VALIDATION OF THE DEARDORFF MODEL FOR ESTIMATING ENERGY BALANCE COMPONENTS FOR A SUGARCANE CROP

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1 Deardor model or estimatin enery balance 35 VALIDATION OF THE DEARDORFF MODEL FOR ESTIMATING ENERGY BALANCE COMPONENTS FOR A SUGARCANE CROP Glauco de Souza Rolim *; João Francisco Escobedo ; Amauri Pereira Oliveira UNESP/FCA - Depto. de Irriação e Drenaem, C.P Botucatu, SP - Brasil. USP/IAG - Depto. de Ciências Atmoséricas, C.P São Paulo, SP - Brasil. *Correspondin author <rolim@iac.sp.ov.br> ABSTRACT: The quantiication o the available enery in the environment is important because it determines photosynthesis, evapotranspiration and, thereore, the inal yield o crops. Instruments or measurin the enery balance are costly and indirect estimation alternatives are desirable. This study assessed the Deardor s model perormance durin a cycle o a suarcane crop in Piracicaba, State o São Paulo, Brazil, in comparison to the aerodynamic method. This mechanistic model simulates the enery luxes (sensible, latent heat and net radiation) at three levels (atmosphere, canopy and soil) usin only air temperature, relative humidity and wind speed measured at a reerence level above the canopy, crop lea area index, and some pre-calibrated parameters (canopy albedo, soil emissivity, atmospheric transmissivity and hydroloical characteristics o the soil). The analysis was made or dierent time scales, insolation conditions and seasons (sprin, summer and autumn). Analyzin all data o 5 minute intervals, the model presented ood perormance or net radiation simulation in dierent insolations and seasons. The latent heat lux in the atmosphere and the sensible heat lux in the atmosphere did not present dierences in comparison to data rom the aerodynamic method durin the autumn. The sensible heat lux in the soil was poorly simulated by the model due to the poor perormance o the soil water balance method. The Deardor s model improved in eneral the lux simulations in comparison to the aerodynamic method when more insolation was available in the environment. Key words: enery budet, net radiation, latent heat lux, sensible heat lux, microclimate VALIDAÇÃO DO MODELO DE DEARDORFF PARA CÁLCULO DO BALANÇO DE ENERGIA DURANTE UM CICLO DE CANA-DE-AÇÚCAR RESUMO: A quantiicação da eneria disponível no ambiente é importante porque ela aeta a otossíntese, a evapotranspiração e conseqüentemente a produtividade inal dos cultivos. Instrumentos para medidas de balanço de eneria são caros e alternativas para estimações são desejáveis. O presente trabalho procura avaliar a perormance do modelo de Deardor (978) ao lono do desenvolvimento de uma cultura de cana-de-açúcar em Piracicaba, SP, Brasil, em comparação ao método aerodinâmico. Este modelo mecanístico simula os luxos eneréticos (calor sensível, latente e saldo de radiação) em três níveis: a atmosera, o dossel veetativo e o solo, usando somente a temperatura do ar, umidade relativa e velocidade do vento medidos num nível de reerência acima do dossel, o índice de área oliar e aluns parâmetros previamente calibrados (albedo do dossel, emissividade do solo e a transmissividade atmosérica e características hidrolóicas do solo). As análises dos resultados oram eitas em diversas escalas de tempo, condições de insolação, nas dierentes estações do ano (primavera, verão, outono). Analisando todos os dados de 5 minutos, o modelo apresentou boa perormance na simulação de radiação líquida em dierentes condições de insolação e estações do ano. O luxo de calor latente e o luxo de calor sensível na atmosera não apresentaram dierenças em comparação ao método aerodinâmico no outono. O calor sensível no solo oi pobremente simulado pelo modelo devido à baixa capacidade de estimação do balanço hídrico do solo. Geralmente as estimações pelo modelo de Deardor oram melhoradas quando mais insolação era disponível no ambiente. Palavras-chave: balanço enerético, radiação líquida, luxo de calor latente, luxo de calor sensível, microclima Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

2 36 Rolim et al. INTRODUCTION Studies on enery balance o aricultural areas allow the understandin o enery chane processes in relation to evapotranspiration and photosynthesis, which directly aect the biomass accumulation and aricultural yield. Several studies can be cited, as those related to evapotranspiration estimations (Villa Nova et al., 7), to lea wetness duration and its consequences on pathoen inection processes (Marta et al., 7), and to the development o mechanistic crop rowth models (Pauwels et al., 7), amon others. Several methods are available to estimate the enery balance o the environment, also when there is data limitation. The models presented by Shuttleworth & Wallace (985), Zapata & Martinez- Cob () and Hemakumara et al. (3) are examples o them. At the mesoclimatic scale, the Deardor s (978) model has been used with success to simulate enery luxes (Soares et al., 996; Tarino & Soares, ). Voel et al. (995) observed that Deardor s (978) model presented a better perormance simulatin the sensible heat lux (in air and soil) than other models, when applied to veetated suraces. At the microclimatic scale, ew aricultural studies can be ound usin the Deardor (978) model. Tattari et al. (995) tested Deardor s (978) model and compared it to the Bowen s ratio method to estimate barley crop evapotranspiration, but the results were not very ood due to problems with measurements made under adverse climatic conditions, such as hih humidity, usts o wind and rain. However, McCumber (98) and Garret (98) stated that amon the methods ound in the literature, the one proposed by Deardor (978) is the most eicient to estimate enery balances with quality and simplicity. Finally, Oliveira et al. (999) workin with maize and rass crops at Candiota, RS, Brazil, obtained ood results in simulations o sensible and latent lux and net radiation. The advantae o usin the model proposed by Deardor (978) is the siniicant reduction o the number o instruments required to estimate the enery balance o a iven crop, since it only requires air temperature, relative humidity, wind speed, lea area index and some hydroloical parameters o the soil. This study analyses the perormance o Deardor s (978) model to estimate net radiation, latent heat lux, sensible heat lux in the atmosphere and in the soil, durin a complete cycle o a suarcane crop, in comparison to the aerodynamic method. MATERIAL AND METHODS Site descriptions and measurements The suarcane cultivar IAC used in this study was sown on /8/ with meter row spacin in the east-west orientation. The experimental ield is characterized by a lat area o about km, located in Piracicaba, Sate o São Paulo, Brazil (º4 S, 47º38 W and altitude 54 m). The meteoroloical data, were collected each second and interated every 5 seconds, rom 8/7/ to 5/3/ usin a Campbell X dataloer and sensors previously calibrated. The sensors were mounted on a tower at the center o the area and the measurements were made at six levels: 5 m rom the surace (rain); m rom the top o the canopy (temperature, relative humidity, wind speed, net radiation, lobal and relected solar radiation); ¾ o canopy heiht (temperature, relative humidity and wind speed); on the soil surace (heat lux); in the soil, 5 and cm below the surace (temperature and humidity). The levels: m rom the top o the canopy and ¾ o canopy heiht were adjusted monthly to ollow crop rowth. The m level mentioned above, contains the necessary data or Deardor s (978) model inputs (temperature, relative humidity and wind speed) and the extra observations were necessary or model comparisons. The suarcane crop was chosen due to its reat economic interest in State o São Paulo, besides its lon cycle which makes possible perormance analyses o the model durin several seasons o the year. Determination o the enery balance components by the aerodynamic method The estimation o the enery balance components (Rn Net radiation, LE Latent heat lux, H sensible heat lux in the atmosphere and G- Sensible heat lux in the soil) by the aerodynamic method usin data observed in the ield was made to compare the simulated data obtained by the Deardor's (978) model. From data obtained every 5 seconds the Richardson number (Ri) was calculated in order to compare the thermal orces responsible or the ree convection, with the mechanical orces responsible or the orced convection. The Richardson number was calculated by the ollowin equation:. dθ / dz Ri = () Θm.( du / dz) where: is the ravitational acceleration (9.8 m s - ), dθ/dz is the potential temperature radient (K m - ), du/ dz is the wind speed radient (s - ). The potential tem- Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

3 Deardor model or estimatin enery balance 37 perature is calculated by Q = air temperature (K).(/8).857. In order to estimate the eect o Ri on the turbulent diusion coeicient (Km), which makes possible to quantiy the transport o atmospheric activity (sensible and latent heat lux) the unction φm was calculated or the ollowin cases: unstable conditions (when Ri < ): φm = ( 6.Ri) -.5 ; stable conditions (when Ri > ): φm = + 5.Ri; and neutral conditions (when Ri = ): φm = The turbulent diusion coeicient (Km) is iven by: Km k.( z du d). dz. φm = () where: k is the von Karman constant (=.4), z the reerence sensor heiht and d is the zero place displacement (considered ¾ o the canopy heiht). The coeicient Km was used to estimate the sensible heat lux: dt H = ρ. Cp. Km. (3) dz where: ρ is air density (=,9 k m -3 ), Cp the speciic heat o dry air at constant pressure (=,5 kj k - K - ) and dt/dz the temperature radient between the two sensors. The values o the sensible heat lux in the soil (G) and net radiation (Rn) were obtained directly rom ield measurements and when H was possible to be calculated, the latent heat lux value (LE) was obtained rom: LE = Rn H G (4) Deardor s (978) model The Deardor s (978) model comprises several staes, however some relevant aspects can be briely described: the model considers that there is only one veetation layer, whose thermal capacity is insiniicant and characterized by a coeicient (σ ) that is associated with the deree to which the canopy prevents the shortwave radiation to reach the soil, which is calculated usin the lea area index (LAI). σ = reers to absent veetation cover and σ = to complete veetation cover (theoretical). With the coeicient σ and considerin the wind loarithmic proile, three heat transer coeicients can be calculated or the ollowin levels: bare soil surace (C H = k.ln(z/z o ) -, where k =.4; z = m above the canopy and z o = rouhness parameter); hih immediately above the canopy top (C Hh = (/ k).ln[(z-d)/z o h]), where d = zero plane displacement = ¾. Canopy hih; z o h = (canopy hih d)/3); soil surace (C H = (-σ ).C H + σ.c Hh ). Usin the coeicient C Hh at the reerence level (u a ), the mean speed inside the canopy (u a ) is calculated by: u a =.38s c Hh / u a + ( s ) u a (m s - ) (5) where: u a is the wind speed (m s - ) measured at reerence level It was assumed that the inner part o the canopy presents averae conditions between the atmosphere and the soil, thus the air temperature inside the veetation (T a ) and the correspondent humidity (q a ) were calculated by the ollowin equations: T a = ( σ ) T a + σ (.3T a +.6T +.T ) (ºC) (6) q a = ( s ) q a + σ (.3q a +.6q +.q ) (cm 3 cm -3 ) (7) where: T = averae lea temperature, T = soil surace temperature, T a = temperature at the reerence level (measured) and q a, q, q a and q are analoous speciic humidities. In a simple way, T, and q have been estimated rom the enery balance at the level o a sinle lea inside the canopy. This is an iterative calculation procedure that aims to minimize the dierences in the ollowin equation: R + R R R R + R R R ) = Sh Lh Sh Lh ( S L S L = H H + λ E E ) (8) sh s ( h where: R S, R L, H s and E are short and lon wave radiative luxes, sensible heat lux and evapotranspiration, respectively, and l is the evaporation latent heat. The subscribed letters h and represent values at the canopy top and on the soil surace, respectively. Finally, the arrows indicate the radiative lux directions. When the Stean-Boltzmann s equation is used in each side o the equation 8 and other chanes mentioned by Deardor (978) are introduced, the result is equation 9, which must be solved to ind the representative canopy lea temperature: ε ε 4 σ [( α ) RSh + ε RLh + σt ( ε + ε ε ε ) ( ε + ε ε ε ) 4 ε σt ] = Hs + λe (9) ( ε + ε ε ε ) where: α and ε are the albedo and the oliae emissivity, ε is the soil emissivity and s is the Stean-- Boltzmann constant ( W m - K -4 ). Another peculiarity o Deardor s (978) model is the use o the F-R method (Force Restore) proposed by Bhumralkar (975) to calculate T. It consists in a resolution o an equation which depends on Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

4 38 Rolim et al. the enery lux sum in the atmosphere and contains a mechanism that causes an inluence o the deep soil layers on the surace temperature. Thus, the soil is divided in two layers: a supericial one, or which the soil temperature is inluenced by the daytime cycle, and a deep one, o ininite depth in which the temperature chanes in an annual scale, as ollows: T ch A T T = c () t ρ c d τ s s Table - Calibrated dimensionless parameters used in the Deardor s (978) model: α - canopy albedo, ε - soil emissivity, ε - canopy emissivity, and t - atmospheric transmissivity. α ε ( = ε ) τ Sprin Summer Autumn where: T is the averae temperature o the soil in the deep layer; c and c are dimensionless constants; ρ s is the soil density; c s the soil speciic heat; d the soil depth under the inluence o daytime cycle; and τ is the photoperiod; H A is the sum o the atmospheric luxes at the surace as a result o the enery balance at the soil surace. Finally, the Deardor s (978) model, besides temperature, relative humidity and wind speed data, requires some parameters that were previously calibrated (Table ). Basically, the calibration o these parameters aimed to an approach between the measured and simulated data by the model, usin the iterative method Simplex with initial values o ε =.95; ε =.95; α =. accordin to results o Tarino & Soares () and τ =.7. A total o days were used or this process (4 days o each season with dierent insolation conditions), considerin the available 49 days. These parameters are similar to those ound in literature, as Monteith & Unsworth (99), who related an emissivity or a suarcane surace o 97.7 ±.4%. Gates (98), on the other hand, ound an albedo o.7 durin the complete development o a iven suarcane crop. Finally, Unsworth & Monteith (97), who made atmospheric transmissivity measurements in Enland, obtained values o.95 or very clear days and.5 or days with too much pollution or or cloudy sky conditions. The Deardor s (978) model also requires three soil hydroloic parameters: water contents at wilttin point (w wilt ), at ield capacity (W k ) and at saturation (W max ). In relation to this a physico-hydric analysis o the soil was accomplished ivin emphasis on the determination o the soil water characteristic curve. The results were: w wilt =.5; W k =.; W max =.3 (cm 3 cm -3 ). Biometrical measurements o the suarcane crop The parameters that aect the loarithmic wind proile above canopy, lea area (LA) and averae heiht o the canopy, were measured every 5 days rom 8/7/ to 5/3/, considerin ive replications. The lea area index (LAI) was determined by collectin and measurin leaves rom a randomized area o m, usin a paper uide with accuracy o mm. Evaluation o Deardor s (978) model The data simulated by the model (): T a, u a, canopy relative humidity (RH canopy ), Rn, LE, H, G, were compared to those calculated by the aerodynamic method () usin the index o areement suested by Willmott (98): i d N i i ( P O ) P O O O i N i i i () where: is dimensionless and ranes rom (zero) to, considerin that the value indicates complete areement between observed and estimated values; P i are values; O i are values; O the mean o values and N the number o observations. RESULTS AND DISCUSSION Meteoroloical elements inside the canopy were directly aected by crop development. The increase o the lea area index and canopy heiht (Fiure 3) aected the wind speed inside the canopy (u a ), which was reduced in relation to the reerence level (Fiure C). Because o that, the dierence u re - u a was smaller durin the sprin than in the autumn. Fiure D shows that soil temperature (5 and cm) was reduced durin the crop rowth. The ive-day movin averae o Rn raned rom 5 W m - to 7 W m - rom summer to sprin and rom 45 W m - to 6 W m - durin autumn (Fiure ). The irst summer weeks presented maximum values o LE, up to 49 W m -, whereas in middle o autumn they reached only 5 W m -. The maximum LAI and heiht ound or suarcane crop were 4.6 and.8 m, respectively (Fiure 3). These results also correspond to those ound in the literature, e.. Leme et al. (984), who observed a maximum LAI o 4.5 or the suarcane cultivar CB47-355, and Bull & Glasziou (975) and Machado et al. (98) that also observed that the crop reached a maximum heiht o.6 m. Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

5 Deardor model or estimatin enery balance 39 Averae air temperature, ºC Wind speed, m s Sprin Summer Autumn A Ta Ta ua ua Julian Day Sprin Summer Autumn C Julian Day Fiure - Five-day movin averaes o measured meteoroloical variables inside the canopy (3/4 o canopy heiht) and at the reerence level ( meters above canopy): A) Temperature, B) Relative humidity and accumulated rain, C) Wind speed, D) Soil temperature (5 and cm below the surace). Eneretic lux, W m Sprin Summer Autumn Rn LE H (-)G Julian Day Fiure - Five-day movin averae o maximum hourly values o enery balance components (Rn Net radiation, LE Latent heat lux, H Sensible heat lux at the atmosphere and G Sensible heat lux in the soil) estimated by the aerodynamic method. The best meteoroloical variable simulated by the Deardor (978) model was the air temperature inside the canopy (T a ). The smallest errors or all seasons were ound next to midday. At other periods, the Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8 Relative Humidity, % Soil Temperature, ºC Sprin Summer Autumn B Rain RHa RHa Julian Day Sprin Summer Autumn D Tsoil cm Tsoil 5cm Julian Day model had a tendency to underestimation, however, mean absolute dierences o no more than 3 o C were ound. As expected, the minimum hourly temperature inside the canopy always occurred between 6h and 7h a.m., with values around 6ºC durin sprin and autumn, and around 8ºC durin summer, while the mean temperature inside the canopy remained around 7ºC in sprin, 3ºC in summer and 8ºC in autumn. Deardor s (978) model also presented a ood perormance or simulatin temperature at the canopy level (T a ) in days with dierent insolation conditions. The index was always hiher than.83, despite o some variability noticed by R values around.49, or moreover, by the coeicient o variation ( ), around % (Table ). The wind speed inside the canopy (u a ), mainly in autumn, was well simulated by the model, showin that the parametrization o the wind aerodynamic proile Rain, mm

6 33 Rolim et al. or veetated suraces was eicient to represent ield conditions. The simulated u a did not dier rom the observed u a, despite to the low values o R (Table ), since the reatest daily mean dierences ound were o.57 m s - in summer,.5 m s - in autumn and a little hiher in sprin, reachin.78 m s -. The small values o R and hih values o, indicated that the model did not ollow instantaneous variations o the wind speed but the manitude o adjustments in subsequent moments was ood. The relationships between and data were less siniicant in sprin, when the suarcane crop was in the irst staes o development. Still considerin the canopy level, the last meteoroloical variable analyzed was the canopy relative humidity (RH canopy ). The values were not close to those ound by due the low values o R, despite o the hih values o, and mainly, because the obtained mean dierences were o 8.96%,.4% and 6.5% in the sprin, summer and autumn, respectively. For all seasons there was a hih variability o or 5 minute averaes o relative humidity, resultin in small R values when compared with. The model presented a tendency o underestimation under hih relative humidity, mostly beore sunrise, and a tendency o overestimation under low relative humidity, close to h p.m. Finally, when and are compared or all meteoroloical variables when extra insolation was available in the environment, there was an increase o and R (Table ). In summary, hih values o indicate that values are close to, that is, close to the : line. On the other hand, the small values o R indicate that and data oten have a hih dispersion. The simulations o soil water content were worse than those at the canopy level, which is related to the low capacity o the Deardor (978) model in simulatin the soil water balance or successive days, as shown in Fiure 4A. The model was not able to simulate the dryin o the soil (Fiure 4), even thouh ater lon drouht periods like at the end o sprin and autumn, yieldin dierent values rom the soil moisture. Thus, 57% o the days in sprin and summer and 86% o the days in autumn, the simulated soil moisture in the root zone was above the observed values. Lea Area Index (m m - ) A Adjusted Observed Canopy heiht (m) 3 B Julian day Fiure 3 - A) Lea area index variation (LAI); B) canopy heiht variation o the variety IAC o suarcane between Auust 7, and May 3, Julian day water content (m 3 m -3 ) A Sprin Summer Autumn Soil moisture OBS Soil moisture Julian day Fiure 4 - Daily mean soil moisture (A) and soil thermal diusivity (ks) (B) simulated by Deardor s (978) model () and calculated by the aerodynamic method () durin sprin, summer and autumn seasons. Soil thermal diusivity - Ks (cm s - ) B Sprin Summer Autumn Ks Ks OBS Julian day Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

7 Deardor model or estimatin enery balance 33 Table - Determination coeicient (R ), Willmott coeicient ( ), averae, standart deviation () and coeicient o variation () or 5 minute data simulated by Deardor s (978) model () and calculated by the aerodynamic method () inside the canopy: air temperature (Ta, ºC), relative humidity (RH, %) and wind speed (u a, m s - ) or dierent seasons o the year and dierent insolation levels. Season Insolation (hour) nº days Canopy air temperature,ta (ºC) anopy wind speed, u Aver. R Aver. R C ( m s a - ) elative Humidity, R H Aver. R R y (% ) c anop S prin A l l <= <= x < x < <= x S ummer Al l <= x < <= x < <= x A utumm A l l <= <= x < x < <= x Averae Al l Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

8 33 Rolim et al. Soil moisture tends to damp the soil aainst sudden chanes in temperature, since the heat moves rom the soil to the water about 5 times easier than rom the soil to the air (Brady, 9). Thereore, i the simulated soil moisture by Deardor s (978) model is hiher than expected, the simulated thermal capacity o this soil is also hiher than the observed one. Consequently, it makes hiher temperature variations in the soil more diicult, indicatin that the simulated thermal diusivity (Fiure 4B) o this soil may be lower as well. This supposition was conirmed by Rolim (3), with the similar data, because the amplitude o soil temperature variations (on surace and at the cm depth) were actually lower than the observed ones, resultin in low values o and R or all seasons. Despite these dierences ound between the observed meteoroloical elements and those simulated by Deardor s model, one can see (Table 3) that simulations o the enery balance components Net Radiation (Rn), Latent heat lux (LE) and Sensible heat lux at the atmosphere (H) (Table 4) do not present distinction in relation to the luxes durin all the seasons o the year and in dierent insolation levels or the suarcane crop, except the sensible heat lux in the soil (G). Dierences between Rn rom and the data at every 5 minute interval were small, considerin the hih values o and R or all seasons (Table 3), with exception to summer (d =.79, R =.5) due to a reater nebulosity and occurrence o rain (Fiure B), because there was as well a tendency to improve Rn estimates as the insolation availability increased (Table 3). This similarity between and data o Rn is also due, amon other reasons, to the act that Deardor s model made a ood approach to the total albedo data o the surace (maximum values: sprin =.34; summer =.36 and autumn =.33), that directly aects the amount o radiation available in the system soil-veetation-atmosphere (Fiure 5). Relationships between the and data at every 5 minute intervals o latent heat lux in the atmosphere (LE) (Table 3) and sensible heat lux in the atmosphere (H) (Table 4) also were hih, takin into account the values o ound or all seasons. The lower values o durin the summer were, on account o the same reasons already discussed in relation to Rn, due to the sensibility o the Deardor s (978) model in relation to the available insolation. Table 3 - Determination Coeicient (R ), Willmott Coeicient ( ), averae, standart deviation () and Coeicient o Variation () o 5 minute data simulated by Deardor s (978) model () and calculated by the aerodynamic method () o Net Radiation (Rn, W m - ) and Latent Heat Flux (LE, W m - ) in dierent seasons o the year and or dierent insolation levels. Season Sprin Insolation (hour) nº days R Net Radiation, Rn (W m - ) atent heat lux, LE (W m R L - ) <= x < <= x Summer <= x < <= x Autumm <= Averae x < <= x Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

9 Deardor model or estimatin enery balance 333 Table 4 - Determination Coeicient (R ), Willmott Coeicient, ( ), Mean, standart deviation () and Coeicient o Variation () o 5 minute data simulated by Deardor s (978) model () and calculated by the aerodynamic method () or the Sensible Heat Flux (H, W m - ) in the atmosphere, Sensible Heat Flux (H, W m ) in the soil (G, W m - ) or dierent seasons o the year and at dierent insolation levels. Season Sprin Insolation (hour) nº days Sensible heat lux in the atmosphere, H (W m - ) ensible heat lux in the soil, G (W m R S - ) R <= x < <= x Summer <= x < <= x Autumm <= Averae x < <= x Albedo A) Sprin B) Summer C) Autumn.4.35 Albedo Fiure 5- Hourly averae albedo simulated by Deardor (978) model () and calculated by aerodynamic method () durin sprin (A), summer (B) and autumn (C) seasons. Sci. Aric. (Piracicaba, Braz.), v.65, n.4, p , July/Auust 8

10 334 Rolim et al. Finally, there was no areement between and data o sensible heat luxes in the soil (G), as veriied in dierent seasons o the year (Table 4). This act is a consequence o the low variation o the simulated thermal diusivity, which is a result o the low variation o the water contents in the soil proile, or in a broad way, is a result o the low capacity o the Deardor model in simulatin o the crop water budet. Despite the low relationships o G, the model could recalculate the enery balance makin the estimatives o Rn, LE and H statistically close. In this way the model becomes interestin or arometeoroloical purposes, since it needs only a ew measured data at a reerence level. CONCLUSIONS The latent heat lux and the sensible heat lux at the atmosphere, simulated by Deardor s (978) model did not presented dierences in comparison to the aerodynamic method in the autumn o Piracicaba, State o São Paulo, Brazil. The reatest dierences between the Deardor (978) model and the aerodynamic method were ound in the simulations o the sensible heat lux in the soil. ACKNOWLEDGEMENTS To FAPESP or inancial support and the Instituto Aronômico- IAC, Piracicaba or the experimental area. REFERENCES BHUMRALKAR, C.M. Numerical experiments on the computation o round surace temperature in an atmospheric eneral circulation model. Journal o Applied Meteoroloy, v.4, p.46-58, 975. BRADY, N.C. Natureza e propriedades dos solos. Rio de Janeiro: Freitas Bastos, p. BULL, T.A.; GLASZIOU, K.T. Suar cane. In: EVANS, L.T. (Ed.) Crop physioloy: some case histories. Cambride: Cambride University Press, 975. cap.3, p.5-7. DEARDORFF, J.W. Eicient prediction o round surace temperature and moisture, with inclusion o a layer o veetation. Journal o Geophysical Research, v.83, p.8-93, 978. GARRET, A.J. A parameter study o interactions between convective clouds, the convective boundary layer, and a orested surace. 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