Calculating Chilling Hours and Chill Units from Daily Maximum and Minimum Temperature Observations

Abstract

Models that require hourly weather data as inputs are being constructed to simulate development of insects and plants. Most agricultural and, climatological weather observation stations, however, do not include the capability to record hourly data. Thus, methods , for simulating hourly observations need to be developed if the wealth of data collected in such stations is to be used in these models. One application for simulated temperature data is in the peach industry. This industry uses chilling hours and chill units to determine progression of fulfillment of chilling requirements through the winter season. In the past, chill hours and chill units have been calculated at a limited number of locations using either manually recorded hourly observations or thermograph charts. Richardson (1974) proposed a very simple model for determining temperatures from which chill units were calculated. He used a straight line with 12 hr between maximum and minimum temperature. Richardson recognized the limitations of this model, especially when assuming the daily temperature curve was symmetrical about 12 hr. He suggested that the time between maximum and minimum temperature may need to be changed to better represent daylength changes during the year. McFarland et al. (1987) compared various mathematical representations of the daily heating wave. In their analysis, most published models used a modified sine function to describe heating during daytime hours. A sine function should be a close representation of the curve because daytime temperatures follow the daily solar cycle. The nighttime cooling curve, however, is not as simple. Cooling depends on many factors , including moisture content of the air, cloud cover, and soil heat flow. One form of the cooling curve suggested by Sutton (1953) depends on the square root of time since sunset. Parton and Logan (1981) used an exponential cooling rate to describe night-time cooling. Eckersten (1986) modified Parton and Logan's model to a sine-sine ex-Received for publication 14 Oct. 1988. Technical Contribution no. 2876, South Carolina Agricultural Experiment Station, Clemson Univ., Clem-son, S.C. Mention of a trade name does not constitute an endorsement of the product by Clem-son Univ. The cost of publishing this paper was defrayed in part by the payment of page charges. Under postal regulations, this paper therefore must be hereby marked advertisement solely to indicate this fact. ponential model that showed improvement in representation of the cooling curve from maximum to minimum temperatures. Mc-Cann (1985) used a sine-sine-sine model to represent the heating and cooling curves. Linvill (1982) used a logarithmic nighttime cooling curve. MODEL DEVELOPMENT In each of the above models, an underlying assumption is that maximum and minimum temperatures occur at regular intervals. The high temperature occurs during afternoon hours and the minimum temperature around dawn. These assumptions may not be valid when using 24-hr temperatures from climatological observation stations. For example , the maximum 24-hr temperature may not have occurred during the afternoon hours. Likewise, the minimum temperature may have occurred at some hour other than dawn. These situations often occur when a weather front moves through a region, exchanging cold (warm) air for warm (cold) air. A second type of problem arises in the data due to time of observation. Data are recorded in climatological stations near 8:00 AM, 5:00 PM, or midnight local time. There are days when temperatures do not reach the preceding day's temperature at observation time. Thus, the recorded minimum (maxi-mum) 24-hr temperature will have occurred at observation time on the preceding day. Although nothing can be done about the time of maximum and minimum temperature occurrence under natural conditions, using a 12-hr minimum (maximum) temperature will eliminate the time of observation problem. A method for representing the daily temperature wave If the time of maximum daily temperature is 2 hr after solar noon and the shape of the temperature curve responds to the daytime solar cycle, the temperature wave from sunrise to sunset can be described by Eq [1]: T(t) = (T max-T min) x sin [(π × t)/(DL + 4)] + T min [1] where T(t) is temperature at time t after sunrise ; T max is maximum temperature; T min is the morning minimum temperature, and DL is daylength (in hours). A second expression is needed to define nighttime cooling starting at sunset. Net ra-diational sunrise occurs ≈0.5 hr after astronomical sunrise. (Outgoing radiation is not balanced by incoming solar radiation until this time.) Thus, minimum daily temperatures are reached near time of sunrise. Ther-mograph records for Clemson, S.C. were used with the assumption that minimum temperature occurs at sunrise to develop an expression (Eq. [2]) for nighttime cooling (Linvill, 1982): T(t) = Ts-[(Ts-T min)/ in (24-DL)] × ln(t), [2]