GHINI, R.

TIBA, C.

Portuguese

Repository Open Access to Scientific Information from Embrapa

Pesq. agropec. bras., Brasília, v.41, n.3, p.533-537, mar. 2006Estimating temperature in solarized soils 533Notas CientíficasNumerical procedure for estimating temperature in solarized soilsChigueru Tiba(1) and Raquel Ghini(2)(1)Universidade Federal de Pernambuco, Dep. de Energia Nuclear, Grupo de Pesquisas em Fontes Alternativas de Energia, Av. Prof. LuizFreire, no 1.000, CEP 50740-540 Recife, PE, Brazil. E-mail: tiba@ufpe.br (2)Embrapa Meio Ambiente, Caixa Postal 69, CEP 13820-000 Jaguariúna,SP, Brazil. E-mail: raquel@cnpma.embrapa.brAbstract – The objective of this work was to develop a simplified numerical procedure for the estimation ofaccumulated monthly hours of solarized soil temperatures. The proposed model requires monthly means of dailysolar radiation and maximum air temperature as input data, and a daily pattern of temperature variation assumedto be sine-shaped. The procedure was verified using observations made during the years 1992 and 1993 inJaguariúna, SP. The proposed procedure can predict monthly temperature hours at 10 cm depth in the solarizedsoil, with acceptable accuracy, in the region for which it was developed.Index terms: soil disinfestation, physical control, soil pathogens, alternative methods, solar energy, numericalmodelling.Procedimento numérico para estimar temperaturas de solos solarizadosResumo – O objetivo deste trabalho foi desenvolver um procedimento numérico simplificado para estimar ashoras mensais acumuladas de temperaturas de solo solarizado. A modelagem proposta requer como dados deentrada as médias mensais de densidade de fluxo de radiação solar diária e temperatura máxima diária do ar, e umperfil diário de variação de temperatura, admitida como senoidal. O procedimento proposto foi verificado usan-do-se observações realizadas durante 1992 e 1993, em Jaguariúna, SP. A modelagem desenvolvida prediz ashoras mensais de temperatura de solo solarizado, a 10 cm de profundidade, para a região em que foi desenvolvi-da.Termos para indexação: desinfestação do solo, controle físico, patógenos de solo, métodos alternativos, energiasolar, modelagem numérica.Solarization is a soil disinfestation method forcontrolling plant pathogens, weeds, and pests, whichconsists of covering the soil with a transparentpolyethylene film in pre-planting, preferably when it ismoist, during the season in which the solar radiation ishigh, for one to two months period. Predictingtemperatures in solarized soils along the year would bevery useful, when selecting the most suitable seasonsfor treatment in each location. Simulation also allowssolarization to be adapted to cropping schedule, bychoosing periods that would result in better use of time.The use of a simulation model to determine temperaturesin solarized soil has been studied by Mahrer (1979),Cenis (1989), Sui et al. (1992), Streck et al. (1996), andWu et al. (1996). The detailed simulation proceduresrequire temporal series of solar radiation, air temperature,precipitation, and temperatures in the solarized soil attwo different depths, and bare soil temperature, at anhourly or daily basis. Moreover, if measurements ofweather variables are not available for these series, theymust be estimated, which requires detailed knowledgeof auto-correlation and cross-correlation coefficients forthe generation of bi-variate or even tri-variate temporalseries. The difficulty remains since these coefficientsare scarcely measured or known, both spatially andtemporally, moreover they also depend on location.Therefore, the present work had the objective ofdeveloping a simplified numerical procedure for theestimation of accumulated monthly hours of solarizedsoil temperatures.Based on solarized soil temperatures, measured at10 cm depth during January, 1989, in São Manuel, SP(22°44'S, 48°34'W), by Lefèvre (1990), a high correlationwas obtained between daily incoming solar irradiationPesq. agropec. bras., Brasília, v.41, n.3, p.533-537, mar. 2006C. Tiba and R. Ghini534and maximum daily temperature in the solarized soil(Figure 1 A).The regression equation for daily solar irradiation (H),in relation to maximum temperature (Tmax) in thesolarized soil at 10 cm depth, is:Tmax (ºC) = 1.12H + 20.89 (R2 =  0.89)           (1)Since this correlation was obtained for January, it isnecessary to adjust it to other months. Due to the factthat long-term means of maximum temperature data donot exist for the location (São Manuel), the nearestlocation for which this information is available wasselected (São Carlos, SP – 22°1'S, 47°53'W). Table 1shows the mean values for monthly maximum airtemperature contained in the 1961–1990 Weather-Normals (Brasil, 1992), and the proposed corrections,considering January as a standard month. The correctionis made by subtracting ∆ from the value obtained inequation 1.This proposed correction is based on the fact thatsolarized soil temperature, at 10 cm of depth, isdetermined by the soil energy exchange between thesoil, the polyethylene and surrounding air. In the interfacebetween polyethylene film and atmosphere, heat fluxesoccur by convection and radiation. The net flux ofconvective heat is proportional to the difference oftemperature between atmospheric air temperature andthe temperature of the polyethylene surface. Theradioactive flux is proportional to the difference betweenthe fourth power of the sky temperature and the fourthpower of the polyethylene surface temperature. The skytemperature can be considered proportional to 1.5 powerof the ambient temperature (Swinbank, 1963). Thus,Tmax of solarized soil depends on the ambient temperature.Based on temperature amplitude variation of solarizedsoil measured by Patrício (2000), in Piracicaba, SP(22°43'S, 47°39'W), a correlation between temperatureamplitude and daily maximum temperature for the 10 cmdepth was obtained (Figure 1 B).The regression equation for daily temperature ampli-tude, as a function of maximum temperature in thesolarized soil at 10 cm depth, is:A(oC) = 0.42Tmax - 7.52 (R2 =  0.76)                   (2)According to Cenis (1989), the temperature of thesolarized soil can be modelled using a Fourier series. Thegeneral expression for the Fourier series with oneharmonic is given by:)tsen(AT)t(T 111 φ+ω+=          (3)where T is the temporal variation of temperature at agiven depth; T  is the mean temperature; A is the ampli-tude; ω =  π/12; t is time; φ is the phase, and index 1indicates the harmonic.The angular phase of the φ wave can be calculatedfor each depth, by means of the expression:         (4)where: h is the time at which the maximum dailytemperature occurs, and z is depth.According to Ferraz et al. (2003), the maximumtemperature of the solarized soil at 10 cm depth, inPiracicaba, SP, occurs around 17h; therefore, the phaseangle calculated by equation (4) results in 3.4. Theminimum temperature value in that research workoccurred at 8h.Hourly temperature data for the solarized soil iscalculated by:T(h) =  Tmaximum daily - Af          (5)where: T(h) is the temperature at a given time;Tmaximum daily is daily maximum temperature;  A is ampli-Figure 1. Correlation between daily maximum temperature (Tmax) of solarized soil, at 10 cm depth, and daily incoming solarirradiation (H) in January 1989 period, in São Manuel, SP (Lefèvre, 1990); and correlation between temperature amplitude anddaily maximum temperature, in solarized soil for 10-cm depth, in Piracicaba, SP (Patrício, 2000).Pesq. agropec. bras., Brasília, v.41, n.3, p.533-537, mar. 2006Estimating temperature in solarized soils 535tude (given by equation 2); and f is the temperatureamplitude fraction at this given time in a sine model.The daily amplitude is the difference between the dailymaximum and minimum values. The temperature am-plitude fraction (f), for each time are: 1h: 0.75, 2h: 0.85,3h: 0.93, 4h: 0.98, 5h: 1.00, 6h: 0.98, 7h: 0.93, 8h: 0.85,9h: 0.75, 10h: 0.63, 11h: 0.50, 12h: 0.37, 13h: 0.25, 14h:0.15, 15h: 0.07, 16h: 0.02, 17h: 0.00, 18h: 0.02, 19h: 0.07,20h: 0.15, 21h: 0.25, 22h: 0.37, 23h: 0.50, and 24h: 0.63.As experimental information on daily incoming solarirradiation is not promptly available for many locationsin Brazil, one alternative to overcome this situation is togenerate synthetic temporal series (Aguiar et al., 1988;Graham et al., 1988). The generated series reproducethe statistical properties of actual series, and are thereforesuitable for numeric simulation purposes.The Solarimetric Atlas of Brazil (Tiba et al., 2003)has a calculation tool that allows temporal series to begenerated using Markov’s Transition Matrix Method(Aguiar et al., 1988). The synthetic series generatorrequires the local geographical coordinates and the meanmonthly incoming solar irradiation value. These data arealso provided by the Atlas.The steps for estimating monthly temperatureaccumulated hours of solarized soil, at a given depthand threshold, are: a) generation of incoming solarradiation daily series using, for example, the calculationtool provided by Tiba et al. (2003); b) calculating, foreach month, the maximum daily temperature in thesolarized soil, using a correlation between daily solarirradiation and solarized soil temperature, according toequation (1); c) correcting the maximum dailytemperature, calculated in the previous item, using thecorrection factor presented in Table 1; d) using themaximum daily temperature, calculated in the previousitem, to determine the daily amplitude, using a correlationbetween temperature amplitude and daily maximumtemperature at 10 cm depth, according to equation (2);e) knowing the daily temperature and amplitude, andassuming that the temperature wave is given by a Fourierseries containing a single harmonic, to calculate thedistribution of hourly temperatures, according to equation(5) and values of f (temperature amplitude fraction);f) estimating the temperatures for all other days of themonth, and calculating the accumulated hours thattemperature is above a given threshold.The solarization experiment conducted by Ghini et al.(1994), at Embrapa Meio Ambiente, in Jaguariúna, SP(22º42'S, 46º59'W), during the period from July 1992 toJune 1993, evaluated the method proposed for estimatingaccumulated solarization hours. Due to the lack of localinformation, for obtaining the several correlationspreviously mentioned, it was assumed that, from aclimatological and pedological standpoint, the variouslocations (São Manuel, Piracicaba, Jaguariúna, and SãoCarlos) are homogeneous.A sufficient number of series was generated for eachmonth, so that the final result would be 10 daily radiationseries (monthly means), each with a deviation lower than10%, in relation to the long-term mean monthly value(input data). The characteristics of series, generated forNovember 1992 and January 1993 for Jaguariúna, showthat it is necessary to generate less than 20 series toultimately produce 10 series, each containing a deviationfrom the mean monthly value smaller than 10% of theinput value (Table 2).Based on synthetic daily incoming solar irradiationseries, for each month for Jaguariúna, and usingequations (1) and (2), the maximum daily temperatureswere calculated for each month of the year. Finally, usingequation (5) and values of f (temperature amplitudefraction), the daily temperature waves were determinedusing a filter, such as the one available in Excelspreadsheet; this filter allows the number of hours withtemperatures above a certain threshold to be determined.The mean values resulting from the ten series of eachmonth were compared to those measured in theexperiment by Ghini et al. (1994) (Table 3).From November to March, in Jaguariúna, SP, theresults were close to the experimental data. Theestimated monthly temperature hours higher than 35°Chad deviations smaller than 20%, in relation to valuesmeasured by Ghini et al. (1994). Considering the periodfrom November to February, when a improved samplingof accumulated hours in the experimental assay couldbe obtained, the deviation was then less than 14%.For temperature above 40°C, from November toFebruary, the deviation between calculated and measuredTable 1. Correction factor (∆) for maximum temperature, for different months.(1)Climatological normals 1961–1990 (Brasil, 1992).Pesq. agropec. bras., Brasília, v.41, n.3, p.533-537, mar. 2006C. Tiba and R. Ghini536data was less than 24%, when the month of February isdisregarded, since the values obtained by Ghini et al.(1994) for that period were atypical. Solarized soiltemperatures in March were higher than those inFebruary, which demonstrates some alteration in theresult, in addition to the fact that February has fewerdays. The measured values presented otherinconsistencies; for example, temperatures for themonths October and January were different, in spite oftheir similarity in solar irradiation and precipitation. Inthis case, the model anticipates closer results. Thesevariations were due to the fact that only a one-year periodwas evaluated, while the model uses mean valuesobtained over 30 years.The model departs from measured data by 41%, forthe month of January, for temperatures higher than 45°C.The comparison for the month of December resulted ina deviation of 120%; however, it must be noted that acertain inconsistency exists in the experimental data, asDecember, with approximately one half of theprecipitation relative to January and about 19% moresolar irradiation, resulted in a practically identical numberof accumulated hours at a temperature higher than 45°C.Also, for the months of November and January, theTable 2. Synthetic daily incoming solar irradiation series (H),for the months of November 1992 and January 1993.Jaguariúna, SP.(1)Ghini et al. (1994). Table 3. Comparison between calculated and measured monthly accumulated temperature (T) hours, in solarized soils (10-cm depth), at various experimentalthresholds. Jaguariúna, SP.(1) Ghini et al. (1994). (2)Values calculated considering maximum air temperatures, monthly means (T max), for São Carlos, SP, with values presented in Brasil (1992) 1961–1990 climatologicalnormals.Pesq. agropec. bras., Brasília, v.41, n.3, p.533-537, mar. 2006Estimating temperature in solarized soils 537experimental precipitation and solar irradiation conditionswere quite similar; therefore, if these dimensions arethe driving forces of the process, they should haveresulted in very close numbers of accumulated hours,as anticipated by the calculations, which did not happen.Monthly accumulated hours for temperatures higherthan 45°C had a very small experimental sampling.A number of monthly hours less than 10 hours could beobserved on a single day, or numbers less than 30 hourscould occur in three or four days, at most. From thestandpoint of solar radiation modelling, i.e., the syntheticgeneration of daily solar irradiation, the mean, auto-correlation coefficient, and other statistical parameterscan be surely reproduced; however, reproduction of theexact sequence and daily experimental values for a singleyear cannot be guaranteed. Therefore, it would be quitecommon to generate a sequence of days, whose dailyirradiations would be below the threshold that results inhigher temperatures, and thus it would also be commonto easily introduce or remove fluctuations of one totwo days, therefore being of 10 to 15 monthly hours.In order to calculate daily maximum soil temperatures,the long-term mean air temperatures used were fromSão Carlos, and were obtained from the 1961–1990Weather Normals. Ghini et al. (1994) conducted theassay, specifically in the second half of 1992 and thefirst half of 1993; thus, air temperatures (monthly means)in the experimental assays are certainly different fromthe model’s, due to monthly interannual variabilities. Theintroduction of monthly mean maximum temperatureinterannual variabilities could improve modeling,especially in the highest temperature threshold region.The procedure described provides estimates of thenumber of monthly solarization hours, for the region ofthe State of São Paulo from which the data wereobtained. Validation of such modeling must be done moreextensively with other experimental data. Thecorrelations used in modeling (such as daily solarirradiation, as a function of daily maximum temperatureand daily amplitude) have to be reviewed for otherlocations.AcknowledgementsTo CNPq, for research grant to second author.ReferencesAGUIAR, R.J.; COLLARES-PEREIRA, M.; CONDE, J.P. A simpleprocedure for the generating of sequences of daily radiation valuesusing a library of Markov transition matrices. Solar Energy, v.40,p.269-279, 1988.BRASIL. Ministério da Agricultura e da Reforma Agrária.Departamento Nacional de Meteorologia. Normais climatológicas(1961-1990). Brasília, 1992. 84p.CENIS, J.L. Temperature evaluation in solarized soils by Fourieranalysis. Phytopathology, v.79, p.506-510, 1989.FERRAZ, L.C.L.; BERGAMIN FILHO, A.; AMORIM, L.;NASSER, L.C.B. Viabilidade de Sclerotinia sclerotiorum após asolarização do solo na presença de cobertura morta. FitopatologiaBrasileira, v.28, p.17-26, 2003.GHINI, R.; PARAIBA, L.C.; LIMA, M.W.P. Determinação deperíodo para solarização do solo na região de Campinas/SP. SummaPhytopathologica, v.20, p.131-133, 1994.GRAHAM, V.A.; HOLLANDS, K.G.T.; UNNY, T.E. A time seriesmodel for Kt with application to global synthetic weather generation.Solar Energy, v.40, p.83-92, 1988.LEFÈVRE, A.F.V. Determinação da temperatura letal paraRhizoctonia solani e Sclerotium rolfsii e efeito da solarizaçãosobre a temperatura do solo. 1990. 94p. Dissertação (Mestrado) -Universidade Estadual Paulista Júlio de Mesquita Filho, Botucatu.MAHRER, Y. Prediction of soil temperatures of a soil mulched withtransparent polyethylene. Journal of Applied Meteorology, v.18,p.1263-1267, 1979.PATRÍCIO, F.R.A. Solarização do solo em ambiente protegidoe sua integração com controle biológico ou químico naviabilidade de Pythium aphanidermathum e Rhizoctonia solani.2000. 89p. Tese (Doutorado) - Escola Superior de Agricultura Luizde Queiroz, Piracicaba.STRECK, N.A.; SCHNEIDER, F.M.; BURIOL, G.A. Soil heatingby solarization inside plastic greenhouse in Santa Maria, Rio Grandedo Sul, Brazil. Agricultural and Forest Meteorology, v.82, p.73-82, 1996.SUI, H.; ZENG, D.; CHEN, F. A numerical model for simulating thetemperature and moisture regimes of soil under various mulches.Agricultural and Forest Meteorology, v.61, p.281-299, 1992.SWINBANK, W.C. Longwave radiation from clear skies. QuarterlyJournal of the Royal Meteorological Society, v.89, p.339-348,1963.TIBA, C.; FRAIDENRAICH, N.; MOSZKOWICZ, M.; LYRA,F.J.M.; NOGUEIRA, A.A.M.B.; GROSSI GALLEGOS, H. Atlassolarimétrico do Brasil. Recife: UFPE, 2003. 1 CD-ROM.WU, Y.; PERRY, K.B.; RISTAINO, J.B. Estimating temperature ofmulched and bare soil from meteorological data. Agricultural andForest Meteorology, v.81, p.299-323, 1996.Received on August 12, 2004 and accepted on November 4, 2005

Numerical procedure for estimating temperature in solarized soils.

http://www.alice.cnptia.embrapa.br/bitstream/doc/9908/1/2006AP051.pdf

Numerical procedure for estimating temperature in solarized soils.

Abstract

Similar works

Full text

Available Versions

Repository Open Access to Scientific Information from Embrapa