Temperature distribution under radiation frost conditions in a central Pennsylvania valley

AgriculturalMeteorology - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands

TEMPERATURE CONDITIONS

DISTRIBUTION

IN A CENTRAL

UNDER

RADIATION

PENNSYLVANIA

FROST

VALLEY

A. HOCEVAR t AND J. D. MARTSOLF Pennsylvania State University, University Park, Pa. (U.S.A.)

(Received October 25, 1968) (Resubmitted August 31, 1970)

ABSTRACT HOCEVAR, A. and MARTSOLF,J. D., 1971. Temperature distribution under radiation frost conditions in a central Pennsylvania valley. Agr. Meteorol., 8: 371-383. Air temperatures, measured with vehicle-mounted thermistor thermometers, are presented for traverses across a broad Pennsylvania valley under radiation frost conditions. The temperature range observed over the breath of the valley on clear, calm mornings was often as much as 10°C or 18°F. Comparisons of the temperature distributions between mornings indicated that the patterns were quite similar under cool, calm and clear conditions. This was interpreted as justification for a radiation frost condition category. Most of the variation in air temperature could be explained by the relative elevation above the bottom of the basin confining the cold air lake. A mean change in temperature of +6.2°C per 100 m change in relative elevation (or +3.4°F/100 ft.) was found to exist near dawn under c a l l and clear conditions. This value is suggested for approximating the relative frost danger from contour maps of similar valleys in which the distribution of temperature is unknown. INTRODUCTION L a r g e t e m p e r a t u r e differences are k n o w n to exist in m o u n t a i n a n d valley t o p o g r a p h y especially on calm, clear nights. Studies in which bicycles, m o t o r cycles, a n d a u t o m o b i l e s were used as p l a t f o r m s f r o m which to observe air temperatures a l o n g traverses a n d at grid p o i n t s have been reviewed b y SCnNFLLE (1965) a n d GFIGER (1965). WOLFE et al. (1942, 1943, 1949) r e p o r t e d large m i n i m u m t e m p e r a t u r e variations within the m i c r o c l i m a t e o f a n e a r b y O h i o valley. The objective o f this study was to observe the t e m p e r a t u r e d i s t r i b u t i o n in a typical P e n n s y l v a n i a valley u n d e r r a d i a t i o n frost c o n d i t i o n s using v e h i c l e - m o u n t e d t h e r m i s t o r t h e r m o m e t e r s a n d to test the thesis t h a t the t e m p e r a t u r e v a r i a t i o n s can be explained b y the relief o f the valley as a first a p p r o x i m a t i o n . One o f the needs for m i n i m u m - t e m p e r a t u r e d i s t r i b u t i o n i n f o r m a t i o n on the mesoscale is for h o r t i c u l t u r a l site selection. G o o d site selection is the best m e t h o d o f p r o t e c t i n g crops f r o m frost damage. A k n o w l e d g e o f the t e m p e r a t u r e field over 1 Visiting Agricultural Climatologist from University of Ljubljana, Ljubljana (Yugoslavia). Agr. Meteorol., 8 (1971) 371-383

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A. HOCEVARAND J. D. MARTSOLF

locations containing sites under consideration or an ability to predict this field is a prime prerequisite to the selection of good sites. Advances in the linearization of thermistor circuity has led to the use of compact hand-held or vehicle-mounted thermometers which respond rapidly to changes in air temperature (e.g., BEAKLEY, 1951; BLACKADAR, 1964). A recent report by LONGLEYand Lou~s-BYNE (1967) described a similar use of a vehiclemounted thermistor thermometer in studying frost hollows in Canada. METHOD Two commercial models of thermistor thermometers and one constructed after a description by BLACKADAR(1964) were installed in automobiles with their probes mounted on the right-hand front fenders about 1 m from the ground. The cylindrical probe approximately 25.4 mm long and 2.5 mm in diameter (Atkins No.3) was mounted vertically to minimize the radiant heat loss to the cold sky and to maximize the convective exchange with the horizontal flow by the vehicle.

Fig.1. Thermistor thermometer probes mounted in tandem. From left ro right they are the Blackadar (Fenwal KA31LI) probe, the Westemp probe, the standard Atkins probe and the Atkins small bead probe. The latter probe projects approximately 12 cm forward of the VW parking light. ,4gr. MeteoroL, 8 (1971) 371-383

TEMPERATURE DISTRIBUTION IN RADIATION FROST

373

Convective transfer from such a cylinder (GATES, 1962) is expected to be three orders of magnitude greater than the nocturnal radiant heat loss when the air speed is as much as 16 km/h (10 mph) and the probe's surface departs 1 °C from air temperature. The Westemp model employed a spheroidal epoxy-coated thermistor of about 2.5 mm in diameter. Both probes were left unshielded and observations were taken only when the vehicle was and had been in motion. The resulting observations are moving averages of the temperature of a horizontal column of air through which the sensor had passed. The extent to which the air temperature fluctuations are smoothed is a function of the time constant of the sensor.

To determine the effect of the coated probes on temperature sensings, the two probes described in the previous paragraph were exposed in tandem with an

Fig.2. A reproduction of a topographical map of a section of Nittany Valley, Pa., with contour lines at 100-ft. intervals. Check points along the traverses at which temperature observations were made are indicated by symbols with every fifth symbol numbered. Basin bottoms are indicated with symbols and a capital letter.

Agr. Meteorol., 8 (1971) 371-383

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A. HOCEVARAND J. D. MARTSOLF

uncoated, spherical, Atkins thermistor of approximately 1.6 mm in diameter (Fig.l). It was assumed that the small bead thermistor followed the air temperature rather closely. Observations using the three probes were compared through 93 check points. The smoothing of the temperature fluctuation due to the time constant of even the steel-jacketed probe was observed to cause less than 0.5 °C errors in the readings even in abrupt dips in elevation. The traverses followed three routes through the relief of Nittany Valley, a broad valley bordered by narrow ridges in central Pennsylvania. Fig.2 presents a map view of the contours of the section of this valley on which the airport, Circle Ville, and Pennsylvania Furnace traverse routes are indicated. References on the

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Fig.4. The variation of temperature for three mornings in relation to the relief along the Pennsylvania Furnace traverse. contours are in feet above sea level. Fig.3 and 4 contain vertical sections of the relief for two of the traverses. The numbered dots on these reliefs indicate the location of the check points to which temperature observations were referenced. These numbered dots may be compared to those on the map in Fig.2 for orientation with the terrain features. The traverses were run during radiant frost conditions. Using a facsimile weather chart recorder monitoring the U.S. Weather Bureau prognostic charts, consultation with members of the Pennsylvania State University, Department of Meteorology, and personal observations of the calmness and clearness of the atmosphere, the "typical radiation frost conditions" were chosen to run the traverses. While it was quite obvious that the traverse should be run on some nights it was a rather arbitrary decision on others as might be expected. The final decision as to whether to run on one of these "border line" nights was made independently by the authors just before the run. A glance at the areas designed "not run" in Table I should indicate some of the nights that were "border line" cases. The traverses were run during the hour just before sunrise. It was assumed that the air temperature change with time at a given location was minimal during Agr. Meteorol., 8 (1971) 371-383

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A. HOCEVARAND J. D. MARTSOLF

TABLE I STATISTICS COMPUTED USING AVERAGE TEMPERATURE VERSUS RELATIVE HEIGHT DATA FROM INDICATED TRAVERSES IN NITTANY VALLEY, PA.

Date

Correlation coefficient

Regression coefficient [°6"/100 m]

1967 May 31June 2

University Airport traverse 0.96i

1968 Feb. 27 Mar. 7 8 26 27 31 Apr. 2 6 7 12 13 16 17 20 28 29 May 2 6 7 8 June 5 6

Circle Ville 0.70 0.50 0.73 0.21 0.63 (not run) 0.49 0.67 (not run) 0.74 0.63 (not run) 0.75 0.71 0.74 0.80 (not run) 0.41 0.67 0.67 0.62 0.79

Standard error [°C/lO0]

6.01 i

0.7i

traverse 4.37 2.00 4.37 2.19 4.56

0.73 0.55 0.73 1.64 0.91

3.46 3.09

1.09 0.55

5.83 4.92

0.73 0.91

6.01 6.56 4.55 6.01

0.73 0.91 0.55 0.73

1.46 3.64 5.28 3.10 6.01

0.55 0.55 0.91 0.36 0.73

Correlation coefficient

Regression coefficient [°C/IO0 m]

Standard error [°C/lO0 m]

Pennsylvania Furnace traverse (not run) (not run) (not run) 0.63 3.28 0.91 (not run) 0.92 6.55 0.55 0.80 6.38 1.09 0.76 4.74 0.91 0.71 4.01 0.91 0.94 6.74 0.55 (not run) 0.68 4.01 0.91 0.86 8.38 1.09 0.88 9.29 1.09 0.61 2.92 0.73 (not run) 0.29 4.19 2.91 (not run) 0.58 6.01 1.82 0.83 4.55 0.55 (instrument used on C.V. traverse) (not run)

1 Average for five runs. this hour. This change in air temperature with time was checked by c o m p a r i n g the temperatures measured at a cheek p o i n t passed two or three times d u r i n g the traverse. The temperature observation for a given check p o i n t was the average o f the observation taken going through the p o i n t a n d that taken while coming back through the location from the opposite direction. This procedure would seem to cancel out bias due to the "lag" o f the p r o b e especially o n slopes where the temperature gradient is often quite steep. The traverses were r u n at an average speed of a b o u t 40 k m / h (25 m p h ) with some variation in speed necessitated by road conditions a n d intersections. The relative height above a basin's b o t t o m was chosen as a n i n d e p e n d e n t variable with which to test the thesis that the temperature distribution near d a w n Agr. Meteorol., 8 (1971) 371-383

TEMPERATURE DISTRIBUTION IN RADIATION FROST

377

on radiation frost nights is largely explained by relief. The bottoms of the basins used in this analysis are indicated by capitalized letters in Fig.2. These letters identify the basin bottom from which the relative elevation for each check point is recorded in Tables I and II. The relative heights of the check points were interpolated from a 1:25,000 scale topographic map and used in the correlation and regression analyses versus the temperature observations. RESULTS

A thermistor thermometer may be constructed (BLACKADAR, 1964) or obtained commercially quite economically. Vehicle-mounted thermistor thermometers were found quite suitable for observing temperature distributions over areas as large as 5 x 15 km. The original data for four runs over two traverses are presented in Tables II and III. Data of this type for five runs through eleven check points per run over a traverse near the University Airport, eighteen runs through fiftyeight check points over a cross-valley traverse through Circle Ville and thirteen runs through twentyeight check points over a cross-valley traverse through Pennsylvania Furnace were analyzed using computer library programs (RoBeRTS, 1964; ROBERTS and WINK, 1964) and the results summarized in Table I. The variation of observed air temperature in relation to relief is illustrated graphically for the cross-valley traverse in Fig.3 and 4. The horizontal axes of these graphs represent distance along the traverse route, which is not an exact cross-section of the valley at that point since the roads do not follow a straight line (Fig.2). The vertical axes of Fig.3 and 4 represent the elevation above mean sea level on the left and the air temperature on the right. The smooth curves representing the variation in temperature with distance resulted from drawing lines through 58 points per date in Fig.3 and through 28 points per date in Fig.4. These points in turn were plotted from the average temperature observed for that location on that date. The average was one-half the sum of the observed temperature going in one direction on the traverse and that observed while returning in the opposite direction. Typical variation in the temperatures observed at one location can be seen in the original data for four rather typical traverses recorded in Tables II and III. The vertical broken line in Fig.3 calls attention to but one of the "thermal belts" evidenced by the observations. The correlation coefficients between the temperature observations on different days for which a correlation coefficient for temperature and height was at least 0.70 on the Circle Ville traverse are reported in Table IV. The correlation coefficient between temperature data for different days for which the correlation of temperature with height was at least 0.75 are reported in Table V.

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TEMPERATURE DISTRIBUTIONIN RADIATIONFROST TABLE IV

CORRELATION COEFFICIENTS BETWEEN TEMPERATURE OBSERVATIONS ON DIFFERENT DAYS FOR CIRCLE VILLE TRAVERSE

Mar. Apr. Apr. Apr. Apr. Apr. June

8 12 17 20 28 29 6

Feb. 27

Mar. 28

Apr. 12

Apr. 17

Apr. 20

Apr. 28

Apr. 29

0.83 0.86 0.88 0.83 0.78 0.88 0.84

0.94 0.90 0.83 0.78 0.90 0.89

0.92 0.89 0.84 0.94 0.94

0.98 0.94 0.96 0.89

0.94 0.97 0.88

0.91 0.83

0.94

TABLE V CORRELATION COEFFICIENTS BETWEEN TEMPERAUTRE OBSERVATIONS ON DIFFERENT DAYS FOR PENNSYLVANIA FURNACE TRAVERSE

Apr. 2 Apr. 6 Apr. 12 Apr. 17 Apr. 20 May 8

Mar. 31

Apr. 2

Apr. 6

Apr. 12

Apr. 17

Apr. 20

0.81 0.85 0.98 0.90 0.91 0.89

0.95 0.83 0.93 0.94 0.92

0.87 0.95 0.94 0.93

0.93 0.94 0.92

0.99 0.98

0,97

DISCUSSION The basic mechanism in the creation o f large air temperature variations nocturnally in rough terrain is the relative buoyancy of air cooled by heat transfer to radiantly cooled surfaces. Observations indicate that cold air drainage is governed by features of the relief (e.g., MASON, 1958). Theories (DEFANT, 1933; PRANDTL, 1942; DEFANT, 1949; FLEAGLE, 1950) describe the density flow resulting from radiant cooling as a function of slope and roughness. Cold air draining down slopes accumulates in basins which fill as cold air lakes. Near dawn, when minimum temperatures occur, the degree to which these basins have filled is primarily dependent upon their volume. I f the slope and roughness of the basins are assumed to be constant the relative height above the basin bottom to sites on the basin sides becomes a parameter describing the basin's volume. Wind and cloudiness are the two variables indicated by these theories that play major roles in determining the temperature near the ground. In the cases Agr. Meteorol., 8 (1971) 371-383

382

A. HOCEVARAND J. D. MARTSOLF

studied the wind was observed to be more variable and harder to predict than the cloudiness. Consequently the variation in the correlation of temperature with relative height exhibited in Table IV is attributed more to the variation in the degree of calmness than to the turbidity of the atmosphere. The higher correlation coefficients for the Pennsylvania Furnace traverse data than those of the Circle Ville traverse data (Table IV) are possibly due to the relative size of the relief features (Fig.3, 4). The average relative height for the former is 18.l m and for the latter, 38.6 m. A curvilinear increase in temperature is expected with height under inversion conditions; i.e., temperature gradient is largest near the ground and decreases with height. A correlation of temperature of 1.0 with height describes a linear increase in temperature with height. The linear assumption simply works better for smaller increments of height. This difference in correlation between the traverses may be enhanced by the presence of "thermal belts" on the slopes of some of the larger terrain features. These are departures from linear increases in temperature with increases in relative height (notice check points 11 and 12 in Fig.3 and check point 26 in Fig.4) and would therefore decrease the linear correlation. The pronounced effect of relatively small dips in the terrain on temperature is illustrated by the temperature depressions over check point 12 in Fig.3 and check point ! 3 in Fig.4. The Nittany Valley, Centre County, Pennsylvania, is representative of the broad valleys separated by narrow ridges that characterize the agriculturally fertile region of the Appalachian Mountains passing from SW to NE through Pennsylvania. To facilitate the prediction of temperature distributions over valleys similar to Nittany Valley the expected change in temperature for a given change in relative height is indicated by the regression coefficients listed in Table I. Making an arbitrary selection of those cases in which the correlation of temperature with relative height was at least 0.7, the regression coefficient for 538 observations was found to be 6.2 + 1.8 ° C/100 m (3.4 _+ 1.0°F/100 ft.) at the 95 ~,~ probability level. This value is suggested for use in those cases in which the valleys are of similar topography to the Nittany Valley in Pennsylvania. Tables IV and V reveal good correlation between the temperature distribution of some of the more typically radiation frost conditions one with another. The persistence of the temperature pattern along the traverses under calm and clear conditions is convincing evidence that the temperature pattern is dependent upon factors that are invariable in space. The relief is such a factor. Therefore, the high correlation of temperatures between days (Tables IV and V) strengthens the argument that relief, i.e., topography, is a prime parameter in the determination of minimum temperatures under radiant frost conditions. The high correlation between days is interpreted as further justification for the use of a general category of conditions termed "radiant frost conditions" to describe the situation that seems to be rather predictable in terms of the terrain on clear, cool and calm nights.

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TEMPERATURE DISTRIBUTIONIN RADIATIONFROST

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ACKNOWLEDGEMENTS The aid that Dr. A. K. Blackadar provided in the calibration o f the l a b o r a tory-constructed thermistor t h e r m o m e t e r used in a p o r t i o n of this study was greatly appreciated. This paper is published u n d e r the P e n n s y l v a n i a State U n i v e r sity, Agricultural Experiment Station Journal, Series No. 3464. REFERENCES

BEAKLEY,W. R., 1951. The design of thermistor thermometers with linear calibration. J. Sci. Instr., 28: 176-179.

BLACKADAR,A. K., 1964. A remotely indicating electric thermometer for amateur construction. Weatherwise, 17(2): 66-68.

DEFANT, A., 1933. Der Abfluss schwerer Luftmassen auf geneigtem Boden nebst einigen Bemerkungen zu der Theorie station~irer Luftstr6me. Sitz. Ber. Preuss. Akad. Wiss., Math. Naturwiss. KI., 18: 624-635. DEFANT, F., 1949. Zur Tbeorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. Arch. Meteorol. Geophys. Bioklimatol., Ser. A, 1: 421-450. FLEAGLE,R. G., 1950. A theory of air drainage. J. Meteorol., 7: 227-232. GATES, D. M., 1962. Energy Exchange in the Biosphere. Harper, New York, N.Y., 151 pp. GEIGER,R., 1965. The Climate Near the Ground. Harvard Univ. Press, Cambridge, 4th ed., 611 pp. LONGLEY,R. W. and LOUIS-BYNE,M., 1967. Frost hollows in west central Alberta. Can. Dept. Transp., Circ., 4532:15 pp. MASON, B., 1958. An example of climatic control of land utilization. Proc. Syrup. Eco-Physiol. U.N.E.S.C.O. ArM Zone Res., 11: 188-194. PRANDTL,L., 1942. Stromungslehre. Vieweg, Braunschweig, 384 pp. ROBERTS, i . E., 1964. Linear regression coefficients. Penn. State Univ., Computation Center, Program LNREG 11.3.009. ROBERTS,M. E. and WINK, A. T., 1964. Symmetrical correlation program. Penn. State Univ., Computation Center, Program COREL 11.3.033 (revised). SCHNELLE,F., 1963. Die meteorologischen und biologischen Grundlagen der Frostschadenverhiitung. In: Frostschutz im Pflanzenbau, 1. Bayerische Landwirtschaftsverlag, Miincben, Basel, Wien, 488 pp. SCHNELLE,V., 1965. Die Praxis der Frostschadensverhiitung. In: Frostschutz im Pflanzenbau, 2. Bayerische Landwirtschaftsverlag, Miinchen, Basel, Wien, 604 pp. WOLFE,J. N., WAREHAM,R. T. and SCOFIELD,H. T., 1942. A report on the progress of a three-year study of plants, microclimates and soil conditions at Neotoma. Ohio J. Sci., 42: 145. WOLFE,J. N., WAREHAM,R. T. and SCOFIELO,H. T., 1943. The microclimates of small valley in central Ohio. Trans. Am. Geophys. Union, 24(1): 154-166. WOLFE,J. N., WAREHAM,R. T. and SCOFIELD,H. T., 1949. Microclimates and macroclimate of Neotoma, a small valley in central Ohio. Ohio Biol. Surv. Bull., 41:267 pp.

Agr. Meteorol., 8 (1971) 371-383