Optimization of the 45th Weather Squadron’s ‘First Guess’ Minimum Temperature Prediction Equation

JAMES S. BROWNLEEFlorida Institute of Technology, Melbourne, Florida

WILLIAM P. ROEDER45th Weather Squadron, Patrick AFB, Florida

ABSTRACT

An upgrade was made to the 45th Weather Squadron’s (45 WS) Minimum Temperature tool. This update was desired since the initial 45 WS minimum temperature tool contained several elements that had been tuned subjectively. More importantly, there was a change in 45 WS operational requirements for minimum temperatures advisories to significantly colder temperatures. The previous warmest low temperature advisory was ≤ 60F. After the end of the Space Shuttle Program in 2011, the warmest 45 WS temperature advisory became ≤ 35 F. Since the post-Space Shuttle temperature advisories represented a significantly colder regime, a re-optimized algorithm was desired. The 45 WS minimum temperature tool consists of a ‘first guess’ based on the 1000-850 mb thickness and correction factors for various local meteorological effects. In this project, the ‘first guess’ equation was re-optimized and represents a substantial improvement over the previous equation. This re-optimized ‘first guess’ equation is the first and most important step for upgrading the entire low temperature tool.

1. Introduction

The 45th Weather Squadron (45 WS) provides weather support for the Cape Canaveral Air Force

Station (CCAFS), NASA’s Kennedy Space Center (KSC), and Patrick Air Force Base (PAFB) (Roeder et

al. 2005). Most of the support provided by the 45 WS is for operations at KSC and CCAFS that includes

space launches, preparation for space launches, personnel safety, and resource protection. One of the

many support functions of the 45 WS are the low temperature advisories, which are listed in Table 1. The

minimum temperature advisories are the most frequently issued warning, watch, or advisory product

issued by the 45 WS during the winter months (Roeder et al. 2005). These minimum temperature

advisories are critical because if the temperature gets too low, icing damage can occur to refrigerated lines

exposed to the outdoors at various facilities (Roeder et al. 2005).

The minimum temperature tool used by the 45 WS needed to be updated because the prior tool was

developed to include Space Shuttle operations. During the Space Shuttle Program, the 45 WS was

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responsible for temperature advisories of ≤ 60F. When the program ended in 2011, the 45 WS low

temperature advisories changed. The warmest low temperature advisory became ≤ 35F. As a result of

this colder temperature regime, an update to the minimum temperature algorithm was needed.

The current minimum temperature forecast tool in use by the 45 WS uses the 1000 mb to 850 mb

thickness to make a ‘first guess’ minimum temperature forecast. This minimum temperature is predicted

through the use of a linear regression equation (Roeder et al. 2005). This method of using thickness

values for predicting both minimum and maximum temperatures has been utilized at many different

forecasting centers (Struthwolf 1995; Massie and Rose 1997; Rose 2000), and many of these forecasting

techniques utilize linear regression equations (Massie and Rose 1997; Rose 2000). In a similar manner to

Rose (2000), the forecasted temperature at the 45 WS is further modified by several correction factors to

incorporate local effects. These local effects are wind speed, cloud cover, wind direction, nocturnal

inversion, dew point, boundary layer humidity, and mid-level humidity. After the correction factors are

applied, the final expected minimum temperature is provided as guidance to the forecaster. This

minimum temperature algorithm is shown in Fig. 1. This ‘first guess’ temperature prediction is the most

critical part of the forecast, if this number is significantly in error, then the entire temperature forecast is

wrong. A new re-optimized linear ‘first guess’ temperature prediction equation was produced by this

research project.

2. Data and methods

The previous ‘first guess’ equation is a linear regression equation that uses the 1000-850 mb

thickness to predict the ‘first guess’ minimum temperature. A linear equation has the following form:

y=mx+b (1 )

The slope ‘m’ and intercept ‘b’ were previously optimized by linear regression by the 14th Weather

Squadron (14 WS), the Air Force climatology center, using radiosonde and temperature data from the 45

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WS tower network with temperatures ≤ 60F. The previous operational ‘first guess’ linear regression

equation is shown below:

MinTemp (° F )=((0 .1979∗Thickness1000−850mb+15 . 592 )−273. 15)∗95+32 (2 )

This previous ‘first guess’ equation was created by the 14 WS in 2004 at the request of the 45 WS. The

45 WS then further refined this linear equation by ‘regression through the origin’, adjusting temperatures

to Kelvin. The optimization of the new ‘first guess’ began with data provided by the 14 WS. These data

included the following for all days where 45F was observed at any of the 45 WS weather towers, or

surface observations at the KSC Shuttle Landing Facility (KTTS) or the CCAFS Skid Strip (KXMR); the

1000-850 mb thickness nearest in time to the lowest temperature, and all surface observations at KTTS

from 2-hr after sunset before the lowest temperature to 1-hr after sunrise after the lowest temperature. The

data for these “cold events” (≤ 45F) were for Jan 1986-Apr 2014. The new ‘first guess’ was optimized

using the data from 1986-2009, while 2010-2014 data were used for independent verification. The sample

size for each of these partitions is listed in Table 2. Even though the warmest threshold for the 45 WS

advisories is ≤ 35F, the threshold of ≤ 45F for cold events was chosen, based on the frequency of

occurrence for CCAFS/KSC, to ensure a large enough sample size for the optimization. In addition, this

ensures that most of the events are for cold front passages, which are the primary mechanism for the

colder events at CCAFS/KSC. This also allows a margin for the forecaster’s guidance as the temperatures

begin to approach the warmest advisory threshold.

The new linear ‘first guess’ equation was optimized using two different methods. The first method

involved using the ‘Solver Tool’ in EXCEL. The ‘Solver Tool’ in the EXCEL spreadsheet optimized the

slope and intercept of the previous ‘first guess’ equation by minimizing Root Mean Square Error (RMSE)

of the previous equation over a certain number of iterations. After the optimization was complete using

the ‘Solver Tool’, the previous ‘first guess’ equation became the following new equation:

MinTemp (° F )=((0 . 0371∗Thickness1000−850mb+228. 15 )−273 .15 )∗95+32

(3 )

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The second version of the new ‘first guess’ equation was created using the ‘Trend Line’ linear regression

function in EXCEL. This second equation is shown below:

MinTemp (° F )=0 . 0091∗Thickness1000−850mb−92 . 4 (4 )

Even though they appear quite different, Equation 3 is virtually identical to Equation 4. Both of these

equations calculate the ‘first guess’ temperature in Fahrenheit. However, the ‘Solver Tool’ equation was

an adaptation of the previous ‘first guess’ equation that solves for the temperature in Kelvin and then

converts it to Fahrenheit. The ‘Trend Line’ equation solves for the low temperature in Fahrenheit directly.

Unlike Equation 3, the ‘Trend Line’ equation is an analytical solution. As expected, the 'Solver Tool'

solution converged to the solution from the least squares linear regression as provided by the EXCEL

'Trend Line' function.  Indeed the least squares 'Tread Line' linear regression solution and the 'Solver

Tool' solution both have the same correlation coefficient (r2 = 0.2459), and the average error between the

two solutions is only 0.11F over the 1986-2014 data set.  A t-test shows they are the same solution at the

99.99992% significance level. Presumably, if more iterations of the 'Solver Tool' solution had been

conducted, its solution would have become even closer to the least squares linear regression solution.

After the optimization of the linear equation was finished, the bias and RMSE were calculated for the new

‘first guess’ equation. Since the linear regression in Equation 4 is statistically optimized, it is the preferred

solution, even though Equation 3 is very similar.

In the data there were six days when the predicted temperatures were exceptionally high. This was

due to the large thickness values reported on each of those days. These large thickness values resulted in

unrealistically high predicted temperatures, and as a result, the errors between the observed temperatures

and predicted temperatures for these six events were very high; these six data points were considered

erroneous outliers and removed from the data set. By removing these outlier points, a more realistic

RMSE and bias could be achieved.

Alternate regressions were also considered. The previous 45 WS minimum temperature tool found a

slight performance improvement using a ‘regression through the origin’ with the 1000-850 mb thickness

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and the minimum temperatures in Kelvin. ‘Regression through the origin’ is justified a priori since the

hypsometric equation would predict zero thickness at zero absolute temperature. With the new data set in

this study, the ‘regression through the origin’ was also slightly better than the normal linear regression.

However, the improvement was not statistically significant and so was not selected for operational use.

In the original upgrade to the 45 WS minimum temperature tool in 2004, the ‘first guess’ based on the

1000-850 mb thickness performed much better than the 1000-500 mb thickness ‘first guess’, which was

replaced at that time. This made good meteorological sense since the cold events are mostly due to arctic

outbreaks, which are much shallower than 500 mb. In this project, the possibility that the arctic layer is

so shallow that its top is closer to 925 mb than 850 mb was also considered. Others have found the 925

mb thickness to be useful in predicting low temperatures (Rose 2000). However, a ‘first guess’ based on

the 1000-925 mb thickness did not perform quite as well as the 1000-850 mb thickness, even after three

outliers were eliminated. Therefore, a 1000-925 mb ‘first guess’ was not selected. The possibility that

the 1000-925 mb thickness might work better than the 1000-850 mb thickness for colder events was also

considered. A 1000-925 mb ‘first guess’ for minimum temperatures ≤ 36F was found to perform slightly

worse than the 1000-850 mb ‘first guess’. Thus this potential two-tiered ‘fist guess’ was not selected,

where the 1000-925 mb thickness would be used at the lower temperatures and the 1000-850 mb

thickness would be used at the warmer temperatures below 45F. Likewise, the 1000-925 mb thickness

was considered for minimum temperatures from ≤ 45F to > 36F performed slightly worse than the 1000-

850 mb thickness. Therefore, the final result is to use the 1000-850 mb thickness ‘first guess’ discussed

previously.

The same temperature stratification used in the 1000-925 mb regressions was also applied to the

1000-850 mb regression. However, neither the ≤ 36F nor the ≤ 45F to > 36F regressions using the

1000-850 mb thicknesses were statistically significantly better than the non-stratified 1000-850 mb

regression. The plot of the colder temperature stratification suggested a 1000-850 mb regression through

the origin with temperatures in Kelvin might be advantageous. However, this regression was not

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statistically superior to the overall 1000-850 mb thickness regression. As a result, none of these alternate

1000-850 mb regressions were selected. Despite the several alternate regressions considered, none

showed a statistically significantly benefit over the 1000-850 mb thickness regression. Therefore, the final

result is to use the 1000-850 mb thickness ‘first guess’ discussed previously and shown in Equation 4.

3. Analysis and discussion

a. Comparison of the Accuracy of the New Linear ‘First Guess’ Equation and the Previous Equation

Table 3 compares the RMSE and bias for the previous and new ‘first guess’ equations for the

development (1986-2009) and verification (2010-2014) with the six outlier 1000-850 mb thicknesses

excluded. Table 4 compares the bias for the previous and new ‘first guess’ equations for the same time

periods. The new ‘first guess’ equation has a RMSE of 4.83F on independent data, compared to the

RMSE of 11.74F in the original equation, an 59% improvement. The new ‘first guess’ has a bias of

1.31F on independent data, compared to the bias of 8.22F in the original equation, an 84% improvement.

The bias indicates that the new ‘first guess’ still tends to over-forecast slightly. The RMSE is the typical

expected magnitude of error for individual forecasts, regardless of polarity, i.e. ±5F. The bias is the

average error over many forecasts, where the individual ± errors tend to cancel out each other. Individual

errors of ~5F may not appear to be good performance, but recall that this is just for the ‘first guess’; the

correction factors will further reduce the error for the entire tool.

Figure 2 shows the linear correlation between the observed minimum temperatures and the observed

1000-850 mb thickness values. From Fig. 2, it is evident that the linear relationship between these two

parameters is rather weak. According to the correlation coefficient in Fig. 2, the linear regression line,

which is Equation 4, only explains 25% (r2 = 0.2459) of the variance. However, the method is still useful

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as a ‘first guess’ given the previous discussion on the ‘first guess’s’ improved performance at predicting

low temperatures. However, it also shows the need for the correction factors to refine the forecast, and the

eventual goal of this project is to optimize all of the correction factors which are listed in Fig. 1.

Figure 3 compares the temperature predictions made by the previous ‘first guess’ equation and the

recorded low temperatures that occurred during each cold event from 1986-2014. Figure 4 compares the

temperature predictions made by the new linear equation, and the observed low temperatures that

occurred on each cold event day during the same time period. These two figures clearly show that the new

equation’s temperature predictions are much more accurate than the previous equation’s predictions

Figures 5 and 6 compare the low temperature prediction accuracy of the previous and new linear

equations for all cold days which occurred during the independent verification period (2010 to 2014). It is

interesting to see how well the new equation can handle predicting temperatures that occur during

extreme cold air outbreaks, and a series of such outbreaks occurred at CCAFS/KSC during the first few

months of 2010. During that year and for the rest of the selected time period, the previous linear equation

had considerable difficulty in predicting the minimum temperatures for each day. On almost every cold

event day, the previous equation predicted temperatures which were higher than the observed minimum

temperatures. From both of these figures, it is quite clear that the new equation made more accurate

temperature predictions. It should be noted that in Figs. 4 and 6, there are some events when the new

equation slightly under predicted the observed low temperatures. Overall, though, Figs. 4 and 6 show that

in most cases, the new equation made fairly accurate temperature predictions.

As a further test of the new equation’s performance a z-test was performed which showed that the

bias of the new ‘first guess’ was not statistically significantly different than zero at the 12.75%

significance level, i.e., the new technique appears to be unbiased.  However, the RMSE is statistically

significantly different than zero at the 1.03 x 10-200% significant level, thus the ‘first guess’ is not a perfect

predictor of the minimum temperatures. This latter result reinforces the need for the correction factors in

the Minimum Temperature Tool to incorporate local effects and refine the final prediction. Overall

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though, it is quite evident that the new equation does a much better job than the previous equation at

predicting low temperatures during cold events at CCAFS/KSC.

b. Reasons for the new equations increased accuracy

The new ‘first guess’ equation is much better at predicting cold events at CCAFS/KSC than the

previous operational equation. One significant reason for this is that the old equation was optimized for

days when the low temperature was ≤ 60F. The data used to construct the previous linear ‘first guess’

equation contained temperatures as high as 60F. Climatologically, there are many more days with

minimum temperatures in the 60-45F range than ≤ 45F, so the previous ‘first guess’ equation may have

been overly tuned to the warmer range of the previous low temperature advisories. Since the previous

linear regression equation was fitted for a data set which included low temperatures that high, the

equation is not as useful in predicting much colder temperatures; the old equation has a warm bias. This

warm bias is responsible for most of the larger RMSE and bias values that occurred when using the old

operational equation. As a result of this warm bias, a new ‘first guess’ equation was needed; an equation

constructed using colder temperatures. Since this new equation has been tuned with much colder

temperatures the equation makes temperature forecasts that better match the 45 WS’s new temperature

advisory regime of ≤ 35F.

c. Other work

As mentioned earlier, the 45 WS minimum temperature tool consists of a ‘first guess’ based on the

1000-850 mb thickness and seven correction factors (Roeder et al. 2005). These correction factors

consider wind speed, clouds, nocturnal inversion, dew point, on-shore/off-shore flow, low altitude

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humidity, and mid-altitude humidity. Most of these correction factors were tuned subjectively and could

be improved by objective optimization. The wind speed correction factor was briefly examined in the

current project reported in this paper. This correction factor appeared to be working well and no further

work was done to optimize this correction factor to concentrate resources on optimizing the ‘first guess’,

which had much more room for improvement and had more impact of the performance of the minimum

temperature tool.

The 45 WS is currently working with a student at the Florida Institute of Technology to optimize the

cloud correction factor. The ‘first guess’ equation might show even better performance if based on the

1000-925 mb thickness since the new colder advisories are mostly due to arctic air mass outbreaks that

are relatively shallow. The remaining correction factors in the 45 WS minimum temperature tool should

be objectively optimized in the future.

4. Conclusions

In this project, the optimization of the linear ‘first guess’ equation was performed. From the analysis,

it was shown that the new optimized linear ‘first guess’ equation is superior to the old operational

equation. The results showed that during all recorded major cold events that occurred in East Central

Florida from 1986 to 2014, the new linear equation made more accurate low temperature predictions than

the old equation. In addition to that, the new equation made low temperature forecasts that are in line with

the new low temperature advisories. This increased accuracy is reflected in the observed reduction of both

the RMSE and bias values. Much of the larger RMSE and bias that occurred with the old operational

equation was due to the warm bias of that particular equation, and thus that equation is not useful with the

new low temperature advisory criteria. In closing, it is recommended that the new linear ‘first guess’

equation be used in place of the previous linear ‘first guess’ equation. Another option would be to use the

new linear equation during very strong cold air outbreaks and use the previous equation during less severe

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cold air outbreaks. Either way, the results of this analysis show that the new linear ‘first guess’ equation is

a major and much needed first step in updating the 45 WS’s low temperature tool.

Acknowledgments. The 14th Weather Squadron, the U.S. Air Force climate center, provided the data

CCAFS/KSC weather data used in this study.

REFERENCES

Massie, D. R. and M. A. Rose, 1997: Predicting Daily Maximum Temperatures Using Linear Regression and Eta

Geopotential Thickness Forecasts. Wea. Forecasting, 12, 799–807.

Roeder, W. P., McAleenan, M., Taylor, T. N., and T. L. Longmire, 2005: Applied Climatology In The Upgraded

Minimum Temperature Prediction Tool For The Cape Canaveral Air Force Station and Kennedy Space Center, 15th

Conference on Applied Climatology, 20-23 Jun 2005, 7 pp.

Rose, M., 2000: Using 1000-925 mb Thicknesses in Forecasting Minimum Temperatures at Nashville, Tennessee.

  Technical Attachment SR/SSD 2000-25.

Struthwolf, M. E. 1995: Forecasting Maximum Temperatures through Use of an Adjusted 850- to 700-mb

Thickness Technique. Wea. Forecasting,10, 160–171.

TABLES AND FIGURES

Table 1. Cold temperature advisories provided by 45 WS.Temperature Threshold Duration Desired Lead-time

≤ 35F any occurrence 4 hr≤ 32F ≥ 4 hr 16 hr≤ 28F any occurrence (if wind > 10 kt) 16 hr

Table 2. Partitioning of the cold weather events (≤ 45F) at CCAFS/KSC in optimizing the 45 WS minimum temperature tool (6 outliers removed).

Time Period Description Number of Events Percent of EventsJan 1986-Apr 2014 All Data 595 100%Jan 1986-Dec 2009 Development Data 476 80%Jan 2010-Apr 2014 Independent Verification 119 20%

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Table 3. RMSE for the previous and new ‘first guess’ equations for all cold events (≤ 45F) at CCAFS/KSC. The bias values were calculated using Equation 4. The six outlier 1000-850 mb thicknesses were excluded in these calculations.

Time Period RMSE of previous ‘First Guess’ Equation(F) RMSE of new ‘First Guess’ Equation (F)Jan 1986–Dec 2009 8.87 3.47Jan 2010-Apr 2014 11.74 4.83

Table 4. Bias for the previous and new ‘first guess’ equations for all cold events (≤ 45F) at CCAFS/KSC. The bias values were calculated using Equation 4. The six outlier 1000-850 mb thicknesses were excluded in these calculations.

Time Period Bias of previous ‘First Guess’ Equation(F) Bias of new ‘First Guess’ Equation (F)Jan 1986-Dec 2009 6.35 0.03Jan 2010-Apr 2014 8.22 1.31

Figure 1. Schematic of the minimum temperature algorithm used by the 45 WS to make low temperature forecasts.

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Figure 2. Linear regression of the observed minimum temperatures and the observed thickness values.275276277278279

Figure 3. Days on which the observed low temperature reached 45F or less from 1986 to 2014 (black line) along with the low temperature predicted for each day by the old operational ‘first guess’ linear equation (red line). The six outliers were removed here.

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Figure 4. Days on which the observed low temperature reached 45F or less from 1986 to 2014 (black line) along with the low temperature predicted for each day by the new ‘first guess’ linear equation (red line). The six outliers were removed here.

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Figure 5. Days on which the observed low temperature reached 45F or less from 2000 to 2014 (black line) along with the low temperature predicted for each day by the old operational ‘first guess’ linear equation (red line).

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Figure 6. Days on which the observed low temperature reached 45F or less from 2000 to 2014 (black line), and the low temperature predicted for each day by the new ‘first guess’ linear equation (red line).

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