The heat balance of apple buds and blossoms. Part II. The water requirements for frost protection by overhead sprinkler irrigation

Agricultural and Forest Meteorology, 37 (1986) 159--174 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

159

THE HEAT BALANCE OF APPLE BUDS AND BLOSSOMS P a r t II. T h e w a t e r requirements for frost protection by o v e r h e a d s p r i n k l e r irrigation P.J.C. HAMER Pomology Department, East Mailing Research Station, Maidstone, Kent (Gt. Britain) (Received November 1, 1985 ; revision accepted January 16, 1986 ) ABSTRACT Hamer, P.J.C., 1986. The heat balance of apple buds and blossoms. Part II. The water requirements for frost protection by overhead sprinkler irrigation. Agric. For. Meteorol., 37:159--174. Measured changes in the temperatures of apple fruit buds subjected to water sprinkling for frost protection during natural and simulated frosts were compared with those predicted from heat transfer theory. Agreement was improved when allowance was made for the partial wetting of the buds during the early stages of frost protection and for the consequences of ice accretion, which changed the "bud" dimensions and heat transfer coefficients. The heat balance equation derived to take these factors into account makes possible accurate calculation of the water requirement for sprinkling under varying environmental conditions. INTRODUCTION I r r i g a t i o n s c h e m e s f o r f r o s t p r o t e c t i o n are designed to a p p l y p r e c i p i t a t i o n at t h e rates r e q u i r e d t o s u p p l y s u f f i c i e n t l a t e n t h e a t o f f u s i o n t o t h e b u d s t o p r e v e n t t h e i r t e m p e r a t u r e falling b e l o w a critical level. T h e r e q u i r e d precipit a t i o n rates h a v e b e e n d e t e r m i n e d e i t h e r in t h e field b y an e m p i r i c a l m e t h o d or f r o m h e a t t r a n s f e r t h e o r y . In S o u t h - E a s t E n g l a n d , Rogers a n d M o d l i b o w s k a ( 1 9 6 2 ) f o u n d b y field e x p e r i m e n t s a n d o b s e r v a t i o n o f d a m a g e t h a t in m o s t spring r a d i a t i o n frosts an average r a t e o f 2.5 m m h -1 was r e q u i r e d t o p r o t e c t b u d s against an air f r o s t o f - - 4 ° C . Such a r e c o m m e n d a t i o n is o f t e n b a s e d o n t h e m o s t severe f r o s t w h i c h is likely in a given p e r i o d o f y e a r s a n d is valid o n l y f o r f r o s t s in similar climatic c o n d i t i o n s : even f o r r a d i a t i o n frosts, w i n d speed, n e t r a d i a t i o n loss a n d h u m i d i t y v a r y f r o m o n e f r o s t night t o a n o t h e r . In t h e h e a t t r a n s f e r t h e o r y m e t h o d , p u b l i s h e d values o f t h e h e a t t r a n s f e r c o e f f i c i e n t s o f f i a t plates ( f o r leaves), c y l i n d e r s o r spheres ( f o r b u d s ) are used to c a l c u l a t e t h e e v a p o r a t i v e a n d c o n v e c t i v e h e a t fluxes a n d t h e c o r r e s p o n d i n g rate at w h i c h w a t e r m u s t b e f r o z e n o n t h e p l a n t t o s u p p l y t h e h e a t lost b y c o n v e c t i o n , e v a p o r a t i o n a n d l o n g - w a v e r a d i a t i o n (Businger, 1 9 6 5 ) . This m e t h o d s h o u l d e n a b l e t h e w a t e r r e q u i r e m e n t s f o r f r o s t p r o t e c t i o n t o be p r e d i c t e d f o r a n y e n v i r o n m e n t a l c o n d i t i o n s . H o w e v e r , in n o r m a l p r a c t i c e 0168-1923/86/$03.50

© 1986 Elsevier Science Publishers B.V.

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water is applied continuously from the onset o f a frost, so that it ~.~difficult to validate the calculation. F u r t h e r m o r e , the choice of values for these dimensions introduces a considerable uncertainty which changes ~!c>t (,nty during the season, because the bud shape becomes more complex as it. ()pens and forms an assembly of leaflets and flowers (Hamer, 1985), but als() during the course o f a single frost., due to the build-up of ice around the t)u(~ tn this paper, the terms in the heat balance equation are examined m detail, with particular reference to the effects of ice accretion on t.he buds and considered in relation to the measured precipitation rates required for frost protection. METHODOLOGY The heat balance e q u a t i o n a n d its validation

The q u an tity o f water needed to p r o t e c t buds from frosts of specified severity can be estimated by setting up a heat balance equation for a single bud. To prevent bud t e m p e r a t u r e falling below the level that would cause damage to the tissue (which depends on the developmental stage), heat is added in the form o f latent heat of fusion of ice, Lp (3.35 × l 0 s J kg -1 ). When the water is applied, evaporative cooling will also occur and a term for the latent heat loss by evaporation must be included. The heat balance equation for the p r o t e c t e d bud in terms o f mean energy fluxes (W m -2 ) per unit surface area is thus

~7~ = 17. + Cp + HL

(1)

where /4~ is the rate o f supply o f heat o f fusion,/~p is the net loss of heat from radiation, Cp is the loss o f sensible heat by convect i on and HL is the loss o f latent heat by evaporation. F o r the p r o t e c t e d bud at t e m p e r a t u r e Tp, mean radiative, sensible and latent heat fluxes can be written as Rp

= R.~ + h~(Tp -- T a)

(2)

Cp = hp(Tp -- Ta)

(3)

HL

(4)

= h~(es(Tp)--ea)/7

where Rm is the isothermal net radiation (a loss), T a is air t em perat ure, es(Tp ) is saturated vapour pressure over ice at the t e m p e r a t u r e o f the b u d , e a (mbar) is the vapour pressure in the surrounding air. Here, hr, hp and hv are the heat transfer coefficients for radiation exchange, heat and latent heat, respectively. F o r t em pe r at ur e s near 0°C, hr ~ 4.5 W m -2 K -1 , hv = 1.08 hp (Hamer, 1984a) and t he p s y c h r o m e t e r constant T = 0.64 mbar K -1 . The rate at which water is applied is usually estimated by collection in a gauge with a horizontal aperture, However, the water droplets applied to buds from sprinklers have a relatively large horizontal velocity c o m p o n e n t ,

161

so t hat the buds intercept more water than would be deposited on a horizontal area o f equal cross-section. Businger (1965) i nt roduced an interception factor for the bud, I, defined as the ratio o f the q u a n t i t y of water intercepted by the bud to th a t measured on a horizontal plane. The value of I depends b o t h on the ratio of surface area to cross-sectional area o f the bud and the direction o f water droplets falling on the bud. Normally, irrigation systems are designed to apply a given d e p t h of water per unit time on a horizontal surface, rather t han to supply a particular flux of heat o f fusion. The corresponding precipitation rate, P, can be expressed in mm h -1 by P = I~qf/pwLp

= II~f/93

(5)

where Pw is the density of water ( ~ 103 k g m -3 ). Combining eqns. 1--5 and using the appropriate values of the constants, the required precipitation rate for effective frost p r o t e c t i o n can be written as:

I p = ~-~{(hp + h r ) ( T p -- Ta) + 1 . 6 9 h p ( e s ( T p ) - - e a ) -4- Rni }

(6)

The required precipitation rate thus varies with air t em perat ure, net radiation, vapour pressure and t he efficiency o f water capture and also with wind speed and ice accretion (which changes the characteristic dimension of the bud) since b o t h o f these influence hp. In the following three sections, the variables in eqn. 6 are examined in detail. The first section examines the change in hp as a consequence of ice accretion. Using measurements made in a frost chamber, the coefficient of heat transfer h , and its d e p e n d e n c e on characteristic dimension is estimated. The values are c o m p a r e d with estimates f r om the heat balance eqn. 6. The second section deals with field measurements of precipitation rates, which were varied automatically according to the severity o f the frost. Measurements were made at three sites where the m a x i m u m rates of water application differed. The third section combines the results of the first two sections to estimate heat fluxes during a frost. Frost chamber studies

To simplify th e estimates of hp, measurements were c o n d u c t e d in a frost chamber, producing t e m p e r a t u r e s d o w n to -- 5°C, where the wind speed was constant and the radiative exchange was small (Slater, 1957). An Eintal pressure-regulated minisprinkler ensured a constant t h r o u g h p u t o f water of 0.1 m 3 h -1 (manufacturer's specification). The nozzle was fixed at one side o f the r o o m at a height o f 1.8 m and about 2 m from a fullyd o r m a n t pot-grown apple tree. The flow o f water to the minisprinkler could

162 be interrupted by means of a 24-v AC solenoid valve controlled by a computer-controlled data-logging system (Hamer, 1985). In order to maintain a sufficiently low ambient temperature in the frost chamber, surplus water was removed (Hamer, 1984a). The temperatures of four buds were measured using fine-wire thermocouples, wired in series, inserted into the buds and referenced to air temperature. A calibrated platinum resistance t h e r m o m e t e r measured air temperature in a well-ventilated psychrometer unit to an accuracy of + 0.1°C (Hamer, 1985}. The " w e t bulb" depression was measured over ice using four thermocouples wired in series, encapsulated in a stainless steel tube. An "icewick" was formed by placing the wet bulb in a 16-mm-diameter test-tube containing water. When the water had frozen, the test-tube was removed by applying hand warmth around the tube. Temperature measurements were recorded every 10 s. The precipitation rate, P, was measured prior to the experiment, in nonfreezing conditions, by using specimen tubes placed adjacent to the buds with their mouths horizontal. Each tube was weighed before and after water had been applied for a measured time and the average precipitation rate unit area calculated. The initial characteristic dimension of the apple buds, d, was estimated from the buds used in the temperature measurements. The buds were assumed to be prolate spheroids and the characteristic dimension calculated from measurements of the semi-minor radius, b. For d o r m a n t buds, d = 2.5b (Hamer, 1985). Ice accretion around the bud was not uniform. Consequently, at the end of the experiment two measurements were made at right angles to one another for each bud and the final diameter, dr, determined as the mean of eight readings. Since water was applied at a constant rate, the diameter, dr, of the icecoated bud at time t was estimated as: d t -- d + d f t / t t

(7)

where t t is the total time of the experiment. For apple buds, the normal m o d e of heat transfer is by forced convection (Hamer, 1985). The characteristic dimension d t (cm) and the wind speed, u (m s -1) are related by: h,

= ~{(4.86/dt) + 32.6 ( u / d t } 0"5)

{8)

where ~ is the rate of observed heat transfer of apple buds in the naturally turbulent o u t d o o r environment to that o f a sphere of similar dimension in laminar flow (Hamer, 1985). The coefficient of heat transfer for the ice-coated bud was estimated by solving the heat balance eqn. 6. R e , r a n g i n g terms and assuming that the isothermal net radiation was zero: hp .

{ ( 9 3 P / I ) - - 4.5(Tp -- Ta)~ . . . . . . . . . {(Tp --T~) + 1.69(es(T,) ea)]"

(9)

163

The frequency of wetting was adjusted by trial and error to ensure that most of the surface area of the bud was coated with water, but that run-off did not occur. The interception, I, was estimated from the values of the initial and final bud diameter measurements, d and d~, respectively, making allowance for ice lost due to evaporation. Assuming the water was deposited uniformly over the surface of the bud, the interception (for a spherical bud) was estimated as:

I

=

2Pt/(d~ + d e -- d)

(10)

where de is the decrement in diameter due to evaporative cooling. This was estimated from the flux of water vapour per unit area,/~, calculated in units of g m -2 S - 1 , as: =

hv(es(Tp)

-- ea)/Le7

(11)

where Le is the latent heat of vaporisation of water (2.501 × 106 J k g -1 at 0°C). In eqn. 11, E represents the thickness of ice evaporated and, therefore, the decrement of diameter per unit time (d e ) is twice/~. Estimation of/~ was simplified by using hv = 1.08 hp and e s ( T p ) ~ •(Tp - - T a ) + es(Ta), where A is the slope of the saturation vapour pressure curve at the mean of Tp and Ta. The "loss" of effective bud diameter due to evaporation, de, was then estimated as:

de

-- 4.7 × 10-3hp{A(Tp --Ta) + es(Ta) --ea~

where

(12)

de was expressed in mm h -1 .

Field experiments

Full details of the experimental orchard and instrumentation were given by Hamer (1985). Three sites, each of which consisted of a pair of Cox's Orange Pippin trees on M.26 rootstock, were frost protected using different types of minisprinkler applying water at different rates. The minisprinklers were supported at a height of 2 m in the tree rows between the pairs of Cox trees. The water supplies to the minisprinklers were controlled independently using solenoid valves. Two similar sites were left unprotected as controls. Bud temperatures were recorded at each site using fine-wire (36 s.w.g.) copper-constantan thermocouples inserted into four separate upward-facing exposed buds at mid-tree height (1.1 m). As in the chamber experiment, the thermocouples were wired in series and referenced to air temperature in a well-ventilated psychrometer unit. The unit also housed wet and dry bulb platinum resistance thermometers at each site at a height of 1.1 m. Measurements were made at 10-s intervals using a computer-controlled data-logger. Mean values for 10-min periods were retained by the logger for analysis. The application of water to each site was controlled according to the

164 measured bud temperature. When Tp was above 0~C, no water was appiieci When Tp fell below .... 1=C. water was applied continuously. When T~ wa: between 0 and .[cC, a t.immg sequence applied water for 10 s in every 20~ ~ to ensure that the water in the supply pipe and minisprinkler did no~, fre~z~, The data-logger recorded the length of time each valve was open. Spray was also applied to the frost-protected sites during the daytime (Hamcr, 1986i and the precipitation rates de t e r m i ne d f r om samples collected during the day to avoid errors due to ice accretion (Hamer, 1984a). The continuot,:s preci pl tation rates for frost conditions were taken as the dayt i m e rate mea,~ured at wind speeds less than 1.4 m ~-~. The precipitation rates during frosts were estimated from the measured continuous rates and the record, for the: particular frost, o f the periods for which the solenoid valves were open. Atmospheric long-wave radiation (L~) and long-wave radiation etmtted from the ground ( L ~ were calculated from two net radiometers, one with and the o th er w i t h o u t a cavity (ttamer, 1985), These were m o u n t e d 2.5 m above the u n p r o t e c t e d orchard. RESULTS

Chamber experiment A cycle o f spray application of 10 s on and 30 s off provided sufficient latent heat o f fusion to raise bud t e m p e r a t u r e by about 1--2°C. The buds were wetted sufficiently, but w i t h o u t run-off and there was little rise in chamber temperature. The i n t e r m i t t e n t sprinkling applied 20.2 mm of water in 12.6 h, the precipitation rate for c o n t i n u o u s application being 6.4 mm h - i . The mean initial diameter of the buds, d, was 4.5 mm and the mean final diameter, dr, 18.3 mm. The d e c r e m e n t of effective bud diameter due to evaporation was estimated from eqn. 12. Typical values o f Tp -- T~ (2°C}, e s ( T ~ ) - - e a ( 0 . 2 5 m b a r ) , A (0.35 mbar K -1) and hp ( 2 0 W m -2 K -1) were used to calculate (~e which was estimated as 0 . 1 m m h -I . The accumulated d e c r e m e n t was estimated as 1.3 mm and I, calculated from eqn. 10, as 2.7. The mean wind speed at the position o f the buds, measured by a calibrated hot-wire a n e m o m e t e r prior to the e xpe r i m e n t , was 0.14 m s -1 . The convective heat transfer coefficient for the ice-coated buds was calculated at 15-min intervals, using mean values of (Tp - - T a ) and (es(Tp) -- ea) (eq. 9). The change o f hp with time (o) is p l o t t e d in Fig. 1. The convective heat transfer coefficient expected from the change in diameter o f the ice-coated bud is also p l o t t e d (cont i nuous line in Fig. 1). The e n h a n c e m e n t }, was assumed to be 1.2, the appropriate value for d o r m a n t buds (Hamer, 1985). The estimated values of hp were remarkably similar to those expect ed for s m o o th spheres of similar diameter (eqn. 8) until after about 8 h sprinkling ( 1 2 m m of water applied). B e y o n d this, the estimated values remained constant at ap p r oxi m at el y 2 0 W m -2 K -1, whereas the theoretical value c o n t in u ed to fall.

165

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Fig. 1. T h e c o e f f i c i e n t o f h e a t t r a n s f e r , hp, f o r f r o s t - p r o t e c t e d a p p l e b u d s p l o t t e d against d u r a t i o n o f p r o t e c t i o n (e). Water was applied at a c o n s t a n t rate o f 1.6 m m h -1 t o d o r m a n t buds. T h e c o n t i n u o u s line s h o w s hp c a l c u l a t e d f r o m eqn. 8 a s s u m i n g t h e b u d s to be t r e a t e d as spheres.

Field experiments In the spring o f 1982, there were no frosts of sufficient severity to cause damage to u n p r o t e c t e d buds or flowers. However, on the night of 7/8 March the air t e m p e r a t u r e fell to a m i n i m u m o f - - 4.5° C. At this time the buds were still d o r m a n t so that no frost damage occurred. The measurements of the heat balance and precipitation rates r e p o r t e d here were obtained during this frost. The diurnal courses of net radiation loss, air temperature, wind speed (measured at 1.2 m above ground level) and vapour pressure are shown in Fig. 2. These environmental conditions are typical of those experienced during a radiation frost in South-East England. The large net loss of radiation and th e low wind speed resulted in air t e m p e r a t u r e falling quickly from 3.8 ° C at 18.00 h to - - 0 . 6 ° C at 2 0 . 0 0 h . The air t e m p e r a t u r e cont i nued t o fall and by dawn it had reached a m i n i m u m o f - - 4.5° C. During the night, after an initial rise, th e vapour pressure fell steadily from 5.1 mbar at about 20.00 h to a min imu m o f 4 . 1 m b a r , c o n c u r r e n t with the m i ni m um temperature. In the evening, bud t em pe r at ur e s were below the air temperature. In consequence, sprinkling began at about 19.00 h, before the start of the air frost and continued until after 08.00 h. At all three sites, rates of water application increased as the frost became m or e severe, as shown in Fig. 3. The small q u a n t i t y o f water applied at the beginning and end of the records was to prevent the water supply system freezing. Outside these times the u n p r o t e c t e d bud t e m p e r a t u r e s were below -- 1.0°C and water was applied i nt erm i t t ent l y until it supplied insufficient heat to maintain bud t e m p e r a t u r e at - - 1 . 0 ° C

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(Fig. 4). Subsequently, the sprinklers were operated continuously at their m a x i m u m rate until the demand fell. The records o f precipitation rate versus time for the three sites are broadly similar, the main differences corresponding to the designed differences in m a x i m u m rates o f application. At the sites with sprinklers giving m a x i m u m application rates of 2.7 (Site 2) and 2.8 (site 4) m m h -1 , the precipitation rates increased during the night until about 02.00 h; from then until 0 7 . 0 0 h the sprinklers were operating continuously. At the site giving a m a x i m u m application rate of 4.6 m m h -I (Site 3), the precipitation rate increased from about 1.2 m m h -I to about 3.0 mm h -1 by 04.00 h. Between this time and dawn, the precipitation rates increased rapidly and on several occasions the sprinkler operated continuously throughout a 10-rain period. When the water supply was limited by the m a x i m u m rates, insufficient

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Fig. 3. T h e r e c o r d e d p r e c i p i t a t i o n rates, P, for t h e n i g h t o f 7 / 8 M a r c h 1 9 8 2 p l o t t e d against t i m e a n d t h e t e m p e r a t u r e d i f f e r e n c e (Tp - - T b ) b e t w e e n t h e p r o t e c t e d a n d u n p r o t e c t e d buds. (a), (b) a n d (c) p r e s e n t d a t a for p l o t s w i t h s p r i n k l e r s giving m a x i m u m a p p l i c a t i o n r a t e s o f 2.7, 2.8 a n d 4.6 m m h - l , respectively. O p e n (o) a n d closed (o) circles i n d i c a t e w i n d speed w a s / > 0.3 a n d ~ 0.3 m s -1 , respectively.

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Fig. 4. T e m p e r a t u r e s m e a s u r e d for r e p r e s e n t a t i v e b u d s o n 7/8 M a r c h 1982. The lines c o r r e s p o n d t o p l o t s w i t h m a x i m u m a p p l i c a t i o n r a t e s o f 2.7 m m h -1 (u), 2.8 m m h -1 (,::~), 4.6 m m h -1 ( - - - - - - ) a n d for t h e c o n t r o l p l o t ( - - ) .

heat was supplied to maintain bud temperature at --1.0°C. Consequently, bud temperatures at Sites 2 and 4 fell below -- 1°C for considerable periods (Fig. 4) with minimum temperatures o f - - 2 . 0 and --2.3°C, respectively. The mean temperature of the control buds was a b o u t 1°C below air temperature early in the night, the difference narrowing gradually to 0.5°C around dawn, when bud temperature was at its minimum of --5.0°C. At 18.00h, the temperatures at Sites 2 and 3 were similar to those of the unwatered buds, but at Site 4 temperatures were up to a degree lower, probably because the buds were still wet from daytime spraying. When the frost protection water was first applied there was an initial cooling effect due to evaporation. The applied precipitation rates plotted against the differences in temperature between protected and unprotected buds (Fig. 3) may be regarded as the measure o f the protection achieved. The data points for low wind speeds ( u ~ 0 . 3 m s -1) are shown as d o s e d circles and for u / > 0 . 3 m s -1 as open circles. To produce the same bud temperature rise, a greater precipitation rate is required at higher wind speeds. Also, the loss of latent heat by evaporation is shown at the onset of the period of frost protection. For example, for the site with the highest maximum precipitation rate (Fig. 3c), the initial temperature of the protected buds was lower than the unprotected (unwetted) buds. Once bud temperature fell below -- 1°C a precipitation rate of about I mm h -1 was required to counteract evaporative cooling so as to maintain bud temperature. Although the equation describing the precipitation rate required for adequate frost protection is complex (eqn. 6), a simple linear relationship with temperature fitted most of the data well (Fig. 3). The temperature difference between protected and unprotected buds corresponding to the

169 r e c o m m e n d e d standard p r e c i p i t a t i o n rate o f 2.5 m m h -1 averaged 2.7°C at all t h r e e sites. This agrees with earlier w o r k ( H a m e r , 1980) f o r similar e n v i r o n m e n t a l c o n d i t i o n s : a l t h o u g h air t e m p e r a t u r e fell o n l y to - - 3 ° C , e x t r a p o l a t i o n o f the data s h o w e d t h a t the standard p r e c i p i t a t i o n rate increased the t e m p e r a t u r e o f a t h e r m i s t o r sensor with h e a t t r a n s f e r p r o p e r t i e s similar to a b u d b y 2.6°C. Heat fluxes during frost p r o t e c t i o n H e a t fluxes were e s t i m a t e d f o r the course o f the f r o s t o f 7/8 March 1982, using the results o f the c h a m b e r e x p e r i m e n t to estimate heat t r a n s f e r coefficients o f ice-coated buds. F o r each site, heat t r a n s f e r coefficients, hp, were e s t i m a t e d f r o m the characteristic d i m e n s i o n (d) o f t h e ice-coated bud and the wind speed (eqn. 8) using t h e a p p r o p r i a t e value o f ~ = 1.2 f o r d o r m a n t buds. The d i a m e t e r o f t h e ice-coated b u d , dt, was r e c a l c u l a t e d at 10-min intervals f r o m t h e m e a s u r e d p r e c i p i t a t i o n rate and t h e d i a m e t e r dr_ 1 calculated for t h e previous period. F r o m eqn. 10: d t = (P/3I) + dt_ 1 - d e / 6 ( m m )

(13)

T h e initial value o f bud d i m e n s i o n was 5.0 m m . O n c e sprinkling had comm e n c e d , a c o n s t a n t rate o f loss d u e t o e v a p o r a t i o n was assumed (de = 0.1 m m h -1 ). T h e i n t e r c e p t i o n f a c t o r (I) was assumed to be 2.0 following Businger ( 1 9 6 5 ) , r a t h e r t h a n the value o f 2.7 d e t e r m i n e d in the c h a m b e r (see Discussion). T h e loss o f sensible heat b y c o n v e c t i o n was e s t i m a t e d f r o m eqn. 3 b y inserting hp and t h e d i f f e r e n c e b e t w e e n the t e m p e r a t u r e o f the ice-coated bud and the m e a n air t e m p e r a t u r e (Tp -- Ta) m e a s u r e d at the u n p r o t e c t e d sites. A l o w e r limit o f 20 W m -2 K -1 was i m p o s e d o n hp. T h e l a t e n t heat flux, / t L , was e s t i m a t e d f r o m eqn. 4 using the c o e f f i c i e n t o f heat transfer (h v = 1 . 0 8 h p ) , the s a t u r a t e d v a p o u r pressure over ice (es(Tp)) at the m e a s u r e d t e m p e r a t u r e o f the p r o t e c t e d bud and the m e a n v a p o u r pressure, ea, m e a s u r e d at t h e u n p r o t e c t e d sites. The net r a d i a t i o n flux (a loss) was e s t i m a t e d f r o m m e a s u r e m e n t s o f a t m o s p h e r i c long-wave r a d i a t i o n (L a) and r a d i a t i o n e m i t t e d f r o m the g r o u n d (Lg) as (Hamer, 1 9 8 5 , eqn. 1): /tp

= aT~ -- (L~ + L g ) / 2

(14)

w h e r e a is t h e S t e f a n - B o l t z m a n n c o n s t a n t ( = 5.67 × 10 -s W m -2 K -4). It was assumed t h a t L a was equal to 235 W m -2 , t h a t it r e m a i n e d c o n s t a n t t h r o u g h o u t t h e night and t h a t t h e u n d e r l y i n g surface and the p r o t e c t e d buds were at the same t e m p e r a t u r e . Since b u d t e m p e r a t u r e s were m a i n t a i n e d at - - I ° C t h r o u g h o u t m o s t o f t h e p e r i o d o f t h e frost, t h e n e t r a d i a t i o n flux was therefore e s t i m a t e d as/~p = (aT~ -- 2 3 5 ) / 2 = 38 W m -2 . T h e heat flux d a t a w e r e r e d u c e d t o h o u r l y values b y taking the m e a n o f

150, (oi IO0

50" 6

O'

_ 5 o L ........

20.00

00.00

22.00

O2.00

04.00

O6.00

08.00

150, (b) g

~T

iO04

E 50'

o t

"t-

O-

-50 - "-20.00

22.00

00.00 04.00 06.00 02.00 06.00

150, (c) i |

IO0o

50'' 6

O'

-50" " 20.00

00.00 04100 08.00 22.00 02.00 06.00 Time (h)

Fig. 5. Fluxes of heat for the night of 7/8 March 1982. (a), (b) and (c) present hourly mean estimates for plots with sprinklers giving m a x i m u m application rates of 2.7, 2.8 and 4.6 m m h -] , respectively. The symbols • and × represent sensible heat, Cp and latent heat of vaporisation, /~L, respectively: o and m represent the combined fluxes ]~p + Cp and ]~p ~- Cp 7t/~L, where .~p is the net loss of radiative heat. For comparison, the continuous line is the estimate flux of heat of fusion (---).

171

six 10-min values. Values of latent heat flux (×) and convective heat flux (o) from 19.00 h on 7 March to 07.00 h on 8 March 1982 are shown in Fig. 5. Initially, Cp was negative and gradually became positive as bud temperature exceeded air temperature. At Sites 2 and 4, Cp reached a plateau when the water was applied at its m a x i m u m rate. During this period, the lower limit of hp was imposed and the bud-to-air temperature difference was approximately constant at 2.5°C. At Site 3, Cp continued to increase throughout the night and reached a m a x i m u m of 64 W m -2 . The mean latent heat flux, HL, varied between 38 and 32 W m-2 at Sites 2 and 4 for most of the period of frost protection, but at Site 3/4L increased to 50 W m -2 at sunrise. The flux of latent heat of fusion, Qt, estimated from the rate of water supply is also shown in Fig. 5 and compared with the combined fluxes/~p + Cp(O) and/~p + Cp + HL (=). The data for Sites 2 and 4 (Fig. 5a and b) were very similar. Initially, Q~ was close to/~_ + ~ and as the frost progressed, Qt tended towards the combined fluxes/~p + Cp + / T L . At Site 3, the results were similar to those for the other sites until the end of the period of frost protection. Between 05.00 and 0 6 . 0 0 h , the flux of latent heat of fusion exceeded the combined fluxes /~p + Cp +/~L by over 20W m -2 , which implied that not all the water applied was converted into heat available to the bud. DISCUSSION AND CONCLUSIONS The coefficient of heat transfer, hp, decreased as a result of ice accretion. In the frost chamber experiment, hp was 35 W m -2 K -1 at the commencement of water sprinkling and decreased to 2 0 W m -2 K -1 after 1 2 m m of water had been applied. Subsequent applications of water did not alter hp, even though the estimated characteristic dimension of the bud increased further. The estimation of hp assumed the bud to be an idealised sphere, the deviation from theory is probably because ice builds up around the bud in a non-uniform shape. Most of the water froze where it hit the bud, on the side facing the sprinkler, while the opposite side of the bud had only a light coating of ice. At low wind speeds, heat transfer was likely to be by mixed convection, so that hp = 2 0 W m -2 K -1 represented a lower limit for the heat transfer coefficient for an ice-coated bud. The justification for using this lower limit of hp was confirmed in the field experiment. For example, towards the end of the frost, the dimension of the ice-covered buds was estimated to be about 3 0 m m . For a sphere of this diameter, the heat transfer coefficient at a wind speed of 0.25 m s -1 should be 13 W m -2 K -1 . Use of this value would underestimate the precipitation rate required for frost protection: the calculated precipitation rate (eqn. 8) required at the end of the frost to maintain bud temperature at the levels experienced at Sites 2 and 4, would be 2.2 mm h -~ , which is below the rates determined by empirical methods. As shown in Fig. 5a and b, towards the

i : h

end o f the frost, with the lower limit of hp = 2 0 W m -: K -~ m~posed, t[-~,: combined heat fluxes /~p ~ Cp + HL agreed well with the applied precipi ration rate {converted to a flux of fusion). The precipitation rate required for frost p r o t e c t i o n is overestimated by the relationship between precipitation rate and heat transfer published by Businger (1965). For the average wind speed observed during the period of frost p r o t e c t i o n (u = 0.28 m s ~ ), the coefficient of heat transfer, treating the bud as a sphere wi~h d 5 mm, [s 34 W m -2 K '~ . For a t e m p e r a t u r e lift of 2.7°C, P = 3 . 4 m m h - " ~ m~ overestimate of 40% compared with tb~ observed rate o f 2.5 mm h ~ . Different interception factors, I, were used for the two experiments. In the frost chamber e xpe r i m e nt , I was calculated from measurements of initial and final diameters anti the loss o f material due t o evaporative cooling. This value (I = 2.7) was used with confidence, since the values of h, calculated from eqn. 9 corresponded closely with those estimated from heat transfer t h e o r y . In the field e x p e r i m e n t it was not possible to apply the same check for consistency. Use of the value of I obtained from the frost chamber e x p e r i m e n t resulted m a value f or t he heat flux of fusion which was unrealistically low, being a smaller value t h a n / ~ u + Cp. The interception factor depends on the efficiency with which buds collect the water applied by the sprinklers. F u r t h e r m o r e , observed rates of water use for daytime evaporative cooling (Hamer, 1986) agree well with empirical calculations based on the heat balance equatiom whe~, I : 2. In the absence of alternative evidence, the interception factor" of 1 : 2 established by Businger (1965) for field conditions was em pl oyed. This p r o d u c e d self-consistent estimates of precipitation rates in the o u t d o o r environment. At Site 3, bud t e m p e r a t u r e was maintained at - 1 . 0 ° C t h r o u g h o u t the period o f the frost. However, towards the end of the frost, the estimated heat flux of fusion (converted f r om the precipitation rate) was greater than the sum o f radiative, convective and evaporative heat fluxes. This was investigated by a separate e x p e r i m e n t in the frost chamber (Hamer, 1984b). The water application was controlled in the same m anner as for the field experiment. During the early period of the frost, a 10-s burst o f water (the minimum " o n " time) was sufficient to raise bud t e m p e r a t u r e above the base level of - - 1 ° C. However, after 1 2 h the ice-coated bud was slow to respond to the input o f latent heat. Consequently, the water remained on for 80 s, more water was applied t ha n necessary and run-off occurred. The excess water also partially melted the ice coating around the bud and the coefficient of heat transfer increased as t he ice-coated bud diameter decreased. In the field exper i m ent , during the early stages of frost protection, the heat balance equation overestimated t he water requirements. When water was applied in term i t t e nt l y the buds may have been only partially wetted, t h e r ef o r e the flux of latent heat o f vaporisation in the heat balance equation would be overestimated. As t he severity of frost increased and a higher

173 precipitation rate was required> a larger p r o p o r t i o n of the surface area of the bud was wetted. At the onset o f a frost it is normal commercial practice to apply water at th e m a x i m u m rate of sprinkling. In this case, it is likely that excess water is applied with run-off occurring. Most of the buds are wetted, but there may be m ut ua l " s h a d o w i n g " in the canopy. In the particular season, no severe frosts occurred at later stages o f develo p m e n t , when the shape had changed. However, Hamer (1985) reports estimates o f the heat transfer coefficient, ha, for u n p r o t e c t e d buds at different stages of development. For typical wind speeds experienced during a frost, h¢ ranged fr om 24 to 40 W m -2 K -1 , which is always greater than the m i n imu m value of 20 W m -2 K -1 . Therefore, at the beginning of a period of frost, the precipitation rate required will be different for buds at different stages o f development. As a frost becomes m ore severe, however, the appropriate heat transfer coefficient, hp, will always decrease due to ice accretion. The lower limit o f hp (20 W m -2 K -I) estimated for d o r m a n t buds may not necessarily be the same for buds at o t h e r stages of development, but it is unlikely to be lower: as ice accumulates the coefficient of heat transfer is likely to b eco me less d e p e n d e n t on the stage o f bud development and m ore d e p e n d e n t o n the size o f t he mass o f ice surrounding the bud or flower. F o r buds co ated with ice, the change of hp with wind speed is uncertain. Figure 3 clearly showed t hat wind speed was having an effect on the required precipitation rate, although it was small. The present measurements make it possible to estimate the minimum air t e m p e r a t u r e at which the usual commercial precipitation rate will be effective. Even at the most sensitive stage o f bud development, frost damage will n o t usually occur at t e m per a t ur es above -- 2°C. Using eqn. 6, if we assume a precipitation rate of 2 . 5 m m h -1 , R,~ = 3 8 W m -2, hp -- 2 0 W m -2 K -1 and that the relative h u m i d i t y is 100% at the time of m i ni m um air temperature, t h e n T a - - - - 4 . 0 ° C . Therefore, under conditions of high radiation loss and low wind speed a precipitation rate o f 2.5 mm h -I will provide p r o t e c t i o n in an air frost o f ca. - - 4 ° C . In this paper, it has been shown that during a frost, sprinkler irrigation changes the heat transfer coefficient due to ice accretion. The heat balance m e t h o d of determining precipitation rates for frost p r o t e c t i o n can be used with confidence providing this change in heat transfer coefficient is considered. ACKNOWLEDGEMENTS I am grateful to Dr. J.A. Clark of the D e p a r t m e n t of Physiology and Environmental Science, University of Nottingham School of Agriculture and to Dr. J.E. Jackson for their constructive c o m m e n t s on this paper and to P. Newman for his general assistance.

17.1 REFERENCES Businger, J.A., 1965. Protection from the cold. Meteorol. Monogr., 6:74--80. Hamer, P.J.C., 1980. An automatic sprinkler system giving variable irrigation rates matched to measured frost protection needs. Agric. Meteorol., 21:281--293. Hamer, P.J.C., 1984a. The heat balance of apple buds and blossoms in frost protection Ph.D. Thesis, University of Nottingham, U.K. Hamer, P.J.C., 1984b. Frost protection by water sprinkling. Rep. E. Mailing Res. Stn~ 1983, p. 24. Hamer, P.J.C., 1985. The heat balance of apple buds and blossoms. Part I. Heat transfer in the outdoor environment. Agric. For. Meteorol., 35:339--352. Hamer, P.J.C., 1986. The heat balance of apple buds and blossoms, Part III. The water requirements for evaporative cooling by overhead sprinkler irrigation. Agric. For. Meteorol., 37:175--188. Rogers, W.S. and Modlibowska, I., 1962. Automatic protection from frost by water sprinkling. Proc. 15th Int. Hortic. Congr., 1958, at Nice, 3:416--425. Slater, C.H.W., 1957. Frost damage research equipment at East Mailing. Rep. E. Mailing Res. Stn. 1956, pp. 93--96.