Evaluation of several degree-day estimation methods in California climates

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1 Int J Biometeorol (1999) 42: ISB 1999 METHODS IN PHENOLOGY selor&:william J. Roltsch Frank G. Zalom Ann J. Strawn Joyce F. Strand Michael J. Pitcairn Evaluation of several degree-day estimation methods in California climates csim&:received: 26 May 1998 / Accepted: 28 October p&:Abstract Procedures for estimating degree-day accumulations are frequently employed instead of the more accurate method of calculating degree-days from hourly temperature data because on-site temperature data are commonly restricted to daily minimum and maximum temperature records. Data from seven methods of estimating degree-days at each of nine locations during 2 years in California were compared by month to degreeday values calculated by hourly summation. Methods included three sine-wave approaches, three triangulation approaches and the averaging (i.e., rectangle) method. Results of the double-sine and corrected-sine (i.e., corrected for day length) methods were nearly identical to those of the single-sine method. The double triangulation and corrected triangulation methods produced very similar results to the single triangulation method. The averaging method and sine-wave methods deviated to a greater extent from degree-day accumulations calculated from hourly temperatures from November through February than did the triangulation methods. Degree-day estimations from the late spring and summer months were more similar to one another for all estimation methods than during the cooler months of the year. Since no advantages were noted in the more complicated double and corrected methods, the single triangulation method or the sine-wave method is preferred as they are less complicated procedures. Of the various temperature threshold cut-off methods evaluated, error levels were unaffected when estimating degree-days using the sine-wave method. The employment of a horizontal cut-off with the triangulation method did not significantly increase the amount of error in the estimation of degree-days. However, an increase in error was observed when employing the intermediate cut-off and vertical threshold W.J. Roltsch F.G. Zalom A.J. Strawn J.F. Strand M.J. Pitcairn Statewide IPM Project, University of California, Davis, California, CA , USA W.J. Roltsch ( ) California Deptartment of Food and Agriculture, Biological Control Program, 3288 Meadowview Road, Sacramento, CA 95832, USA&/fn-block: cut-off techniques with the triangulation method for computing degree-days. dwk&:key words Degree-days Temperature effects Phenology models Developmental threshold Thermal unit&bdy: Introduction The use of degree-days for calculating the temperaturedependent development of poikilotherms and plants is widely accepted as a basis for building phenology and population dynamics models. While nonlinear developmental rate models are common, linear-based degreeday models have, in some instances, been shown to provide a better predictive capability in the field (Hochberg et al. 1986; Roltsch et al. 1990; Fan et al. 1992). Higley et al. (1986) discussed a range of factors that influence the predictive capability of degree-day accumulations. They identified conditions that impact the physiological state of an organism (such as nutrition and behaviorally based thermoregulation), error associated with the assumptions and approximation processes used in estimating developmental rates and thresholds, and the limitations of available weather data. In addition, they emphasized that regardless of calculation method, degreedays are never more than estimates of developmental time. When employing degree-day models in the field, two factors are of particular concern. First, how well do available temperature readings reflect the microclimatic temperatures that an organism actually experiences within the field environment? This issue was addressed for organisms living in tomato plant canopies in northern California (Davidson et al. 1990). Weather station temperature data over several years were found both to overestimate or underestimate canopy temperatures. Differences in degree-day accumulations comparing standard weather station temperatures and canopy temperatures were approximately 10% for several tomato pests.

2 170 A second factor that complicates the use of degreeday models in the field pertains to how well estimates that are calculated by using daily minimum and maximum (i.e., min/max) temperature data correspond to degree-days that are calculated from curves consisting of hourly temperature records. That is, actual daily temperature curves are not symmetrical and their shape may vary considerably due to the specific weather characteristics of a given location and time of year. The calculation of degree-days based on daily min/max values relies upon the assumption that a daily temperature profile can be represented by a specific geometric shape. A sinewave curve has commonly been used for this purpose, in which a single, symmetrical curve is fitted to min/max daily temperatures (Arnold 1960; Baskerville and Emin 1969; Allen 1976). Pruess (1983) urged a standardization of technique, requesting that the sine-wave be used in future studies to estimate degree-days from daily min/max data. Improvements in using the sine-wave method have been sought by calculating degree-days from half-day curves (i.e., a double sine-method), utilizing the morning low temperature and high afternoon temperature of a day for determining degree-days during the first half of the day, followed by the same afternoon temperature and the next day s low morning temperature to calculate degreedays for the second half of the day (Allen 1976). This was similarly done using the triangulation method of calculation (Sevacherian et al. 1977). Furthermore, efforts have been made to employ correction measures so that calculated degree-days correspond more closely to those derived from daily temperature curves based on hourly data (Allen 1976). To date, such attempts to refine degree-day estimates have achieved only minor improvement (Pruess 1983; Higley et al. 1986). An alternative to this general approach is to develop an empirical model, with parameters set to local conditions, that is capable of simulating hourly diurnal temperature profiles (Parton and Logan 1981; Raworth 1994). This approach has shown promise; however, its error has also been shown to vary considerably depending on the specific climatic characteristics of a site (Worner and Penman 1983). High temperature cut-off thresholds are commonly employed when calculating degree-days. These techniques represent a means of addressing changes in the developmental rate of an organism under daily time periods of high ambient temperatures. The horizontal cut-off technique and, to a lesser extent, the vertical threshold technique have been in use for a number of years (Baskerville and Emin 1969; Zalom et al. 1983; Seaman and Barnes 1984; Sanderson et al. 1989). Briefly, the horizontal threshold cut-off is the temperature above which the development rate of a poikilothermic animal or plant does not increase. The vertical threshold cut-off is the temperature above which the development rate of such an organism equals zero. The objective of the present study was to determine whether: (1) if among several degree-day estimation methods that utilize min/max daily temperature data, there is one method that consistently provides more accurate estimates, (2) the currently available approaches are generally well suited for the widely differing climatic locations in California, and (3) any of the upper threshold cut-off approaches are incompatible with degree-day estimation methods. Methods Hourly temperature data were obtained from nine California Irrigation Management Information System (CIMIS a service of the California Department of Water Resources) automated weather stations (Fig. 1). With the exception of the Five Points station, these data consisted of year-long records from each site during 1989 and Data for the Five Points weather station are based on records from 1988 and These station locations and years were selected because they provided complete records of hourly temperature data and are representative of a range of California climates, including those occurring in coastal, intermediate valley, interior valley and low elevation ( 1 km) mountain regions in California. A FORTRAN 77 computer program was created to calculate degree-days using hourly summation. These results were used as a standard with which to compare the output obtained from each of seven degree-day estimation methods utilizing daily min/max temperatures. Each method is listed in Table 1, along with references. Except for the corrected-sine and corrected-triangulation methods, each is available on the University of California s IPM Worldwide Web Site ( and was formerly utilized on its IMPACT computer program (Anonymous 1991). The corrected-sine and corrected-triangulation methods use the double-sine and double-triangulation methods respectively, corrected for day length. The minimum for the day is assigned to 20 min after sunrise and the maximum for the day is assigned to 1 h after solar noon. The contribution of each portion of the double calculations (i.e., pre-solar noon and post-solar noon calcula- Fig. 1 Location of selected California Irrigation Management Information System weather stations in California. (elev Elevation)&/f :c.gi

3 171 Table 1 Names and references of the degree-day estimation methods evaluated&/tbl.c:&tbl.b: Methods a References Averaging [rectangle] Arnold (1960) Single-sine Baskerville and Emin (1969), Allen (1976) Double-sine Allen (1976) Corrected-sine none [in-house; UC Statewide IPM b Project] Single-triangle Lindsey and Newman (1956) Double-triangle Sevacherian et al. (1977) Correct-triangle none [in-house, UC Statewide IPM Project] a Use of most methods is reviewed by Zalom et al. (1983) b Integrated Pest Management&/tbl.b: tions) correspond to the number of hours between the time of the minimum and maximum temperatures (i.e., the rising part of the diurnal curve) and the remainder of the day (i.e., the falling part of the diurnal curve). The time of solar noon and sunrise were calculated using an algorithm (based on longitude, latitude and date) published by Blackadar (1984). For all degree-day calculation methods, a lower threshold of 10 C was utilized. This is a commonly used lower threshold temperature representative of many insect species (Pruess 1983). Horizontal, vertical and intermediate high temperature threshold cutoff techniques were assessed for whether they increased the error levels. The horizontal- and vertical-threshold cut-off techniques were the same as described elsewhere (e.g., Baskerville and Emin 1969; Zalom et al. 1983; Seaman and Barnes 1984; Sanderson et al. 1989). The intermediate threshold cut-off has not been published. It represents a decline in growth rate at temperatures above an upper threshold value and is estimated as the difference in degree-days between a horizontal threshold calculation and calculation using no high temperature threshold. This difference is subtracted from the horizontal threshold calculation and constitutes a dip in the horizontal threshold rather than a constant value, thereby mirroring the area above the threshold temperature in a diurnal temperature curve. The compatibility of each upper threshold cut-off method when used with triangulation and sine-wave degree-day estimation methods was assessed using upper thresholds of 26.7 and 32 C. Although 32 C is representative of many upper thresholds, 26.7 C was used because it provided a more frequent employment of the upper-threshold cut-off routine. This provided a more rigorous testing of each upper-threshold cut-off method s impact on error associated with the estimation of degree-days. Five warm season months for four sites were included in the analysis. These were sites where daily high temperatures commonly exceeded 32 C from May through September. Data analysis Monthly cumulative degree-days calculated by each method, with a lower threshold of 10 C, were compared. Using the hourly summation results as a standard, the extent to which each method deviated from the standard was calculated as a percentage. For each site, the monthly percent deviation from the standard is plotted for all seven degree-day methods (Fig. 2). In addition, the mean diurnal temperature profiles for each month, and cumulative monthly degree-day totals are presented by location. To estimate the degree of variation between years that is associated with each site, we have created a table showing the variation in percent deviation between 2 years. Season-long means of monthly error values (min/max-based estimate vs. hourly summation) were calculated using one method to identify sites where problems are most likely to occur. For this comparison, the degree-day estimation method demonstrating the least error in the graphical analysis was used. Results Method performance A comparison of seven degree-day estimation methods is presented for each of the nine sites (Fig. 2a i). The graphical comparison indicates that the single, double and corrected triangulation methods (solid lines) perform similarly among themselves, as do the different sinewave methods (broken lines). It is particularly noteworthy that less deviation from hourly summation estimates is consistently associated with the triangulation method from November through February at all sites. The difference in results between the triangulation and sine-wave methods during March and October was variable among locations. The mean (SD) error among the nine sites from April through September was nearly identical for the single triangulation versus single sine-wave methods (4.8%±4.4 vs. 4.7%±4.3, respectively). Both methods performed erratically at the McArthur site (Fig. 2i). When the McArthur site was eliminated from the mean calculations, the mean error from April through September for all remaining sites combined was 4.3%±3.9 vs. 4.5%±4.5 for the single triangulation and sine-wave methods, respectively. Although the averaging method (dotted lines) often produced similar results to those of the triangulation and sine-wave methods from April through September, there were large discrepancies that occurred sporadically. Most notably, large differences representing a considerable increase in error occurred in May at Castroville and McArthur, and during April, September and October in Watsonville (Fig. 2e, f, i). Method suitability across climatic locations The annual and monthly mean error by site resulting from the triangulation method was nearly always less than 10% for the three low-elevation, interior valley sites (Brawley, Five Points, and Davis; Figs. 2a c, 3). During the warmer months at these locations, the error was less than 5% for both the triangulation and sine-wave methods. Errors for coastal, intermediate valley and mountainous sites were high in some instances, especially from late fall to spring (Figs. 2 and 3). For most sites, error by month did not greatly change between years, as illustrated by the triangulation method estimations (Table 2). The greatest difference in error between years occurred from November through February, at a time when cumulative degree-days are very low and therefore the impact of each degree-day on summary statistics is high. Compatibility of threshold cut-off approaches with triangulation and sine-wave methods An assessment of high temperature threshold cut-off approaches was limited to identifying their effect on error

4 172 Fig. 2a i Monthly error of each degree-day estimation method, mean hourly diurnal temperature profiles by month, and monthly degree-day accumulations (top axis of each graph) for each weatherstation. Percent values that are out of range for certain months are presented in parentheses. (S. Single, D. double, C. corrected, TRIA triangulation)&/f :c.gi associated with the single triangulation and single sinewave estimation methods. None of the upper-threshold procedures increased the error obtained when used with the single sine-wave method (Table 3). Results were variable when using the high temperature threshold cutoff approaches with the triangulation method. The horizontal cut-off technique did not appreciably increase the error associated with the triangulation method at temperature cut-off points of 26.7 and 32 C (Table 3). The error increased substantially while using the triangulation

5 173 Fig. 2e h (Legend see p. 172) method when the vertical threshold cut-off technique was used at either upper threshold temperature. The error resulting from the intermediate cut-off approach was not greatly increased at 32 C, however an increase in error was noted (3.2% vs. 7.7% error) with a cut-off temperature of 26.7 C. Discussion The single triangulation and single sine-wave methods estimate degree-days relatively well. However, the use of these methods requires that consideration be given to the time of year, geographical location and biology of the organism under study. Comparatively more error was associated with the single sine-wave method during the winter months from November to February. At some loca-

6 174 Fig. 2i (Legend see p. 172) Fig. 3 Mean percent error associated with degree-day estimates by triangulation versus hourly summations, averaged over all months by site. Station sites are grouped by climatic similarity. Five Points station records from 1988 and 1990&/f :c.gi tions, single sine-wave error was also greater during March. From April through October, the two methods produced similar results. Therefore, during the winter and early spring months of the year, the triangulation method may be preferable over the sine-wave or averaging method at many locations across California s climatic zones. For some locations along the coast (e.g., Salinas), none of the methods provide suitable estimates during most of the year. The averaging method s performance is the poorest among the three primary methods, having an elevated error for a greater portion of the year while temperatures are relatively cool. This method is uniquely affected by minimum temperatures that are below the lower threshold. That is, with a lower threshold of 10 C, an incorrect total of zero degree-days will be calculated if daily temperatures range from a low of 5 C and a high of 15 C (i.e., dd=[(mint+maxt)/2 LT; 0=(5+15)/2 10], where mint = minimum daily temperature, maxt = maximum daily temperature, LT = lower threshold. Within the interior valleys, there is very little difference between approximation methods from mid-spring to fall. For organisms that are predominantly active during the warm periods of a year in the interior valleys, the error associated with the sine-wave versus triangulation methods may have little impact because the number of degree-days that accumulate during the cool months represent only a small proportion of the thermal units that would drive their development and population growth over the course of the season. Obviously, this issue must be addressed carefully for each species for which the approximations are to be applied. The mean daily temperature profiles by month suggest that the triangulation method is favored by a particular curve form. That curve form is best illustrated by the

7 175 Table 2 Monthly triangulation estimates of degree-days above 10 o C as a percentage of hourly summation degree-days&/tbl.c:&tbl.b: Site Years Month Mean (SD) & of Diff. a Jan Feb Mar Apr May Jun July Aug Sep Oct Nov Dec Difference Davis Diff ±4.9 b (2.2±3.3) c Five Points Diff ±4.9 (1.2±0.9) Brawley Diff ±4.6 (1.4±1.2) Salinas Diff ±6.6 (5.0±4.4) Riverside Diff ±2.0 (1.8±2.0) Castroville Diff ±7.5 (6.6±5.3) Watsonville Diff ±5.0 (8.8±5.4) McArthur Diff ±7.4 (5.0±2.5) Camino Diff ±3.2 (2.6±2.7) a Difference in mean error between years by month b Mean monthly difference of percent error between years c Nov., Dec., Jan. and Feb. omitted from calculation&/tbl.b: Table 3 Error in degree-days when using triangulation and sinewave estimation methods with various upper threshold cut-off techniques&/tbl.c:&tbl.b: Upper Cut-off Percent Percent threshold temp. difference difference Cut-off oc in single in single triangulation sine vs. vs. summation summation [mean ±SD] [mean ±SD] None None 3.2±2.22 a 3.0±2.30 Horizontal ± ±2.22 Horizontal ± ±2.00 Intermediate ± ±2.15 Intermediate ± ±1.80 Vertical ± ±2.08 Vertical ± ±2.74 a Mean percent difference in degree-day estimates using triangulation or sine-wave methods (using min/max data) versus degreedays by hourly summation. Data records from May to October at one California weather station in 1988 and four stations in 1989&/tbl.b:&roles: Brawley and Five Points locations. Temperature profiles at these locations are strongly convex during the morning period, followed by a late afternoon rapid drop in temperature. In comparing three locations in an agricultural setting near Monterey Bay, it is noted that the Watsonville and Castroville morning temperature profiles are similarly convex (most evident from May to September), while those of Salinas are either straight or somewhat concave during this time of year. The Castroville and Watsonville stations are very close (<8 km) to the coast, while the Salinas station is located in a narrow valley approximately 21 km inland from the coast. Estimates for the Watsonville and Castroville locations are much closer to their respective hourly summation values than those calculated for Salinas. The weather in Salinas is often represented by a strong cloud bank that clears in late morning. High temperature threshold cut-off techniques were assessed to characterize their compatibility with the tri-

8 176 angulation and sine-wave degree-day approximation methods. It is evident that the error is elevated when combining certain threshold cut-off techniques with the triangulation method. Therefore, it is necessary to evaluate the impact of each newly devised high temperature threshold cut-off approach before incorporating it with a given degree-day estimation method for general application. The use of empirical models for simulating daily temperature profiles, whereby an hourly model output is used to run a degree-day summation procedure when provided with only min/max daily temperature values, may help to further reduce error. The method developed by Parton and Logan (1981) shows versatility, however its use would require a considerable investment in obtaining parameters for each weather station, and would require access to hourly temperature profiles for at least 1 entire year. In addition, limitations in its usefulness have been identified; apparently, not all diurnal temperature curves are well represented by this method (Worner and Penman 1983). In California, hourly temperature records are currently available for only a limited number of stations statewide because of instrumentation constraints in rural agricultural areas, and memory limitations of computers storing hourly (or even more frequent) temperature observations. With rapidly occurring advances in instrumentation, computer, and communication technology, the ease by which hourly temperatures can be conveniently collected and stored is greatly improving. In fact, some relatively inexpensive instrumentation is available which can accumulate thermal units continuously. As a result, it is most likely that estimation procedures will experience declining use into the future; however, the time frame over which this will occur is uncertain. 2.p&:Acknowledgements The authors wish to thank Catalina Phan for her diligent assistance in preparing many of the graphics used in the manuscript. References Allen JC (1976) A modified sine wave method for calculating degree days. Environ Entomol 5: Anonymous (1991) IMPACT (integrated management of production in agriculture using computer technology) user s manual. University of California IPM Pub. 15. Davis, Calif. Arnold CY (1960) Maximum-minimum temperatures as a basis for computing heat units. Am Soc Hort Sci 76: Baskerville GL, Emin P (1969) Rapid estimation of heat accumulation from maximum and minimum temperatures. Ecology 50: Blackadar A (1984) A computer almanac. Weatherwise 37: Davidson NA, Wilson LT, Hoffmann MP, Zalom FG (1990) Comparisons of temperature measurements from local weather stations and the tomato plant canopy: implications for crop and pest forecasting. J Am Soc Hort Sci 115: Fan Y, Groden E, Drummond FA (1992) Temperature-dependent development of Mexican bean beetle (Coleoptera: Coccinellidae) under constant and variable temperatures. J Econ Entomol 85: Higley LG, Pedigo LP, Ostlie KR (1986) DEGDAY: a program for calculating degree-days, and assumptions behind the degreeday approach. Environ Entomol 15: Hochberg ME, Pickering J, Getz WM (1986) Evaluation of phenology models using field data: case study for the pea aphid, Acyrthosiphon pisum, and the blue alfalfa aphid, Acyrthosiphon kondoi (Homoptera: Aphididae). Environ Entomol 15: Lindsey AA, Newman JE (1956) Use of official weather data in spring time-temperature analysis of an Indiana phenological record. Ecology 37: Parton WJ, Logan JA (1981) A model for diurnal variation in soil and air temperature. Agric Meteorol 23: Pruess KP (1983) Day-degree methods for pest management. Environ Entomol 12: Raworth DA (1994) Estimation of degree-days using temperature data recorded at regular intervals. Environ Entomol 23: Roltsch WJ, Mayse MA, Clausen K (1990) Temperature-dependent development under constant and fluctuating temperatures: comparison of linear versus nonlinear methods for modeling development of western grapeleaf skeletonizer (Lepidoptera: Zygaenidae). Environ Entomol 19: Sanderson JP, Barnes MM, Seaman WS (1989) Synthesis and validation of a degree-day model for navel orangeworm (Lepidoptera: Pyralidae) development in California almond orchards. Environ Entomol 18: Seaman WS, Barnes MM (1984) Thermal summation for the development of the navel orangeworm in almond (Lepidoptera: Pyralidae). Environ Entomol 13:81 85 Sevacherian V, Stern VM, Mueller AJ (1977) Heat accumulation for timing Lygus control measures in a safflower-cotton complex. J Econ Entomol 70: Worner SP, Penman DR (1983) Analysis of thermal summation models. In: Proceedings, Thirty-sixth New Zealand Weed and Pest Control Conference. New Zealand Weed and Pest Control Society, August 1983, pp Zalom FG, Goodell PB, Wilson LT, Barnett WW, Bentley WJ (1983) Degree-days: the calculation and use of heat units in pest management. University of California, Division of Agriculture and Natural Resources, Leaflet 21373, pp 10