this

paper we present further evidence of a relationship between the derived

M parameter and antecedent precipitation over regional-scale areas

covered by short grassy vegetation.

An analysis of both HCMM and GOES satellite temperature

measurements was made on 27-28 July 1978 over a region in eastern

Kansas (Figure 8). This area was chosen because of the extreme

variation in precipitation and in the crop moisture index over eastern

and central Kansas during the summer of 1978 (Figure 9). HCMM

images 36 h apart on July 27 and 28 and GOES images on July 27 were

obtained over the target areas (the solid and dot-dash rectangles shown

in Figure 8). During this two-day period clear skies and light winds

characterized the weather over Kansas. Over the target area the terrain

consists largely of unirrigated range and crop land with corn and winter

wheat the dominant cash crops. Very light rainfall (less than 0.5 inches)

had fallen during the previous three-week period over the southwest

corner of the target area. Low values of the crop moisture index ( — 2 to

-3) occurred over the southwestern corner of the domain with

relatively higher indices (—1 to +1) over the extreme northern and

eastern portions of the working area.J Similarly, the three-week

cumulative rainfall totals were less than 1.0 over the southwestern

t Harlan, J. C. (1980). Dryland pasture and crop conditions as seen by HCMM. Report

to HCMM Investigators Meeting. Nov. 24-26, 1980, NASA.GSFC. Greenbelt, MD.

Unpublished and undated manuscript.

{U.S. crop moisture index published in the Weekly Weather and Crop Bulletin, U.S.

Department of Commerce.
224 T. N. CARLSON

/

L

MISSOURI

ZOO KM '

FIGURE 8 Sketch of Kansas and adjoining state boundaries, showing analysis areas

for HCMM and GOES.

quadrant (Category 3 in Figure 9) with amounts above 2.0 inches

(Category 4) over eastern and northern portions of the domain.!

Clearly, if soil moisture variations associated with rainfall anomalies

are to be detected by satellite, they will certainly be most noticeable in

situations where there are large horizontal gradients of rainfall, such as

appeared over Kansas during July 1978. Moreover, errors in measurement and model are less serious where M is small (Section 5). The

surface temperature analysis derived from HCMM for the afternoon of

July 28 appears to confirm this expectation (Figure 10). Thus, in

comparing Figure 10 with Figure 9, high temperatures (generally

tCumuIative precipitation is here defined as the total precipitation over a three-week

period preceding the date of the analysis. Antecedent precipitation (API) is defined

according to Saxlon and Lang (1967) and Blanchard etal. (1981) using formula API

= kAPl,., + P, in which the precipitation P, on day i is added to a weighted value of the

existing API on day i - I. The result is a precipitation amount which decays toward zero

when no new rainfall occurs. The weighting factor (k) was taken as 0.92.

MODELING SURFACE ENERGY BALANCE 225

100 KM

FIGURE 9 Three-week cumulative rainfall (solid lines) and crop moisture index

(dashed lines) for the Kansas case over the HCMM domain of Figure 8, 29 July I978.

Contours of precipitation represent logarithmic scaje: I =0.25 inch: 2 = 0.5 inch;

3 = 1.0 inch; 4 = 2.0 inch. Background shows streams and lakes.

40-50°C) are found over the arid southwestern sector and relatively

cool temperatures (about 35°C) over the north and east. Similar

patterns were obtained for analyses based on GOES infrared satellite

measurements over the larger rectangle in Figure 8.

Not surprisingly, these satellite temperature patterns translate into

similar patterns of the moisture availability M, which is less than 0.25

over the southwestern portion of the working area and greater than

0.75 but less than 1.0 over the east and north of the area, as shown in

Figure II. Similarly, the patterns of surface heat flux (Figure 12)

resemble both the daytime temperature and moisture availability

patterns with high values over the southwest corner of the area and low

fluxes, corresponding to the relatively moist terrain, over the eastern
226 T. N. CARLSON

\0 Y

*4Ct-/

40

100 KM

FIGURE 10 Surface temperature analyses (:C) over the smaller rectangular area of

Figures at approximately I330 LST, 27 July 1978.

and northern quadrants of the figure. Contours of total daily evaporation (not shown) closely resemble those of M.

The correspondence between M (or £„) and precipitation is not an

exact one. There are obviously some areas where agreement between

rainfall and moisture availability is lacking, as might be expected since

precipitation is only one component in the hydrological budget, which

depends upon evaporation, runoff, and local water sources such as

underground aquifers and irrigation. Nevertheless, the linear correlation coefficient (R) between the moisture availability and precipitation

fields (Figure 9 Versus 11) exceeds 0.6, indicating a significant degree of

sensitivity of M to precipitation. In a similar case study, for an area over

southern Illinois and Indiana (not presented), the correlation between

M and precipitation was found to be about 0.6 for.both HCMM and

GOES analyses. Wetzel and Atlas (1983) found a log-linear correlation

exceeding 0.8 between antecedent precipitation and the morning rise in

MODELING SURFACE ENERGY BALANCE 221

\

100 KM

FIGURE 11 Moisture availability (AH 23 August 1978 determined from a day-night

HCMM image pair over the area of Figure 10.

temperature for the same July 1978 period over the Great Plains.

Recently, we reworked all of the 1978 GOES satellite measurements

ever the Kansas target area, adding 10 more cases from the dry summer

of 1980 (Carlson el at., 1984). The mean correlation coefficient for all 12

cases for a log-linear relationship between API and Af is about 0.7, but

the relationship is clearly based on agreement between API and M on

the larger scales, the fine details of the patterns showing relatively poor

agreement. The results were better for a log-linear relationship (rather

than a linear one) because M becomes relatively insensitive to changes

in precipitation when it approaches 1.0 or as the soil reaches field

saturation. Wetzel and Atlas (1983) also analyzed a much larger area

than that shown in Figures 9-12 and derived a relatively smooth

pattern. Inspection of the moisture availability pattern (Figure II)

indicates that the poorest correlation between A/ and rainfall is on the

smaller scales, possibly because such scales are inherently more noisy or

because the rainfall observations are not sufficiently dense to capture
228 T. N. CARLSON

•4

100 KM

FIGURE 12 Surface heat Rm analysis (H,) determined from a day-night HCMM

image pair over the area of Figure 10 at approximately 1330 LST 23 August 1978.

Contours have the following values; l = !05Wm'J: 2=l40Wm~ 2; 3 = 210 Wm" 2;

; 7 = 305Wm- 2.

small-scale variations in M. Our results show an improvement in

correlation when the data is smoothed. Wetzel and Atlas' analyses were

derived from GOES but there is no evidence to suggest that this satellite

is superior to HCMM in this regard; on the contrary, we have found

slightly better correlations between M and precipitation with HCMM

than those of GOES.

The presence of relatively high temperatures over the arid portion of

the working area is somewhat puzzling. It is unlikely that the vegetation

itself can reach temperatures as high as those shown in Figure 10. Our

experience with the operation of manual radiometric measurements

over vegetation during periods of low rainfall indicates that, while leaf

temperatures may rise slightly above air temperature, the temperatures

of bare soil and short grass between the plant rows or surrounding the

cultivated fields may rise by a considerable amount during periods of

MODELING SURFACE ENERGY BALASCE 229

drying (Myers and Heilman, 1969; Cooper, 1981). Although a single

satellite pixel may contain both vegetation and bare soil, remote

temperature measurements made over areas the size of a satellite pixel

appear to respond rather sensitively to the elevated warmth of bare soil

and grass clumps which are interspersed throughout the taller vegetation. In the case of Kansas, the vegetation consists largely of grassland

and unirrigated crops. On the other hand, the vegetation cover is more

luxuriant over southern Indiana and Illinois where a significant

correlation between M and rainfall was also found using both HCMM

and GOES measurements (Polansky, 1982).

The response of moisture availability to precipitation over a regionalscale area was noted by Kocin (1979) in a study involving the analysis of

HCMM temperatures over the Goodwater Creek watershed in

Missouri (Figure 13). Approximately eighty-five percent of the watershed is cultivated, three-quarters of which consist of corn, wheat,

soybeans and various other grains and grasses. HCMM measurements

were made for a pair of orbits 36 h apart on 9-10 June 1978, a period

FIGURE 13 Location of Goodwaler Watershed and surrounding countryside.
:3o T. N. CARLSON

when the fields would have been relatively bare. The weather during

this period was clear and cool.

The moisture availability pattern for this case (Figure 14) contains a

considerable amount of small-scale detail, some of which must be

related to the type of land surface and crop cover. Nevertheless, the

correlation between M and cumulative precipitation is about 0.6.

FCocin's results, however, show virtually no correlation between M and

rainfall for analyses made for a case during late September 1978.

Although it is likely that the vegetation would have been relatively

dense and perhaps at least partially senescent, the crucial factor in the

lack of correlation is that the horizontal rainfall variations over the

watershed were quite small in September.

good water watershed

6 _ .5 .5 .6 .6

area

10 KM

H

FIGURE 14 Enlargement of unsmoothed moisture availability analysis over the

Goodwatcr Watershed area (outlined by thin dashed border), a sub-set of ihe rectangular

are in Figure 13. Analysis for 10 June 1978, as determined from day-night HCMM image

pair.

MODELING SURFACE ENERGY BALANCE 231

5 AN EXAMINATION OF ERRORS AND UNCERTAINTIES IN THE

INFRARED METHOD

(a) Model uncertainties

Model uncertainties can be described as (I) conceptual in origin, (2) the

result of empirical physics and (3) due to limiting assumptions.

Conceptual errors are related to the fact that a model represents a naive

idealization of the ground surface, representing it as flat and homogeneous, overlying a purely diffusing substrate. Most boundary layer

models currently in operation inadequately represent complex surfaces.

Those which attempt to incorporate details of a vegetation canopy,

such as the model of DeardorfT (1978), tend to be based on untested

relationships and, in any case, require more information than can be

supplied or specify parameters whose values are virtually unknown and

perhaps unknowable. There has been some attempt by European

workers (e.g. Nieuwenhuisand Klaassen(l978)and Klaassen(l978)) to

parameterize explicitly the soil and leaf resistances within a canopy-air

layer corresponding closely in concept and formulation to the transition layer of CM. Thus, coefficients similar to C\ or C,. in Eqs. (18a)

and (I8b), are determined from direct aerodynamic measurements over

leaves. Deardorf's model has been tested against real data using a

boundary layer model (Jersey, 1982), which is that of Blackadar (I978a,

I978b). The results of this study were inconclusive regarding the

possible improvements in accuracy to be made by inclusion of the

Deardorff vegetation formulations. Klaassen (I978). however, found

that the European TELL-US model yielded relatively accurate evaporation values, when compared to measurement made under controlled

conditions with carefully chosen resistance parameters.

If the inclusion of an explicit vegetation parameterization for a wellknown canopy can sometimes result in improvements in predicting

surface evaporation, it does not solve the problem of defining the real

nature of the surface under general conditions. That surface can consist

of vegetation and other complex surface features, such as buildings or

irregular terrain, which possess a bulk surface temperature which may

vary with both the viewing angle of the sensor and the geometry of the

sun and the surface. A model temperature, however, is obtained by

solution of equations for some idealized surface. Both the predictive

and analytic models suffer from their dependence upon a solution of the

substrate diffusion Eq. (2), which is often applied indiscriminately to
232 T. N. CARLSON MODELING SURFACE ENERGY BALANCE 233

any type of surface, even that which is not a truly diffusing one.

Deardorff (1978) eliminates the need for using the diffusion equation

within a vegetation canopy by explicitly parameterizing the transfer of

heat between the canopy surface and the ground. He also deals

separately with ground covered by vegetation by specifying a fractional

coverage of biomass, an approach also used by Wetzel (1978).

Diagnostic models, in depending on a bulk canopy temperature

alone, are independent of any substrate formulation, although they

nevertheless suffer from conceptual ambiguities regarding the nature of

the surface and from an inability to determine representative and

internally consistent atmospheric properties. CM suggests that the

conceptual problem of incompatibility between model temperatures

and those measured remotely can be circumvented partially by considering the model parameters as effective values which are required to

yield the correct (i.e. measured) surface temperatures in a similar

boundary layer model. Since it is clear that the measured surface

temperatures do vary in some systematic fashion with the moisture

availability and since the physical relationships used in most models are

very similar to each other, the model parameters should possess a

physical meaning, although they do not necessarily lend themselves

easily to direct measurement.

In regard to the model physics, the general laws governing the

vertical turbulent transfer of heat from the surface to the atmosphere

are fairly well-known (Panofsky, 1974). Nevertheless, the transfer

.coefficients for the eddy, molecular and radiative diffusion of heat, for

example, are based on empirical relationships derived from an average

of measurements made over relatively homogeneous terrain. Underlying these diffusion laws is the concept of the logarithmic profile, which

applies to temperature, moisture and momentum. These profiles are

subject to considerable deviation from a pure logarithmic behavior

when the static stability (the change in potential temperature with

height) deviates from its neutral (isentropic) state or when the terrain is

jnhomogeneous. Corrections to the logarithmic profile can be made for

stability but since the stability is intimately dependent upon the heat

flux and wind speed, the non-neutral temperature, moisture, momentum profiles require a knowledge of that which one is attempting to

calculate. In practice, a solution to this problem is achieved by a process

of iteration, as in CM, or by simply neglecting the stability corrections.

Immediately adjacent to the surface, eddy transfer of atmospheric

00

si

quantities becomes quite inefficient and the process of diffusion is

carried out by a combination of eddy, molecular and (in the case of

heat) radiative processes. This near-surface transfer, discussed by

Klaassen( 1978) and others, is itself highly dependent upon the nature of

the surface, particularly the roughness. Large values of the near-surface

resistance allow large gradients of the temperature and humidity to be

established at the ground-air interface. The correct values for these

near-surface resistances are unknown in most cases, being highly

dependent on the details of the surface canopy. In most models the

near-surface resistances are simply included in the bulk atmospheric

resistance to eddy diffusion.

Various limiting assumptions are made in all models, the most

serious of which, in the case of one-dimensional models, is the neglect of

advection. Advection can be considered to be of two types, large-scale

and local. Large-scale advections occur as the result of gradients

(temperature, moisture and wind) which exist over a broad area. Local

advection occurs as the result of horizontal gradients in atmospheric

properties which exist as the result of spatial variations in the surface

heating imposed by variations at the surface. Although it is possible to

minimize the effects of large-scale advections by simply choosing to

investigate situations when the meteorological conditions are appropriate, the small-scale advections are inherent in the nature of inhomogeneous surfaces and their neglect will tend to underestimate the

magnitudes of the atmospheric fluxes in the model and may, in some

instances, when vegetation is surrounded by expanses of arid terrain,

result in the calculated fluxes being of the wrong sign (Brakke et al.,

1978). Our own experiences suggest that neglect of advection does not

seriously degrade the results.

Another limitation which is particularly important in predictive and

analytic models lies in the specification of various internal parameters,

such as roughness, albedo, and the ambient meteorological conditions.

In order to achieve a tractable solution a relatively few number of

unknowns are allowed. In analytic models, such as that of Price (I982a,

1982b), the atmospheric parameters, temperature, moisture and wind,

are determined as daily averages. In truly predictive models atmospheric parameters are specified as initial conditions, whereas in analytic

models a single set of daily averages must be provided from large-scale

data. These data must be obtained from soundings and weather maps,

and may not precisely represent the real atmospheric conditions at any
234 T. N. CARLSON MODELING SURFACE ENERGY BALANCE 235

given pixel point. Even more difficult to specify is the initial temperature profile in the ground including the substrate reservoir temperature which is presumed to remain a constant lower boundary

condition. Tests with the CM show that the night-time temperature is

sensitive to the value of temperature at the lower substrate boundary

although the initial temperature profile in the layer between the

substrate reservoir and the surface is not a significant source of

uncertainty. Deardorff (1978) shows, in fact, that ihe depth of the

substrate reservoir is not an arbitrary choice. Moreover, the calculated

surface temperatures are somewhat affected in predictive models by the

vertical grid spacing, particularly in the upper substrate layer. Analytic

or diagnostic models do not suffer from such uncertainty, being

independent of an explicity substrate formulation, but they are more

afflicted by uncertainties in the atmospheric conditions. In addition to

the somewhat arbitrary manner in which albedo, roughness and other

model parameters are assigned, the primary model unknowns, moisture

availability and thermal inertia, are presumed to be invariant in time;

Jackson's (1973) data indicates that the fractional amount of soil

moisture may possess significant diurnal variation at the surface but it

is relatively constant when averaged over typical vegetation rooting

depth.

A further source of error, which is numerical in origin and peculiar to

time-dependent models, is due to the method of inverting the model to

calculate M, P and other parameters. In the CM, the information

contained in Figure 4 is expressed by a series of second-order multiple

regression equations. Regardless of how the model output is expressed,

however, a certain amount of inexactness occurs in deriving the

governing parameters. Raffy and Becker (1984) address the problem of

model inversion, maintaining that with proper constraints, an accuracy

of a few percent is achievable. For the CM a 5 to 10 percent inversion

error is typical for determining M.

(b) Measurement error

Measurement error can be divided into two classes; that arising from

sensor error and that from uncertainties introduced by the intervening

atmosphere and by the substrate itself. Sensor error is often quoted as a

noise equivalent T (called the NE&T), which is usually much less than

1°C. Sensor drift, which is often unknown, may be quite large. HCMM,

lor example, was found to have a 5.5:C calibration error which

is thought to be sensor drift which occurred shortly after launch.

To a great extent, however, absolute calibration errors can be

eliminated by considering temperature differences rather than absolute

temperatures in the model, as in analytic models, in the three-image

method of Polansky (1982) or in the method of Wetzel and Atlas

(1983) who treat the rate of morning temperature rise as their measured

variable.

Atmospheric attenuation can introduce a more serious error in the

temperatures than thermal noise, even in the water vapor window

region customarily used in thermal scanners. The relationship between

the water vapor correction and surface temperature is almost linear

with surface temperature over the range of temperatures normally

measured and it is exceedingly sensitive to the static stability and

moisture content near the ground. The correction may be as much as

several degrees centigrade or more during the day but can be negative

under stable night-time conditions (Nieuwenhuis, 1979; Price, 1983).

Since the atmosphere is seldom homogeneous with regard to moisture,

sizeable temperature errors, possibly amounting to a degree or more,

can arise from uncertainties in the water vapor correction. These errors

are magnified in moist atmospheres. Error also can be introduced by

neglect in horizontal variations in the surface emissivity, Although

emissivities of most natural surfaces such as vegetation are very close to

1.0, an error of 0.01 corresponds to an error in the measured blackbody

temperature of up to 0.75 C. Oke (1972) suggests that there may be an

effective decrease in ground emissivity and in albedo as the result of the

blocking of outgoing long and short wave radiation over rough surfaces

such as those covered by buildings. Over certain types of dry surfaces,

the ground emissivity may be significantly lower than 1.0.

Perhaps the greatest measurement problem is due to the presence of

cloud, both seen and unseen. Figure 15 is an illustration of how a

predictive model behaves when a cloud, defined as a reduction in the

net surface radiation (Rn) of 60 per cent, is imposed suddenly in the

model for one hour between 1100 and 1200 local time. Total recovery of

the surface temperature to the cloud-free case never quite occurs,

although by 1500 local time, 3 hours after the cloud has vanished, the

. residual error in temperature is less than a degree. It is evident that even

if cloud is absent at the time of satellite observations, the presence of

cloud at any other time can influence the surface temperature.
236

330

320

T. N. CARLSON

300

Q.

S.

UJ

290

280,

= 0.05 CAL/CM'K SEC*

No cloud

Cloud (11-12 LSI)

9 10 II 12 13 14 15 16 17 18 19 20 21 22 23 24 01 02 03 04

TIME (LST)

FIGURE 15. Simulated surface temperature for two values of M and a P of

0.05 cal cm"1 K "'s'"1 for clear skies throughout the day (solid curves) and for a case

when a cloud decreases the net radiative flux by 60% between 1100 and 1200 LST

(dashed lines branching after 1100 LST). The vertical lines at 1400 and 0200 LST denote

the approximate HCMM image times. Model initial conditions same as for Figure 3.

Moreover, the presence of undetected cloud in the form of thin cirrus

streaks or small cumulus can lead to anomalously cool temperatures

which bias the results in a manner which is not necessarily uniform in

time or space. To some extent, obviously cloudy areas can be ignored,

as in the scalloped regions of Figures 10-12. The presence of cloud at

time other than those of the satellite measurements cannot be determined easily, however. In our experience, it is very rare to find a

regional-scale scene completely free of clouds over an entire day. Wetzel

and Atlas'(1983) use of the morning rate of temperature rise minimizes

but by no means eliminates, the problem of cloud. Satellites such as

GOES afford a greater freedom in the choice of measurement times but

they suffer more from cloud contamination because of their lower

resolution with respect to that of HCMM or the NO A A vehicles.

Diagnostic models, of course, are least affected by cloud but more

sensitive to the need for an accurate water vapor correction.

MODELING SURFACE ENERGY BALANCE 237

One inherent error in all satellite measurements is that due to

averaging of radiances within individual pixels. Price (1982a) addresses

the problem of deriving large-scale averages of surface parameters from

an array of individual pixel measurements. He reasons that averages of

the derived surface parameters may not necessarily yield the correct

average surface fluxes in a model. Similarly, individual pixels contain a

multitude of surface elements, whose total emittance is integrated in

some fashion by the sensor to yield a single temperature measurement.

Although CM maintained that the integrative nature of a pixel

measurement is an advantage because it allows one to define an

effective radiating temperature of the surface, there are instances when

that temperature can be misleading and lead to erroneous values in a

model when large variations in the surface temperature and surface

properties exist within a pixel as, for example, when a body pf cool

water lies adjacent to hot, dry ground. Errors generated by surface

inhomogeneities are generally not large, however.

Registration errors in satellite images can produce serious pattern

distortion in the vicinity of large surface temperature gradients and can

lead to fictitious patterns of the derived model parameters where there

are strong gradients in surface character. A careful analysis of ground

control points can minimize registration error but it is unlikely that a

pair of images can be rectified to identical ground coordinates to within

an average error of one or two pixels. Registration error most seriously

affects models which make use of more than one image but this error

probably becomes relatively less important as the scale of analysis and

the degree of image smoothing is increased.

Finally, a potentially serious source of error arises from the presence

of non-uniform terrain height and terrain slope. While it is theoretically

possible to correct for incident solar radiation on a sloping surface,

knowing the elevation and aximuth angles of the slope at each point

(Watson, 1975), the implementation of such a correction is cumbersome

and perhaps futile in view of the equally deleterious effects of terrain

slope on the validity of the flux equations. Moreover, since temperature,

moisture and wind vary with height in some fashion, the ambient

meteorological parameters used in a model would need to be adjusted

accordingly in order to be consistent with the slope corrections.

Sensitivity tests performed with solar models over sloping terrain

suggests that the temperature errors due to terrain slope become

crippling only when the slope angle exceeds about ten degrees.
238 T. N. CARLSON

(c) Overall impact of error on the results

It is clear that errors in the derived moisture availability and thermal

inertia are dependent on the type of model and the scale and degree of

smoothing of the thermal images. Although no definitive assessment of

the total error on the results can be made for this reason, a reasonable

estimate for the net error of predictive or analytic models is likely to lie

between one and two degrees centigrade. It is quite probable that the

net random error in satellite measurement and image rectification is

also between one and two degrees centigrade, a value of which has also

been suggested by Boldyrev and Kharmarink (1973) as a representative

lower limit for satellite temperature sensor errors. Consequently, an

effective but probably irreducible error in the derived values of M and P

is about plus or minus 0.1-0.2 and 0.01-0.02 cat crrT2 s"' K~' ,

respectively.

The effects of a random 2°C error on M and P can be seen by

inspection of Figure 4, in which the isotherms have been drawn at two

degree intervals. Solenoids formed by the intersection of day and night

temperatures therefore form a typical "error space" for both M and P.

Evidently, serious or crippling errors can arise under relatively moist

conditions, especially where P is large. Errors are relatively small over

dry terrain where P is small. Under some meteorological conditions,

however, the error solenoids become very large near values of M = 1.0

so that slight temperature errors can produce unreasonably large values

of M where the terrain is moist.

The host of model and measurement error limit the accuracy of the

derived parameters but also justify many simplifying assumptions made

in the various methods, such as the use of large-scale meteorological'

data for initial conditions, the neglect of advection when the atmospheric gradients are small, the neglect of higher order components in

the Fourier expansion, the choice of a lower substrate boundary

temperature from climatological data, etc. Similarly, no single source of

the two degree temperature measurement error can be identified as

being the main contributor.

Both the predictive and analytic models require either two or three

satellite temperature measurements over the duration of one solar cycle.

The relative importance of any error magnifies error in the results,

however, as the difference in temperature between image pairs decreases; the effect of model and measurement error on the results

become overwhelming when these temperature differences are small.

MODELING SURFACE ENERGY BALANCE 239

Consequently, as Wetzel and Atlas (1981) and Polansky (1982) demonstrate, there are relatively narrow time (and perhaps seasonal) windows

within which satellite measurements can prove useable. Sensitivity tests

with the model CM (see Polansky, 1982) show that a suitable image pair

can be made only when the daytime image is made close to solar noon

(1130-1500 local time) and the other image made either the following

night (1100-0300 local time) or during the early morning, preferably

one to two hours after sunrise (0730-0900 local time for midwestern

summertime images). The three-image method of Polansky (1982),

while capturing more of the diurnal temperature variation than the

two-image method used by Wetzel and Atlas (1983) with GOE.S and by

CM with HCMM, is also subject to greater uncertainties due to

measurement and image registration error.

6 CONCLUSIONS

It is clear that despite limitations of the IR method, reasonable patterns

of surface moisture and thermal inertia can be determined. Patterns of

surface moisture or heat flux are probably most valid over flat, arid,

sparsely vegetated terrain under conditions of weak large-scale advection, few clouds and strong sunshine. A primary model limitation is the

inability to represent the vertical transfer of heat, momentum and

moisture properly over complex terrain, such as forests or cities, and

over deep water bodies. In regard to measurement, the greatest source

of error lies in the interference by clouds, both seen and unseen, and the

presence of other moisture inhomogeneities in the atmosphere.

Both the predictive and analytical techniques offer the greatest

promise for use in remote soil moisture analysis. Because of the various

sources of error, it is unlikely that predictive models are demonstrably

superior to analytic ones, even with the fuller treatment of the

atmosphere (Hechinger et «/., 1982). Regardless of the technique used to

derive soil moisture or thermal inertia, it is unlikely that the derived

moisture values are correct to within plus or minus 10-20 per cent.

Thus, moisture availability, which varies in nature between 0 and 0.1,

cannot be determined to within about plus or minus one-half to one

category in a range of four or five categories which one can designate as:

extremely dry (0.2 or less), moderately dry (0.2-0.4), neither dry nor

moist (6.4-0.6), moist (0.6-0.8).and very moist (0.8 or greater). In the
240 T. N. CARLSON

final analysis, the purpose of a soil-atmosphere model is to serve as a

rather imperfect filter of extraneous atmospheric noise embedded in a

rather ambiguous measurement and to allow that measurement to be

replaced by a purer representation of the soil moisture.

7 PERSPECTIVES

The moisture availability patterns presented in Figures 6, 11 and 14

correlate significantly with antecedent rainfall and represent an effective

soil moisture parameter which, when inserted into a boundary layer

model, will presumably yield the measured surface temperatures and

the correct surface evaporation and sensible heat fluxes. Heilman et al.

(1976) and Heilman and Moore (1980) have demonstrated not only that

there is a strong correlation between soil moisture and the remotely

determined surface temperature response over grassland but that those

measured surface temperatures can be used to predict crop yields.

Recent numerical modeling experiments (McCumber, 1980; Shukla and

Mintz, 1982; Benjamin, 1983) underscore the importance of soil

moisture in prediction of both large and small-scale atmospheric

circulations. Moreover, soil moisture is undeniably a vital parameter

for agriculture and hydrology.

The question is not whether soil moisture is a useful parameter but

whether the soil moisture values derived from the infrared method can

be sufficiently detailed and accurate to be of use and whether the

information derived from the satellite can be delivered efficiently to

potential users. Much more investigation must be done in order to

assess the applicability and practicality of the method. Interpretation of

the meaning of the soil moisture parameter must remain tentative until

more is understood about it. Specifically, several theoretical problems

need to be addressed:

1) How is M defined in a vegetative canopy or over other complex

surfaces, especially where the radiating surface lies a significant distance

above the ground? How can the heat transport be parameterized within

the canopy and substrate without resorting to in-situ measurements

and still achieve a closure?

2) To what extent is the temperature of the effective radiating surface

MODELING SURFACE ENERGY BALANCE 241

affected by ventilation when the radiating surface is at some distance

above the ground?

3) Does the moisture parameter vary significantly during the day as

plant stomata open and close in response to a variety of stresses? What

rooting depth does the soil moisture parameter represent?

4) Are the values of evapotranspiration and sensible heat flux

calculated with the derived .V/ fields essentially correct even if the exact

nature of the surface cannot be defined or realistically modeled?

5) What resolution of the satellite is necessary to achieve optimum

results and what scale of analysis yields the best agreement with ground

truth measurements? Is the higher resolution of a satellite such as

HCMM desirable (compared to that of GOES), as Polansky (1982)

suggested, or will the derived soil moisture parameter prove more useful

when analyzed on a large scale with relatively crude resolution, as

Wetzel and Atlas (1983) seem to suggest?

At present the institution of an operational remote soil moisture

analysis program is technically, if not practically, feasible. The chief

impediments to the operational use of the infrared method are (1) lack

of rapid acquisition and alignment of satellite sub-images, (2) the

presence of cloud, and (3) the necessity of incorporating large-scale

meteorological data into the models and, therefore, the requirement

that numerous sub-images, each corresponding to a separate weather

regime or radiosonde station, be analyzed.

Our experience suggests that even with the problem of clouds, a

portion of a designated target area, say the Great Plains, could be

mapped each day using either GOES or NOAA satellite data. With the

aid of continuity, an updated pattern of M could be determined every

several days and represent a weekly average in much the same way that

the Crop Moisture Index currently represents a highly smoothed and

time-averaged parameter. (The analyses would be performed only over

relatively flat terrain.)

Remote sensing of soil moisture is potentially a very valuable tool,

the exact value of which remains to be determined. Highest priority in

future work on this problem should be placed on facilitating image

acquisition and alignment and evaluating the results of existing models.

Further model improvement should await the acquisition of ground

truth information since it would be difficult to evaluate any theoretical
242 T. N. CARLSON MODELING SURFACE ENERGY BALANCE 243

innovation in a model without independent measurements and since

various technical difficulties are more pressing and produce errors

which may greatly exceed any likely model improvement. Such model

improvement should concentrate on parameterizing plant canopies in a

manner that allows the solutions to be closed with available satellite

and large-scale meteorological data.

Acknowledgements

I would like lo lhank my students and associates, Don Dicristofaro, Paul Kocin, Eileen

Perry and Arthur Polansky for their help with the image analysis and model execution.

This research was sponsored by NASA under grants No. NCA2-09589-201 and No. NAG

5-184.

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