DEVELOPMENT OF A FORECAST EQUATION TO PREDICT MINIMUM TEMPERATURES IN COLDER LOCATIONS WITHIN THE BINGHAMTON NY FORECAST AREA

DANIEL J. PADAVONA
NOAA / National Weather Service Forecast Office, Johnson City, New York

1. Introduction

Forecasters at the National Weather Service (NWS) Weather Forecast Office (WFO) at Binghamton, NY (BGM) are responsible for forecasting temperatures for a wide range of varying terrain stretching across 24 counties. Temperature guidance provided by model output statistics (MOS) is available for a handful of locations scattered throughout the forecast area; however, examination of cooperative observer data reveals a range of observed overnight minimum temperatures (minT) far greater than the range suggested by the MOS. Particularly sensitive to the lower portion of this range are area growers who use NWS forecasts to plan for frost and freeze events. This study is an effort to provide more accurate growing season minimum temperature predictions for 2 locations that often report a minT far lower than what is indicated by the MOS forecasts available for nearby stations. Cooperative observer temperatures from these stations, and MOS from a nearby location are utilized to create best fit regression equations that will provide this improved guidance.

2. Methodology

The 2 sites chosen for improved temperature guidance are Norwich and Walton, NY. Those 2 sites have observations available daily, both observers are among the most reliable in our COOP network, and each represents a location prone to minTs that are much lower than MOS forecasts for nearby locations. The Norwich, NY cooperative observer site is at an elevation of 1020 feet, approximately 600 feet lower than BGM, which is the closest station for which MOS is available. The Walton, NY cooperative observer site is slightly higher at an elevation of 1240 feet, and represents an elevated valley.

MOS data utilized for the study came from MOS forecasts for the Binghamton, New York (BGM) location, based on the Global Forecast System (GFS) (Dallavalle and Erickson 2000). The GFS MOS guidance was used, since local verification studies have shown that GFS MOS has performed better locally than MOS from the Eta and Nested Grid Model (NGM). MinT data was taken from the reported 24-hour minimum temperature Norwich and Walton, NY cooperative observer reports, as reported daily in the Hydrological Observations product (AWIPS product ALBHYDBGM). The 24-hour minimum temperature reported on a given day is defined as the minimum temperature that occurred during the 24 hours ending at 1200 UTC on the day of the report. As a result of this convention, it is sometimes difficult to tell whether a reported low temperature occurred during the early morning on the day of the report, or during the morning on the previous day. In this study, only days with an easily determined minT were used. If any such confusion occurred, the data for that day was not used.

The data set was limited to several months of study ranging from July 2002 to November 2003. It should be noted that the summer of 2002 was unusually hot and dry. The spring months of May and June 2003 were unusually cool and wet. It is recognized that additional data may be needed to produce a more reliable regression equation.

Statistical analysis was used to develop a regression equation to forecast minT at Norwich and Walton, NY. A multiple linear regression analysis relating meteorological variables predicted within the GFS MOS forecast for BGM ( MAVBGM) to the actual observed temperatures at Norwich and Walton, NY was used. When available, the 1800 UTC MAVBGM was utilized to collect the forecast data used in the study. The 1200 UTC guidance was utilized when the 1800 UTC product was missing from the archive. The 0000 UTC guidance was not used in the study, since it is not available early enough to be utilized in any updates that would be valuable to users who require accurate forecasts for the upcoming overnight low temperature.

Approximately one-third of the data between July 2002 and November 2003 was unavailable due to either the GFS Model Output Statistical guidance (MAV) or the observed temperatures missing from the archive on any given day. An additional 20 percent of the remaining dates were eliminated due to possible confusion over when the low temperature occurred. In the case of a frontal passage, MOS forecasts of 0600 UTC to 1200 UTC dew point temperature, sky cover, and wind speed may not have been relevant to a low which occurred prior to 0600 UTC. Therefore, any 24-hour period that featured a strong frontal passage during the final 12-hours was removed from the data set. This processes left 118 days for the development of the regression equations and an additional 59 days with which to test the equation.

3. Regression Analysis

Equations were developed for Norwich and Walton, NY, using the advanced statistical analysis techniques provided in Quattro Pro from Corel. Scatter plot diagrams (not shown) enabled the selection of the four predictors from a choice of seven, which demonstrated the best correlation with the observed minT at Norwich and minT at Walton, NY. The predictors selected for the regression analysis were taken from the MAV for BGM, which includes the predicted: minimum temperature at BGM between 0000 UTC and 1200 UTC
average wind speed between 0600 UTC and 1200 UTC
average sky cover between 0600 UTC and 1200 UTC
dew point temperature at 1200 UTC

MOS forecast sky cover values valid at 0600 UTC, 0900 UTC, and 1200 UTC were averaged to produce a representative sky cover. At each time, a value of 0 was assigned for clear skies, 1 for scattered, 2 for broken, and 3 for overcast. The wind speed is a simple average of the guidance produced for 0600 UTC, 0900 UTC, and 1200 UTC.

Using these 4 predictors, the advanced regression analysis provided within Quattro Pro was utilized to produce a best fit equation relating the predictors to observed minT at Walton, NY and Norwich, NY. Equation 1 shows the regression equation to predict the minimum temperature at the Norwich, NY cooperative observer site. Similarly, the Walton, NY regression equation is displayed in Equation 2. Norwich Min T = 0 - 0.81 + (0.0362 x BGM MinT) + (0.400 x BGM 6-12UTC avg. wind speed) + (1.043 x BGM 6-12UTC avg. sky cover) + (0.552 x BGM 12UTC Td) (Eq. 1)

Walton Min T = 0 - 3.39 + (0.136 x BGM MinT) + (0.482 x BGM 6-12UTC avg. wind speed) + (1.415 x BGM 6-12UTC avg. sky cover) + (0.772 x BGM 12UTC Td) (Eq. 2)

Tables 1 and 2 show the statistical correlations for the predictors in the regression equations developed for Norwich, NY and Walton, NY, respectively. The Norwich regression equation produced an R-square value of 0.908 and the Walton equation produced an R-square value of 0.897. The R-square value describes the variance around the regression line, and therefore how well the model fits the data. A value closer to 1.0 accounts for more of the variability.

The p-value is an indication of how significant the predictor is in the equation. Specifically, the p value for a given predictor is the probability that the predictor is not significant. Therefore, the smaller the p-value, the more significant the predictor is in predicting the minT. For both equations the p-values (p 0.0001 at Walton, p=0.0009 at Norwich) suggest the dew point value at 1200 UTC is the most significant predictor of the minT. The average sky cover and wind speed predictors show more value than the predicted minimum temperature at BGM. This follows theoretical thinking that the temperature cannot fall lower than the dew point temperature; less sky cover and lower wind speed implies less mixing in the boundary layer, allowing the temperature to fall closer to the dew point temperature. The p values for each equation indicate the value of Td has strong statistical significance for predicting overnight minimum temperatures during the growing season.

4. Test of Regression Equations

A test for each equation was conducted from data from 59 days that were not used to develop the regression equation. This subset of days is not utilized in the regression, so as to diminish the potential of over fitting the data. The test was conducted in real time after the initial compilation of data. The results were analyzed to compare the average absolute error for the regression equation, and the absolute error if the MAVBGM was used to predict the Norwich and Walton, NY minT. (Tables 3 and 4). The MAVBGM minT prediction was included within the tables to provide a comparison between the predicted minT and observed minT values.

Table 3 shows test results for the Norwich equation. An average absolute error was calculated for each day for the MAVBGM minT and Norwich minT. The absolute error for each day is the absolute value of the observed minT minus the predicted minT. The average absolute error for the Norwich equation was 2.7 F, and the average absolute error for the MAVBGM applied to Norwich was 4.2 F. Therefore, the initial regression equation for Norwich provided a temperature which averaged 1.5 F more accurate than relying on the MAVBGM forecast minimum temperature. More encouragingly, the data in Table 3 also indicate that the regression equation provides the most improvement over the MAVBGM forecast, when MAVBGM forecast errors were large. For example for days in which the MAVBGM came within 5 degrees F of the observed Norwich minimum temperature, there was almost no difference in the performance accuracy between the MAVBGM and the regression equation (MAVBGM average error 2.1, Norwich equation average error 2.0). By contrast, on days in which the MAVBGM missed the forecast by more than 5 degrees F at Norwich, the Norwich equation showed several degrees of improvement (MAVBGM average error 7.7, Norwich equation average error 4.0).

Table 4 shows the test results for the Walton equation. An average absolute error was calculated for each day for the MAVBGM minT and Walton minT. The average absolute error for the Walton equation was 2.9 F, and the average absolute error for the MAVBGM applied to Walton was 5.4 F. Therefore, the initial regression equation for Walton provided a temperature which averaged 2.5 F more accurate than relying on the MAVBGM forecast minimum temperature. As with the Norwich example, the regression equation provided a greater improvement when MAVBGM forecasts errors were large. For days in which the MAVBGM came within 5 degrees F of the Walton minimum temperature, there was almost no difference in the performance accuracy (MAVBGM average error 1.9, Walton equation average error 2.2). For days in which the MAVBGM missed the forecast by greater than 5 degrees F at Walton, the Walton equation showed several degrees of improvement (MAVBGM average error 8.7, Walton equation average error 3.6).

Further examination of the test results was conducted for instances in which the MAVBGM minT had a large error for Walton and Norwich. It was found the majority of these cases were typified by MAVBGM predictions of light winds and mainly clear skies.

5. Conclusion

Data from cooperative observation locations at Norwich and Walton, NY indicate that both locations are prone to very low minT s which can deviate greatly from MOS forecast minT s at nearby locations. NWS customers rely on accurate minT forecasts for those and other similar locations, where the local topography frequently results in minT s that are much lower than locations covered by MOS forecasts. A regression equation was developed for both Norwich and Walton in order to facilitate predicting more accurate minT s for these types of cold locations. Seven meteorological parameters from the GFS MOS for BGM were analyzed on scatter plot diagrams (not shown) and four variables were selected for the regression equations: 1200 UTC minT, 1200 UTC dew point, average sky cover, and average wind speed. Results indicate that significant improvement over MOS is possible for these colder locations utilizing the developed regression equations.

In testing the regression equations fit to the data, it was found that the 1200 UTC BGM Td was by far the most significant predictor for Norwich (p<=0.0001) and was also significant for Walton (p=0.0009) Average sky cover (p=0.023 for Norwich, p=0.0001 for Walton) and average wind speed (p=0.0021 for Norwich, p=0.0006 for Walton) also showed statistical significance. It was also found the MAVBGM minT was not significant for Walton (p=0.4645). As a result the BGM minT will be removed from future versions of the Walton equation if additional data suggests no statistical significance. The MAVBGM minT showed statistical significance for Norwich (p=0.0380) but was the least significant of the four Norwich predictors.

The utility of these equations were tested to illustrate the amount of improvement that would occur if the regression equation was used to forecast minT at Norwich and Walton, vs. the MAVBGM. The promising results from this test indicate that the equations were likely to provide better guidance for these locations than the MAVBGM, especially on clear, calm nights when large errors are likely with the MAVBGM.

Post-analysis of the test showed the most significant regression equation prediction errors in temperature at Walton, NY may be related to directional flow. A southwesterly flow provides the cooperative observer s location with upslope flow from the valley, potentially importing cold valley air and cooling the air adiabatically. Northeasterly flow provides the cooperative observer s location with downslope flow, potentially warming air parcels in their descent. Several cases within the Walton data set showed unusually cold conditions associated with a predicted southwesterly flow. This suggests further versions of the equation may benefit from the wind predictor being split into u and v components. No such potential trend was identified at Norwich.

As WFO BGM s archiving capabilities continue to increase, new data will allow for a larger data set to be incorporated into future versions and fine tune these regression equations. Similar techniques could be employed in other regions to offer improved minT forecasts for a wide range of forecast locations.

Acknowledgements

The author wishes to thank Ron Murphy, Information Technology program manager at National Weather Service Johnson City NY, for instituting our archival procedure. He also wishes to thank Michael Evans, Science and Operations Officer at National Weather Service Johnson City, for providing support for this project.

REFERENCES

Dallavalle, J.P., and M.C. Erickson, 2000: Avn-based MOS guidance - the alphanumeric messages. NWS Technical Procedures Bulletin No. 463, National Oceanic and Atmospheric Administration, U.S. Department of Commerce.

Table 1 - Norwich, NY

The coefficients and statistical correlations for the regression equation for Norwich

	*Coefficients*	*�� P-value*
�� Intercept	�� -0.8131	0.6871
BGM Min T	0.3619	0.0380
Avg Wind Speed	0.4002	0.0021
Avg Sky Cover	1.0425	0.0023
1200 UTC Td	0.5515	0.0009

�� R-squared: 0.908

Table 2 - Walton, NY

The coefficients and statistical correlations for the regression equation for Walton

	*Coefficients*	�� *P-value*
�� Intercept	�� �� -3.386	0.1204
BGM Min T	0.1360	0.4645
Avg Wind Speed	0.4819	0.0006
Avg Sky Cover	1.4145	0.0001
1200 UTC Td	0.7720	0.0001

�� R-squared: 0.897

Table 3 - Norwich, NY� test

Average absolute errors of the MAVBGM forecast, and regression equation for observed minimum temperature (�F) at Norwich, NY.� Errors are categorized by instances where MAVBGM forecast error was greater than or equal to 5 � F, 10 � F,� less than 5 � F, and all forecasts.

��

Average Error

Error >= 5

Error >=10

Error < 5

Overall Avg Error

Regression Equation

4.0

6.7

2.0

2.7

BGM MAV Guidance

7.7

11.7

2.1

4.2

Table 4 - Walton, NY test

Average absolute errors of MAVBGM forecast, and regression equation for observed minimum temperature (�F) at Walton, NY.� Errors are categorized by instances where MAVBGM forecast error was greater than or equal to 5 � F, 10 � F, less than 5 � F, and all forecasts.

��