An improved model for determining degree-day values from daily temperature data

Although using hourly weather data offers the greatest accuracy for estimating growing degree-day values, daily maximum and minimum temperature data are often used to estimate these values by approximating the diurnal temperature trends. This paper presents a new empirical model for estimating the hourly mean temperature. The model describes the diurnal variation using a sine function from the minimum temperature at sunrise until the maximum temperature is reached, another sine function from the maximum temperature until sunset, and a square-root function from then until sunrise the next morning. The model was developed and calibrated using several years of hourly data obtained from five automated weather stations located in California and representing a wide range of climate conditions. The model was tested against an additional data-set at each location. The temperature model gave good results, the root-mean-square error being less than 2.0 °C for most years and locations. The comparison with published models from the literature showed that the model was superior to the other methods. Hourly temperatures from the model were used to calculate degree-day values. A comparison between degree-day estimates determined from the model and those obtained other selected methods is presented. The results showed that the model had the best accuracy in general regardless of the season. Received: 25 October 2000 / Revised: 2 July 2001 / Accepted: 2 July 2001     

Temperature data for phenological models

In an arid environment, the effect of evaporation on energy balance can affect air temperature recordings and greatly impact on degree-day calculations. This is an important consideration when choosing a site or climate data for phenological models. To our knowledge, there is no literature showing the effect of the underlying surface and its fetch around a weather station on degree-day accumulations. In this paper, we present data to show that this is a serious consideration, and it can lead to dubious models. Microscale measurements of temperature and energy balance are presented to explain why the differences occur. For example, the effect of fetch of irrigated grass and wetting of bare soil around a weather station on diurnal temperature are reported. A 43-day experiment showed that temperature measured on the upwind edge of an irrigated grass area averaged 4% higher than temperatures recorded 200 m inside the grass field. When the single-triangle method was used with a 10°C threshold and starting on May 19, the station on the upwind edge recorded 900 degree-days on June 28, whereas the interior station recorded 900 degree-days on July 1. Clearly, a difference in fetch can lead to big errors for large degree-day accumulations. Immediately after wetting, the temperature over a wet soil surface was similar to that measured over grass. However, the temperature over the soil increased more than that over the grass as the soil surface dried. Therefore, the observed difference between temperatures measured over bare soil and those over grass increases with longer periods between wettings. In most arid locations, measuring temperature over irrigated grass gives a lower mean annual temperature, resulting in lower annual cumulative degree-day values. This was verified by comparing measurements over grass with those over bare soil at several weather stations in a range of climates. To eliminate the effect of rainfall frequency, using temperature data collected only over irrigated grass, is recommended for long-term assessment of climate change effects on degree-day accumulation. In high evaporative conditions, a fetch of at least 100 m of grass is recommended. Our results clearly indicate that weather stations sited over bare soil have consistently higher degree-day accumulations. Therefore, especially in arid environments, phenology models based on temperature collected over bare soil are not transferable to those based on temperature recorded over irrigated grass. At a minimum, all degree-day-based phenology models reported in the literature should clearly describe the weather station site. Received: 25 October 2000 / Revised: 10 July 2001 / Accepted: 10 July 2001     

Effect of temperature on development and activity periods of the leek moth Acrolepiopsis assectella Zell. (Lep., Acrolepiidae)

Effects of temperature on egg, larval and pupal developmental times of the leek moth were examined at five constant temperatures ranging from 12 to 20°C. Using this data, a linear degree-day model for the leek moth was developed. The model gave the threshold temperature of T _h =6°C, and 630 degree-days were required above the threshold temperature, to complete the development of the leek moth. To validate the model in the field, flight activity during the summers of 1998 and 1999 was studied using pheromone traps. If the summer is warm the leek moth can have two generations per year in Sweden, but the probability of completing two generations within leek plantations is very limited. The likelihood of the leek moth becoming a pest is highly dependent on access to alternative host plants for the first generation of leek moths.     

Developmental Models for Estimating Ecological Responses to Environmental Variability: Structural,Parametric, and Experimental Issues

Developmental models that account for the metabolic effect of temperature variability on poikilotherms, such as degree-day models, have been widely used to study organism emergence, range and development, particularly in agricultural and vector-borne disease contexts. Though simple and easy to use, structural and parametric issues can influence the outputs of such models, often substantially. Because the underlying assumptions and limitations of these models have rarely been considered, this paper reviews the structural, parametric, and experimental issues that arise when using degree-day models, including the implications of particular structural or parametric choices, as well as assumptions that underlie commonly used models. Linear and non-linear developmental functions are compared, as are common methods used to incorporate temperature thresholds and calculate daily degree-days. Substantial differences in predicted emergence time arose when using linear versus non-linear developmental functions to model the emergence time in a model organism. The optimal method for calculating degree-days depends upon where key temperature threshold parameters fall relative to the daily minimum and maximum temperatures, as well as the shape of the daily temperature curve. No method is shown to be universally superior, though one commonly used method, the daily average method, consistently provides accurate results. The sensitivity of model projections to these methodological issues highlights the need to make structural and parametric selections based on a careful consideration of the specific biological response of the organism under study, and the specific temperature conditions of the geographic regions of interest. When degree-day model limitations are considered and model assumptions met, the models can be a powerful tool for studying temperature-dependent development.     

Degree-day Models for Predicting Egg Hatch and Population Increase of Criconemella xenoplax

A degree-day model was derived to predict egg hatch for Criconemella xenoplax. Eggs collected from gravid females were incubated in distilled water at constant temperatures of 10-35 C. Sixty-six percent of all eggs hatched between 13 and 32 C, and 42% hatched at 10 C. All eggs aborted above 32.5 C. Between 25 and 32 C, 8.5 ± 0.5 days were required for egg hatch. Degree-day requirement for egg hatch at 10-30 C was estimated to be 154 ± 5 with a base of 9.03 ± 0.04 C. This base of 9 C was adopted in studies of the relationship between degree-days and nematode population increase on Prunus seedlings grown 9-11 weeks in a greenhouse. Degree-day accumulations were based upon daily averages from maximum and minimum air temperatures. Ratios of final to initial population densities exhibited an exponential pattern in relation to degree-day accumulations with proportionate doubling increment of 0.100 ± 0.049 every 139 ± 8 degree-days. These results provide a means of predicting nematode population increase under greenhouse conditions and a basis for choosing sampling intervals when evaluating nematode multiplication.     

A physiologically based approach for degree-day calculation in pest phenology models: the case of the European Corn Borer (<Emphasis Type="BoldItalic">Ostrinia nubilalis</Emphasis> Hbn.) in Northern Italy

Phenological models based on degree-day accumulation have been developed to support the integrated pest management of many insects. Most of these models are based on linear relationships between temperature and development, and on daily time step simulations using daily minimum and maximum temperatures. This approach represents an approximation that does not take into account the insect physiological response to temperature, and daily temperature fluctuations. The objective of this work has been to develop a phenological model for the European corn borer (ECB) based on the insect physiological response to temperature and running at an hourly time step. Two modeling solutions based on the same generic compartmental system have been compared: the first based on a physiologically based relationship between temperature and development, and using hourly derived temperatures as input (HNL modeling solution); and the second based on a linear relationship between temperature and degree-day accumulation and using daily temperature (DL modeling solution). The two approaches have been compared using ECB moth capture data from the Piemonte region in Northern Italy. The HNL modeling solution showed the best results for all the accuracy indicators. The DL modeling solution showed a tendency to anticipate ECB phenological development too early. This tendency is attributable to the linear relationship between temperature and development, which does not take into account (1) the decline of this relationship at high temperatures, and (2) the daily fluctuation of temperature. As a consequence, degree-days accumulation is accelerated in the DL modeling solution and the phenological development anticipated.     

A degree-day model of sheep grazing influence on alfalfa weevil and crop characteristics

Domestic sheep (Ovis spp.) grazing is emerging as an integrated pest management tactic for alfalfa weevil, Hypera postica (Gyllenhal), management and a degree-day model is needed as a decision and support tool. In response to this need, grazing exclosures with unique degree-days and stocking rates were established at weekly intervals in a central Montana alfalfa field during 2008 and 2009. Analyses indicate that increased stocking rates and grazing degree-days were associated with decreased crop levels of weevil larvae. Larval data collected from grazing treatments were regressed against on-site and near-site temperatures that produced the same accuracy. The near-site model was chosen to encourage producer acceptance. The regression slope differed from zero, had an r2 of 0.83, and a root mean square error of 0.2. Crop data were collected to achieve optimal weevil management with forage quality and yield. Differences were recorded in crude protein, acid and neutral detergent fibers, total digestible nutrients, and mean stage by weight. Stem heights differed with higher stocking rates and degree-days recording the shortest alfalfa canopy height at harvest. The degree-day model was validated at four sites during 2010 with a mean square prediction error of 0.74. The recommendation from this research is to stock alfalfa fields in the spring before 63 DD with rates between 251 and 583 sheep days per hectare (d/ha). Sheep should be allowed to graze to a minimum of 106 and maximum of 150 DD before removal. This model gives field entomologists a new method for implementing grazing in an integrated pest management program.     

Assessing the distribution of the Argentine ant using physiological data

To address the lack of physiological approaches in current models assessing the potential distribution of the Argentine ant, we used data on brood development from distinct sources to evaluate a series of degree-day models for Catalonia (NE Iberian Peninsula), and data on the brood survival and oviposition rates to develop a worker production model. The degree-day model generated using data from Newell and Barber (1913) and Benois (1973) indicated that the number of degree-days required for the complete development from egg to adult worker was 445.4 degree-days above a threshold of 15.9 °C, while the model calibrated using data from Abril et al. (2008, in press) suggested 599.5 degree-days above 18.4 °C. Comparisons between the degree-day model predictions and the currently known distribution of the Argentine ant suggested that the one generated using data from Newell and Barber (1913) and Benois (1973) overestimated the presence of the species, while the one calibrated using data from Abril et al. (2008; in press) underestimated it. On the other hand, the predicted daily net production of Argentine ant workers generated by the worker production model predicted more accurately the distribution of the Argentine ant than the degree-day models. Our results show the utility of incorporating physiological data in models to assess the distribution limits of the Argentine ant, which up to date have taken little account of the physiological needs of the species in terms of its establishment and dispersion in its introduced ranges.     

Determining degree-day thresholds from field observations

 This paper compares several methods for determining degree-day (°D) threshold temperatures from field observations. Three of the methods use the mean developmental period temperature and simple equations to estimate: (1) the smallest standard deviation in °D, (2) the least standard deviation in days, and (3) a linear regression intercept. Two additional methods use iterations of cumulative °D and threshold temperatures to determine the smallest root mean square error (RMSE). One of the iteration methods uses a linear model and the other uses a single triangle °D calculation method. The method giving the best results was verified by comparing observed and predicted phenological periods using 7 years of kiwifruit data and 10 years of cherry tree data. In general, the iteration method using the single triangle method to calculate °D provided threshold temperatures with the smallest RMSE values. However, the iteration method using a linear °D model also worked well. Simply using a threshold of zero gave predictions that were nearly as good as those obtained using the other two methods. The smallest standard deviation in °D performed the worst. The least standard deviation in days and the regression methods did well sometimes; however, the threshold temperatures were sometimes negative, which does not support the idea that development rates are related to heat units. Received: 26 May 1998 / Accepted: 28 October 1998     

Statistical estimation of degree days of mosquito development under fluctuating temperatures in the field.

Degree-days are important parameters for developing predictive models of mosquito populations. Conventional methods of estimation of degree-days are typically applied to observations under constant temperatures in the laboratory. These methods are difficult to apply in the field where temperatures fluctuate. For estimating degree-days of larval developments of mosquitoes in the field, we applied Dennis' stochastic phenological model to a semi-field observation of Culex restuans. A parametric bootstrap approach was introduced to estimate standard errors of the parameters. We found that the estimated degree-days varied with various assumptions about the temperature base. Given the latter, the model can satisfactorily estimate the degree-days of larval and pupal developments of Cx. resturans. This approach is especially useful to measure spatio-temporal variability in larval development among various types of aquatic habitats.     

Phenology of Lacanobia subjuncta (Lepidoptera: Noctuidae) in Washington and Oregon apple orchards

The phenology of Lacanobia subjuncta (Grote & Robinson) (Lepidoptera: Noctuidae) was investigated in 30 apple orchards in central Washington state and northeastern Oregon from 1998 to 2001 (57 total orchard-yr). Adult captures in pheromone-baited traps were fit to a Weibull distribution to model emergence of the first and second generations. Initial capture of first generation adults was observed at 216.2 +/- 2.6 degree-days (DD) (mean +/- SEM) from 1 March by using a base temperature of 6.7 degrees C. The model predicted that flight was 5 and 95% complete by 240 and 700 degree-days (DD), respectively. Monitoring of oviposition and hatch was used to establish a protandry plus preoviposition degree-day requirement of 160.0 +/- 7.7 DD, as well as to provide data to describe the entire hatch period. Egg hatch was 5 and 95% complete by 395 and 630 DD, respectively. The start of the second flight was observed at 1217.1 +/- 8.3 DD by using an upper threshold for development of 32 degrees C and a horizontal cutoff. The model indicated that the second flight was 5 and 95% complete by 1220 and 1690 DD, respectively. Second generation hatch was 5 and 95% complete by 1440 and 1740 DD, respectively. A discussion of the potential uses of these detailed phenology data in optimizing management strategies is presented.     

红体色麦长管蚜发育起点温度和有效积温

研究观测红体色麦长管蚜Macrosiphum avenae(Fabricius)无性世代各个若虫龄期在14,17,20,23和26℃条件下的生长发育速率。结果表明,红体色麦长管蚜各龄期若虫的发育历期随着温度的上升而缩短。采用不同的方法计算得到的红体色麦长管蚜发育起点温度和有效积温不同,而直线回归法计算的变异系数较小,其结果显示红色麦长管蚜若虫期的发育起点温度和有效积温分别是4.478℃和110.662日.度。     

有效积温Sine函数拟合模型及其应用

阐述了昆虫物候分析的SSPM模型（single sine phonological model）计算方程和过程,该模型采用Sine函数拟合每天温度变化,并利用积分,获取每天有效积温和一定时间内日度累积值.SSPM重要的参数有发育起点温度和上限温度,参与模型计算包括日最高气温和日最低气温2个输入值,在输入值和参数值组合条件下,模型有6个不同计算方程.以棉铃虫（Helicoverpa armigera）为例,介绍了SSPM在昆虫发育历期分析过程,简单表述了模型预测功能.随自动化气象站分布密度增加和Internet技术的发展,模型在区域化害虫管理中有着重要的应用前景.     

Logistic模型预测东北越冬代水稻二化螟发生期

2001~2003年在吉林省柳河县绿色大米生产稻区,采用Logistic模型拟合越冬代二化螟Chilosuppressalis(Walker),有效积温和诱捕器诱蛾百分率的关系。结果表明logistic模型有较好的拟合性。由模型拟合结果预测当地越冬代二化螟发蛾始盛期、高峰期和盛末期所需有效积温分别为275.9,358.4和440.8日.度,可以适时指导大田防治。     

Physiological time model for predicting adult emergence of western corn rootworm (Coleoptera: Chrysomelidae) in the Texas High Plains

Field observations at three locations in the Texas High Plains were used to develop and validate a degree-day phenology model to predict the onset and proportional emergence of adult Diabrotica virgifera virgifera LeConte (Coleoptera: Chrysomelidae) adults. Climatic data from the Texas High Plains Potential Evapotranspiration network were used with records of cumulative proportional adult emergence to determine the functional lower developmental temperature, optimum starting date, and the sum of degree-days for phenological events from onset to 99% adult emergence. The model base temperature, 10 degrees C (50 degrees F), corresponds closely to known physiological lower limits for development. The model uses a modified Gompertz equation, y = 96.5 x exp (-(exp(6.0 - 0.00404 x (x - 4.0), where x is cumulative heat (degree-days), to predict y, cumulative proportional emergence expressed as a percentage. The model starts degree-day accumulation on the date of corn, Zea mays L., emergence, and predictions correspond closely to corn phenological stages from tasseling to black layer development. Validation shows the model predicts cumulative proportional adult emergence within a satisfactory interval of 4.5 d. The model is flexible enough to accommodate early planting, late emergence, and the effects of drought and heat stress. The model provides corn producers ample lead time to anticipate and implement adult control practices.     

Evaluation of different methods for determining growing degree-day thresholds in apricot cultivars

The aim of this study was to examine different methods for determining growing degree-day (GDD) threshold temperatures for two phenological stages (full bloom and harvest) and select the optimal thresholds for a greater number of apricot (Prunus armeniaca L.) cultivars grown in the Belgrade region. A 10-year data series were used to conduct the study. Several commonly used methods to determine the threshold temperatures from field observation were evaluated: (1) the least standard deviation in GDD; (2) the least standard deviation in days; (3) the least coefficient of variation in GDD; (4) regression coefficient; (5) the least standard deviation in days with a mean temperature above the threshold; (6) the least coefficient of variation in days with a mean temperature above the threshold; and (7) the smallest root mean square error between the observed and predicted number of days. In addition, two methods for calculating daily GDD, and two methods for calculating daily mean air temperatures were tested to emphasize the differences that can arise by different interpretations of basic GDD equation. The best agreement with observations was attained by method (7). The lower threshold temperature obtained by this method differed among cultivars from −5.6 to −1.7°C for full bloom, and from −0.5 to 6.6°C for harvest. However, the “Null” method (lower threshold set to 0°C) and “Fixed Value” method (lower threshold set to −2°C for full bloom and to 3°C for harvest) gave very good results. The limitations of the widely used method (1) and methods (5) and (6), which generally performed worst, are discussed in the paper.     

An empirical predictive model for the flight period of Platypus koryoensis (Coleoptera: Platypodinae)

Between 2007 and 2009, field studies were conducted in four Quercus mongolica Fischer ex Ledebour forests in Korea to develop an empirical degree-day model for the flight period of the ambrosia beetle, Platypus koryoensis (Murayama). The lower developmental threshold temperature was estimated using an iterative method based on field trap catches and temperatures. The pooled proportion of the total number of beetles found in the traps at the end of the experiment was plotted against the accumulated degree-days at selected baseline temperatures, and these plots were fitted by the Weibull function. The baseline temperature with the highest coefficient of determination was considered the lower developmental threshold temperature, and this was estimated to be 5.8 °C. The explanatory power of the model was 89 %. Moreover, the model accurately predicted the time distributions of P. koryoensis flights in 2011 and 2012 at one of the sites. The estimated median flight dates in 2011 and 2012 were 4 days earlier and 5 days later than the corresponding observed flight dates, respectively. The estimated median date of flight advanced progressively during 1970–2010 by a total of 9 days due to an increase in annual mean temperature.     

Temperature-Dependent Development of Pasteuria penetrans in Meloidogyne arenaria

Pasteuria penetrans is a promising biological control agent of plant-parasitic nematodes. This study was conducted to determine effects of temperature on the bacterium''s development in Meloidogyne arenaria. Developmental stages of P. penetrans were viewed with a compound microscope and verified with scanning electron microscopy within each nematode at 100 accumulated degree-day intervals by tracking accumulated degree-days at three temperatures (21, 28, and 35 °C). Five predominant developmental stages of P. penetrans were identified with light microscopy: endospore germination, vegetative growth, differentiation, sporulation, and maturation. Mature endospores were detected at 28, 35, and >90 calendar days at 35, 28, and 21 °C, respectively. The number of accumulated degree-days required for P. penetrans to reach a specific developmental stage was different for each temperature. Differences were observed in the development of P. penetrans at 21, 28, and 35 °C based on regression values fitted for data from 100 to 600 accumulated degree-days. A linear response was observed between 100 to 600 accumulated degree-days; however, after 600 accumulated degree-days the rate of development of P. penetrans leveled off at 21 and 28 °C, whereas at 35 °C the rate decreased. Results suggest that accumulated degree-days may be useful only in predicting early-developmental stages of P. penetrans.     

Age structure of overwintered face fly populations estimated by pteridine concentrations and ovarian dynamics

Pteridines in the head capsules of face flies, Musca autumnalis DeGeer, were measured spectrofluorometrically to provide estimates of age. The flies also were dissected to determine ovarian development and fat body hypertrophy. Physiological ages in terms of degree-day accumulations were estimated among late autumn, winter, and early spring face flies. The reproductive history of eight overwintered face fly populations near Ames, Iowa, U.S.A., suggested that each had behaved as a single cohort, maturing their eggs and ovipositing according to a simple heat unit model. 83.8 +/- 16.4 degree-days above a 12 degrees threshold (DD > 12 degrees) were estimated to elapse between 1 January and the date at which 50% of overwintered cohorts had oviposited. Pteridine deposits indicated that diapausing females in late autumn had acquired a mean 96 +/- 36 DD > 9.8 degrees and the males 135 +/- 39 DD > 9.8 degrees. Soon after emergence from hibernaculae, females were average physiological ages of 135 +/- 25 DD > 9.8 degrees and the males were 152 +/- 28 DD > 9.8 degrees. Mean physiological age of overwintered females was 155 +/- 37 DD > 9.8 degrees compared with 110 +/- 38 DD > 9.8 degrees among parous flies in summer. Overwintered males in spring were an average 175 +/- 41 DD > 9.8 degrees compared with 144 +/- 65 DD > 9.8 degrees among summer flies.     

双斑长跗萤叶甲的发育起点温度与有效积温

双斑长跗萤叶甲Monolepta hieroglyphica(Motschulsky)已成为新疆北疆棉区的一重大新害虫,至今该虫各虫态的发育历期都不清楚。在室内5个恒温下(19,22,25,28和31℃),利用有效积温法则和"最小二乘法"对双斑长跗萤叶甲各虫态的发育起点温度和有效积温进行研究。结果表明,卵期、幼虫期、蛹期和产卵前期的发育起点温度分别为9.8,10.8,12.6和10.1℃;有效积温分别为1 182.2,401.2,111.9和269.0日.度;整个世代完成发育所需要的有效积温为1 971.6日.度,预测在新疆北疆1年发生1代。