Predicting Daily Maximum Temperatures Using Linear Regression and Geopotential Thickness Forecasts

Mark A. Rose
WFO Nashville, TN

1. Introduction

In 1997, Massie and Rose investigated the usefulness of using Eta thickness forecasts in predicting daily maximum temperatures at Nashville, Tennessee. This method was employed with some operational success, however, it soon became evident that the original set of regression equations employed in this study were not necessarily useful for all seasons of each and every year. This is probably because the original study used only one year of data, and did not consider year-to-year variations in the thickness/temperature relationship. While the study provided useful information on model initialization and forecast biases, it was not as useful as a "climatological forecast tool" (due to the limited data source). It was decided that to maintain the relevancy of the 1997 study, more data would be needed.

2. Methodology

A subsequent study of 1000-850 mb thickness values versus maximum temperatures was conducted for 802 mostly sunny days (at least 65% of possible sunshine) from 1991 to 1995. Observed sounding data at Nashville and corresponding maximum temperatures were collected for these cases. Regression equations were subsequently derived for these data. For a more detailed explanation of the methodology employed, refer to Massie and Rose (1997).

3. Results

A regression equation correlating the two fields (thickness and maximum temperature) was derived. The equation is,

Tmax = 0.36 * Tk1000-850 - 421,

where Tmax is the forecast maximum temperature, and Tk1000-850 is the 1000-850 mb thickness in meters. A high correlation coefficient (0.970) suggests strong linearity between the two fields.

The 802 cases were subsequently subdivided in order that seasonal regression equations could be calculated with the intent of refining temperature forecasts. The number of cases per season are: spring, 229; summer, 207; autumn, 188; winter, 178. These equations are,

Tmax = 0.33 * Tk1000-850 - 381 (spring),
Tmax = 0.30 * Tk1000-850 - 338 (summer),
Tmax = 0.35 * Tk1000-850 - 414 (autumn),
Tmax = 0.36 * Tk1000-850 - 422 (winter).

4. Conclusion

The refined climatological (low level) thickness equations listed in the previous section were used with the Eta and Nested Grid Models for more than a year. The author concludes that the present study, expanded to five years, is complimentary to the original study conducted by Massie and Rose (1997), especially in regard to the reliability of climatological thicknesses (as a forecast tool). This is because more cases have been assessed, 802 versus 142 for the 1997 study, and that the five year span of data collection allowed year-to-year variations in the thickness/temperature relationship to be included.


The author thanks Darrell Massie, Lead Forecaster, and Henry Steigerwaldt, Science and Operations Officer, NWSFO Nashville, for their reviews of this paper.


Massie, D. and M. Rose, 1997: Predicting daily maximum temperatures using linear regression and Eta geopotential thickness forecasts. Wea. Forecasting, 12, 799-807. is the U.S. government's official web portal to all federal, state and local government web resources and services.