This is the final paper for the project that I collaborated on with William P. Roeder at the 45th Weather Squadron (45 WS). The goal of this project was to improve the minimum temperature predictions that are made by the 45 WS for space launch operations at the Cape Canaveral Air Force Station (CCAFS) and the Kennedy Space Center (KSC). At the end of this project, the minimum temperature predictions made by the 45 WS were significantly improved, and the 45 WS began using the new minimum temperature algorithm during the 2014/2015 winter season. This project was one major step aimed at improving the minimum temperature tool.

1. 1
Optimization of the 45th Weather Squadron’s ‘First Guess’1
Minimum Temperature Prediction Equation2
3
JAMES S. BROWNLEE4
Florida Institute of Technology, Melbourne, Florida5
6
WILLIAM P. ROEDER7
45th
Weather Squadron, Patrick AFB, Florida8
9
ABSTRACT10
An upgrade was made to the 45th Weather Squadron’s (45 WS) Minimum Temperature tool.11
This update was desired since the initial 45 WS minimum temperature tool contained several12
elements that had been tuned subjectively. More importantly, there was a change in 45 WS13
operational requirements for minimum temperatures advisories to significantly colder14
temperatures. The previous warmest low temperature advisory was ≤ 60F. After the end of the15
Space Shuttle Program in 2011,the warmest 45 WS temperature advisory became ≤ 35 F. Since16
the post-Space Shuttle temperature advisories represented a significantly colder regime, a re-17
optimized algorithm was desired. The 45 WS minimum temperature tool consists of a ‘first18
guess’based on the 1000-850 mb thickness and correction factors for various local19
meteorological effects. In this project, the ‘first guess’equation was re-optimized and represents20
a substantial improvement over the previous equation. This re-optimized ‘first guess’ equation is21
the first and most important step for upgrading the entire low temperature tool.22
23
1. Introduction24
25
The 45th
Weather Squadron (45 WS) provides weather support for the Cape CanaveralAir Force26
Station (CCAFS), NASA’s Kennedy Space Center (KSC),and Patrick Air Force Base (PAFB) (Roeder et27
al. 2005). Most of the support provided by the 45 WS is for operations at KSC and CCAFS that includes28
space launches, preparation for space launches, personnel safety,and resource protection. One of the29
many support functions of the 45 WS are the low temperature advisories, which are listed in Table 1. The30
minimum temperature advisories are the most frequently issued warning, watch,or advisory product31
issued by the 45 WS during the winter months (Roeder et al. 2005). These minimum temperature32
advisories are critical because if the temperature gets too low, icing damage can occur to refrigerated lines33
exposed to the outdoors at various facilities (Roeder et al. 2005).34
The minimum temperature tool used by the 45 WS needed to be updated because the prior tool was35
developed to include Space Shuttle operations. During the Space Shuttle Program, the 45 WS was36

2. responsible for temperature advisories of ≤ 60F. When the program ended in 2011, the 45 WS low37
temperature advisories changed. The warmest low temperature advisory became ≤ 35F. As a result of38
this colder temperature regime, an update to the minimum temperature algorithm was needed.39
The current minimum temperature forecast tool in use by the 45 WS uses the 1000 mb to 850 mb40
thickness to make a ‘first guess’ minimum temperature forecast. This minimum temperature is predicted41
through the use of a linear regression equation (Roeder et al. 2005). This method of using thickness42
values for predicting both minimum and maximum temperatures has been utilized at many different43
forecasting centers (Struthwolf 1995; Massie and Rose 1997; Rose 2000), and many of these forecasting44
techniques utilize linear regression equations (Massie and Rose 1997; Rose 2000). In a similar manner to45
Rose (2000), the forecasted temperature at the 45 WS is further modified by severalcorrection factors to46
incorporate local effects. These localeffects are wind speed, cloud cover, wind direction, nocturnal47
inversion, dew point, boundary layer humidity, and mid-level humidity. After the correction factors are48
applied, the final expected minimum temperature is provided as guidance to the forecaster. This49
minimum temperature algorithm is shown in Fig. 1. This ‘first guess’ temperature prediction is the most50
critical part of the forecast,if this number is significantly in error, then the entire temperature forecast is51
wrong. A new re-optimized linear ‘first guess’ temperature prediction equation was produced by this52
research project.53
54
2. Data and methods55
56
The previous ‘first guess’ equation is a linear regression equation that uses the 1000-850 mb thickness57
to predict the ‘first guess’ minimum temperature. A linear equation has the following form:58
bmxy   159

3. The slope ‘m’ and intercept ‘b’ were previously optimized by linear regression by the 14th
Weather60
Squadron (14 WS), the Air Force climatology center,using radiosonde and temperature data from the 4561
WS tower network with temperatures ≤ 60F. The previous operational ‘first guess’ linear regression62
equation is shown below:63
     32
5
9
*15.273592.15*1979.0 8501000  

mbThicknessFMinTemp  264
This previous ‘first guess’ equation was created by the 14 WS in 2004 at the request of the 45 WS. The 4565
WS then further refined this linear equation by ‘regression through the origin’, adjusting temperatures to66
Kelvin. The optimization of the new ‘first guess’ began with data provided by the 14 WS. These data67
included the following for all days where 45F was observed at any of the 45 WS weather towers,or68
surface observations at the KSC Shuttle Landing Facility (KTTS) or the CCAFS Skid Strip (KXMR); the69
1000-850 mb thickness nearest in time to the lowest temperature, and all surface observations at KTTS70
from 2-hr after sunset before the lowest temperature to 1-hr after sunrise after the lowest temperature. The71
data for these “cold events” (≤ 45F) were for Jan 1986-Apr 2014. The new ‘first guess’ was optimized72
using the data from 1986-2009, while 2010-2014 data were used for independent verification. The sample73
size for each of these partitions is listed in Table 2. Even though the warmest threshold for the 45 WS74
advisories is ≤ 35F, the threshold of ≤ 45F for cold events was chosen, based on the frequency of75
occurrence for CCAFS/KSC,to ensure a large enough sample size for the optimization. In addition, this76
ensures that most of the events are for cold front passages,which are the primary mechanism for the77
colder events at CCAFS/KSC. This also allows a margin for the forecaster’s guidance as the temperatures78
begin to approach the warmest advisory threshold.79
The new linear ‘first guess’ equation was optimized using two different methods. The first method80
involved using the ‘Solver Tool’ in EXCEL. The ‘Solver Tool’ in the EXCEL spreadsheet optimized the81
slope and intercept of the previous ‘first guess’ equation by minimizing Root Mean Square Error (RMSE)82

4. of the previous equation over a certain number of iterations. After the optimization was complete using83
the ‘Solver Tool’, the previous ‘first guess’ equation became the following new equation:84
     32
5
9
*15.27315.228*0371.0 8501000  

mbThicknessFMinTemp  385
The second version of the new ‘first guess’ equation was created using the ‘Trend Line’ linear regression86
function in EXCEL. This second equation is shown below:87
  4.92*0091.0 8501000  

mbThicknessFMinTemp  488
Even though they appear quite different, Equation 3 is virtually identical to Equation 4. Both of these89
equations calculate the ‘first guess’ temperature in Fahrenheit. However,the ‘Solver Tool’ equation was90
an adaptation of the previous ‘first guess’ equation that solves for the temperature in Kelvin and then91
converts it to Fahrenheit. The ‘Trend Line’ equation solves for the low temperature in Fahrenheit directly.92
Unlike Equation 3, the ‘Trend Line’ equation is an analytical solution. As expected, the 'Solver Tool'93
solution converged to the solution from the least squares linear regression as provided by the EXCEL94
'Trend Line' function. Indeed the least squares 'Tread Line' linear regression solution and the 'Solver95
Tool' solution both have the same correlation coefficient (r2
= 0.2459), and the average error between the96
two solutions is only 0.11F over the 1986-2014 data set. A t-test shows they are the same solution at the97
99.99992% significance level. Presumably, if more iterations of the 'Solver Tool' solution had been98
conducted, its solution would have become even closer to the least squares linear regression solution.99
After the optimization of the linear equation was finished, the bias and RMSE were calculated for the new100
‘first guess’ equation. Since the linear regression in Equation 4 is statistically optimized, it is the preferred101
solution, even though Equation 3 is very similar.102
In the data there were six days when the predicted temperatures were exceptionally high. This was103
due to the large thickness values reported on each of those days. These large thickness values resulted in104
unrealistically high predicted temperatures,and as a result, the errors between the observed temperatures105
and predicted temperatures for these six events were very high; these six data points were considered106

5. erroneous outliers and removed from the data set. By removing these outlier points, a more realistic107
RMSE and bias could be achieved.108
Alternate regressions were also considered. The previous 45 WS minimum temperature tool found a109
slight performance improvement using a ‘regression through the origin’ with the 1000-850 mb thickness110
and the minimum temperatures in Kelvin. ‘Regression through the origin’ is justified a priori since the111
hypsometric equation would predict zero thickness at zero absolute temperature. With the new data set in112
this study, the ‘regression through the origin’ was also slightly better than the normal linear regression.113
However,the improvement was not statistically significant and so was not selected for operational use.114
In the original upgrade to the 45 WS minimum temperature tool in 2004, the ‘first guess’ based on the115
1000-850 mb thickness performed much better than the 1000-500 mb thickness ‘first guess’, which was116
replaced at that time. This made good meteorological sense since the cold events are mostly due to arctic117
outbreaks, which are much shallower than 500 mb. In this project, the possibility that the arctic layer is118
so shallow that its top is closer to 925 mb than 850 mb was also considered. Others have found the 925119
mb thickness to be useful in predicting low temperatures (Rose 2000). However,a ‘first guess’ based on120
the 1000-925 mb thickness did not perform quite as well as the 1000-850 mb thickness, even after three121
outliers were eliminated. Therefore,a 1000-925 mb ‘first guess’ was not selected. The possibility that122
the 1000-925 mb thickness might work better than the 1000-850 mb thickness for colder events was also123
considered. A 1000-925 mb ‘first guess’ for minimum temperatures ≤ 36F was found to perform slightly124
worse than the 1000-850 mb ‘first guess’. Thus this potential two-tiered ‘fist guess’ was not selected,125
where the 1000-925 mb thickness would be used at the lower temperatures and the 1000-850 mb126
thickness would be used at the warmer temperatures below 45F. Likewise, the 1000-925 mb thickness127
was considered for minimum temperatures from ≤ 45F to > 36F performed slightly worse than the128
1000-850 mb thickness. Therefore,the final result is to use the 1000-850 mb thickness ‘first guess’129
discussed previously.130

6. The same temperature stratification used in the 1000-925 mb regressions was also applied to the131
1000-850 mb regression. However,neither the ≤ 36F nor the ≤ 45F to > 36F regressions using the132
1000-850 mb thicknesses were statistically significantly better than the non-stratified 1000-850 mb133
regression. The plot of the colder temperature stratification suggested a 1000-850 mb regression through134
the origin with temperatures in Kelvin might be advantageous. However,this regression was not135
statistically superior to the overall 1000-850 mb thickness regression. As a result, none of these alternate136
1000-850 mb regressions were selected. Despite the severalalternate regressions considered, none137
showed a statistically significantly benefit over the 1000-850 mb thickness regression. Therefore,the final138
result is to use the 1000-850 mb thickness ‘first guess’ discussed previously and shown in Equation 4.139
140
141
3. Analysisand discussion142
143
a. Comparison of the Accuracy of the New Linear ‘First Guess’ Equation and the Previous Equation144
145
Table 3 compares the RMSE and bias for the previous and new ‘first guess’ equations for the146
development (1986-2009) and verification (2010-2014) with the six outlier 1000-850 mb thicknesses147
excluded. Table 4 compares the bias for the previous and new ‘first guess’ equations for the same time148
periods. The new ‘first guess’ equation has a RMSE of 4.83F on independent data,compared to the149
RMSE of 11.74F in the original equation, an 59% improvement. The new ‘first guess’ has a bias of150
1.31F on independent data, compared to the bias of 8.22F in the original equation, an 84%151
improvement. The bias indicates that the new ‘first guess’ still tends to over-forecast slightly. The RMSE152
is the typical expected magnitude of error for individual forecasts,regardless of polarity, i.e. ±5F. The153
bias is the average error over many forecasts,where the individual ± errors tend to cancelout each other.154

7. Individual errors of ~5F may not appear to be good performance, but recall that this is just for the ‘first155
guess’; the correction factors will further reduce the error for the entire tool.156
Figure 2 shows the linear correlation between the observed minimum temperatures and the observed157
1000-850 mb thickness values. From Fig. 2, it is evident that the linear relationship between these two158
parameters is rather weak. According to the correlation coefficient in Fig. 2, the linear regression line,159
which is Equation 4, only explains 25% (r2
= 0.2459) of the variance. However,the method is still useful160
as a ‘first guess’ given the previous discussion on the ‘first guess’s’ improved performance at predicting161
low temperatures. However,it also shows the need for the correction factors to refine the forecast,and the162
eventual goal of this project is to optimize all of the correction factors which are listed in Fig. 1.163
Figure 3 compares the temperature predictions made by the previous ‘first guess’ equation and the164
recorded low temperatures that occurred during each cold event from 1986-2014. Figure 4 compares the165
temperature predictions made by the new linear equation, and the observed low temperatures that166
occurred on each cold event day during the same time period. These two figures clearly show that the new167
equation’s temperature predictions are much more accurate than the previous equation’s predictions168
Figures 5 and 6 compare the low temperature prediction accuracy of the previous and new linear169
equations for all cold days which occurred during the independent verification period (2010 to 2014). It is170
interesting to see how well the new equation can handle predicting temperatures that occur during171
extreme cold air outbreaks, and a series of such outbreaks occurred at CCAFS/KSC during the first few172
months of 2010. During that year and for the rest of the selected time period, the previous linear equation173
had considerable difficulty in predicting the minimum temperatures for each day. On almost every cold174
event day, the previous equation predicted temperatures which were higher than the observed minimum175
temperatures. From both of these figures, it is quite clear that the new equation made more accurate176
temperature predictions. It should be noted that in Figs. 4 and 6, there are some events when the new177
equation slightly under predicted the observed low temperatures. Overall, though, Figs. 4 and 6 show that178
in most cases, the new equation made fairly accurate temperature predictions.179

8. As a further test of the new equation’s performance a z-test was performed which showed that the180
bias of the new ‘first guess’ was not statistically significantly different than zero at the 12.75%181
significance level, i.e., the new technique appears to be unbiased. However,the RMSE is statistically182
significantly different than zero at the 1.03 x 10-200
% significant level, thus the ‘first guess’ is not a perfect183
predictor of the minimum temperatures. This latter result reinforces the need for the correction factors in184
the Minimum Temperature Tool to incorporate local effects and refine the final prediction. Overall185
though, it is quite evident that the new equation does a much better job than the previous equation at186
predicting low temperatures during cold events at CCAFS/KSC.187
188
b. Reasonsforthenew equationsincreased accuracy189
190
The new ‘first guess’ equation is much better at predicting cold events at CCAFS/KSC than the191
previous operational equation. One significant reason for this is that the old equation was optimized for192
days when the low temperature was ≤ 60F. The data used to construct the previous linear ‘first guess’193
equation contained temperatures as high as 60F. Climatologically, there are many more days with194
minimum temperatures in the 60-45F range than ≤ 45F, so the previous ‘first guess’ equation may have195
been overly tuned to the warmer range of the previous low temperature advisories. Since the previous196
linear regression equation was fitted for a data set which included low temperatures that high, the197
equation is not as useful in predicting much colder temperatures; the old equation has a warm bias. This198
warm bias is responsible for most of the larger RMSE and bias values that occurred when using the old199
operational equation. As a result of this warm bias, a new ‘first guess’ equation was needed; an equation200
constructed using colder temperatures. Since this new equation has been tuned with much colder201
temperatures the equation makes temperature forecasts that better match the 45 WS’s new temperature202
advisory regime of ≤ 35F.203

9. 204
c. Other work205
206
As mentioned earlier, the 45 WS minimum temperature tool consists of a ‘first guess’ based on the207
1000-850 mb thickness and seven correction factors (Roeder et al. 2005). These correction factors208
consider wind speed, clouds, nocturnal inversion, dew point, on-shore/off-shore flow, low altitude209
humidity, and mid-altitude humidity. Most of these correction factors were tuned subjectively and could210
be improved by objective optimization. The wind speed correction factor was briefly examined in the211
current project reported in this paper. This correction factor appeared to be working well and no further212
work was done to optimize this correction factor to concentrate resources on optimizing the ‘first guess’,213
which had much more room for improvement and had more impact of the performance of the minimum214
temperature tool.215
The 45 WS is currently working with a student at the Florida Institute of Technology to optimize the216
cloud correction factor. The ‘first guess’ equation might show even better performance if based on the217
1000-925 mb thickness since the new colder advisories are mostly due to arctic air mass outbreaks that218
are relatively shallow. The remaining correction factors in the 45 WS minimum temperature tool should219
be objectively optimized in the future.220
221
4. Conclusions222
223
In this project, the optimization of the linear ‘first guess’ equation was performed. From the analysis,224
it was shown that the new optimized linear ‘first guess’ equation is superior to the old operational225
equation. The results showed that during all recorded major cold events that occurred in East Central226
Florida from 1986 to 2014, the new linear equation made more accurate low temperature predictions than227

10. the old equation. In addition to that, the new equation made low temperature forecasts that are in line with228
the new low temperature advisories. This increased accuracy is reflected in the observed reduction of both229
the RMSE and bias values. Much of the larger RMSE and bias that occurred with the old operational230
equation was due to the warm bias of that particular equation, and thus that equation is not useful with the231
new low temperature advisory criteria. In closing, it is recommended that the new linear ‘first guess’232
equation be used in place of the previous linear ‘first guess’ equation. Another option would be to use the233
new linear equation during very strong cold air outbreaks and use the previous equation during less severe234
cold air outbreaks. Either way, the results of this analysis show that the new linear ‘first guess’ equation is235
a major and much needed first step in updating the 45 WS’s low temperature tool.236
Acknowledgments. The 14th Weather Squadron, the U.S. Air Force climate center, provided the data237
CCAFS/KSC weather data used in this study.238
239
240
REFERENCES241
Massie, D. R. and M. A. Rose, 1997: Predicting Daily Maximum Temperatures Using Linear Regression and Eta242
Geopotential Thickness Forecasts. Wea. Forecasting, 12, 799–807.243
Roeder, W. P., McAleenan, M., Taylor, T. N., and T. L. Longmire, 2005: Applied Climatology In The Upgraded244
Minimum Temperature Prediction Tool For The Cape Canaveral Air Force Station and Kennedy Space Center, 15th245
Conference on Applied Climatology, 20-23 Jun 2005, 7 pp.246
Rose, M., 2000: Using 1000-925 mb Thicknesses in Forecasting Minimum Temperatures at Nashville, Tennessee.247
Technical Attachment SR/SSD 2000-25.248
Struthwolf, M. E. 1995: Forecasting Maximum Temperatures through Use of an Adjusted 850- to 700-mb249
Thickness Technique. Wea. Forecasting,10, 160–171.250
TABLES AND FIGURES251

11. Table 1. Cold temperature advisories provided by 45 WS.252
Temperature Threshold Duration Desired Lead-time
≤ 35F any occurrence 4 hr
≤ 32F ≥ 4 hr 16 hr
≤ 28F any occurrence (if wind > 10 kt) 16 hr
253
254
255
Table 2. Partitioning of the cold weather events (≤ 45F) at CCAFS/KSC in optimizing the 45 WS256
minimum temperature tool (6 outliers removed).257
Time Period Description Number of Events Percent of Events
Jan 1986-Apr 2014 All Data 595 100%
Jan 1986-Dec 2009 Development Data 476 80%
Jan 2010-Apr 2014 Independent Verification 119 20%
258
Table 3. RMSE for the previous and new ‘first guess’ equations for all cold events (≤ 45F) at259
CCAFS/KSC. The bias values were calculated using Equation 4. The six outlier 1000-850 mb thicknesses260
were excluded in these calculations.261
262
Time Period RMSE of previous ‘First Guess’ Equation(F) RMSEof new ‘First Guess’ Equation (F)
Jan 1986–Dec 2009 8.87 3.47
Jan 2010-Apr 2014 11.74 4.83
263
264
265
Table 4. Bias for the previous and new ‘first guess’ equations for all cold events (≤ 45F) at266
CCAFS/KSC. The bias values were calculated using Equation 4. The six outlier 1000-850 mb thicknesses267
were excluded in these calculations.268
269
Time Period Bias of previous ‘First Guess’ Equation(F) Bias of new ‘First Guess’ Equation (F)
Jan 1986-Dec 2009 6.35 0.03
Jan 2010-Apr 2014 8.22 1.31
270
271
272
273

12. Figure 1. Schematic of the minimum temperature algorithm used by the 45 WS to make low temperature274
forecasts.275
276
277
Figure 2. Linear regression of the observed minimum temperatures and the observed thickness values.278
279
280
281

13. 282
Figure 3. Days on which the observed low temperature reached 45F or less from 1986 to 2014 (black283
line) along with the low temperature predicted for each day by the old operational ‘first guess’ linear284
equation (red line). The six outliers were removed here.285
286
287
288

14. 289
Figure 4.Days on which the observed low temperature reached 45F or less from 1986 to 2014 (black290
line) along with the low temperature predicted for each day by the new ‘first guess’ linear equation (red291
line). The six outliers were removed here.292
293

15. 294
Figure 5. Days on which the observed low temperature reached 45F or less from 2000 to 2014 (black295
line) along with the low temperature predicted for each day by the old operational ‘first guess’ linear296
equation (red line).297
298

16. 299
Figure 6.Days on which the observed low temperature reached 45F or less from 2000 to 2014 (black300
line), and the low temperature predicted for each day by the new ‘first guess’ linear equation (red line).301
302
303