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Richard L. Lehman

The non-linear part of the relationship between monthly degree days and temperature was studied by use of 23 years of daily temperature data at 64 stations representing all major climatic zones in the coterminous U.S. The data reveal that errors in estimating monthly degree days by the fast method range from a few percent to more than 300%, when the differences between the base and the mean temperature range, respectively, from + 8 to −2°C (+ 14 to −4°F). The errors can be reduced to less than 10% if the fast method is used together with an additional parameters, the estimated standard deviation of the daily mean temperature for the period of interest, and an appropriate model for the temperature distribution. The exact expression, valid for any model, is given for the relationship between degree day and mean temperature normals.

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Richard L. Lehman

Abstract

A Gaussian model for evaluating the probability of occurrence of forecast-contingent monthly average temperature and degree day outcomes is developed by use of forecast-verification data, and proposed for use in decision making. The model 1) guides current National Weather Service forecasting to ensure consistency with demonstrated skill, and 2) interprets the forecast statements i as projected perturbations of the mean and variance of a standard temperature variable t. A forecast thus specifies at each map point a local perturbed variable (t|i) that should be the basis for local decision making. A figure showing t and t|i curves on normal probability paper makes clear how significantly the probabilities of a given outcome of interest can differ for different forecast statements. Use of model results in decision making and in setting priorities for forecast development is discussed.

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Richard L. Lehman

Abstract

This paper examines the question of how strongly the skewness of the daily temperature variable (t) affects estimating the mean value and variance of the corresponding degree day variable (q) at U.S. stations where the q(t) relationship is nonlinear. Mean and variance values for monthly q were estimated from t statistics for monthly periods by use of two t models, one using skewness data and one not, and the results were compared with observed data. When q(t) is nonlinear, i.e., for months when the average daily temperature (μ) differs by fewer than 10°C (18°F) from the degree day base temperature (b), the accuracy of estimation was improved from about 5–10% to 1–3% when a one-parameter gamma function model instead of a Gaussian model was used. The gamma function model provided estimates that fall within the sampling error of the verification data for both daily and monthly average q parameters. The results suggest that when |b−μ|<10°C, q parameters can be estimated accurately only by use of models that take t skewness into account. Data are also presented suggesting that the variation of (a) skewness and (b) number of unique temperature “events” in a month between neighboring stations and from month to month at the same station is gradual. This opens the possibility of accurate estimation of daily and monthly average q parameters at intermediate locations and periods for which temperature data do not exist.

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Nathaniel B. Guttman and Richard L. Lehman

Abstract

Degree-hours have many applications in fields such as agriculture, architecture, and power generation. Since daily mean temperatures are more readily available than hourly temperatures, the difference between mean daily degree-hours computed from daily mean temperatures and those computed from hourly data is examined.

Mean daily degree-hours were modeled assuming normal probability distributions for temperatures and homogeneous variances of hourly temperatures throughout a day. The validity of the assumptions, which is dependent upon time of year and location, as well as the effect of the assumptions on four models of daily degree-hours are discussed. Two of the models require mean hourly temperatures and two require the readily available daily mean temperatures as input. Comparisons among models and observed data show that estimates made from mean hourly temperatures are better than those made from daily mean temperatures. The difference is sizable during the transition months between warm and cool seasons. An aid to computing the difference is presented.

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Richard L. Lehman and Henry E. Warren

Abstract

The problem of projecting monthly residential natural gas sales and evaluating interannual changes in demand is investigated using a linear regression model adjusted monthly. with lagged monthly heating degree-days as the independent variable. The relationship between sales and degree-day data for customers of Columbia Gas Company (serving the Columbus, Ohio, area) is studied for a 20-yr period ending in June 1990. Analysis of the phases of the monthly billed sales and the degree-day data indicated that monthly sales reports lagged degree-days and gas consumption by 15 days on average. Running 12-month regressions of Columbia Gas sales on 15-day-lagged degree-days show that lagged degree-days explain, on average, 97% of the variability in the monthly sales reports for the study years. Annualized trends in the regression coefficients indicate changes in consumption due to conservation and changes in price. Since 1974–75 the trends indicate declines of 50% in non-weather- sensitive sales per customer, and 35% in monthly sales per degree-day per customer, with most of the changes occurring prior to 1985. The mode is adapted by using a regression equation based on historical data through the prior 12 months with degree-days as the independent variable. Estimates for sales in the coming period are based on official National Oceanic and Atmospheric Administration (NOAA) monthly temperature outlooks (outlooks) for the Columbus region. For comparison purposes, four lagged monthly degree-day sets are used in a model: 1) a set of degree-day normals, 2) a set of 100% projected degree-day values obtained by use of NOAA outlooks, 3) a set in which the first half of the degree-days in each monthly period are observations and the second half are projected, and 4) a set that is 100% observed (the perfect case). The skill of the degree-day sets for projecting monthly sales is evaluated by a statistical analysis of the projection errors (differences between projected and reported sales). Errors from the sales projection models using the four different degree-day sets are compared with errors from two sets of baseline sales. The first set of baseline sales is estimated with and the second set without foreknowledge of monthly sales norms and annual total sales. The models using partially and fully projected degree-days are found to have measurable skill over models using climatology in projecting monthly gas sales during the heating season.

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