A Case Study of the Persistence of 

Weather Forecast Model Errors 

by Barbara Sauter 

ARL-TR-3418 January 2005 

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Army Research Laboratory 

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ARL-TR-3418 January 2005 

A Case Study of the Persistence of 

Weather Forecast Model Errors 

Barbara Sauter 

Computational and Information Sciences Directorate

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A Case Study of the Persistence of Weather Forecast Model Errors 

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14. ABSTRACT 

Decision makers could frequently benefit from information about the amount of uncertainty associated with a specific weather 

forecast. Automated numerical weather prediction models provide deterministic weather forecast values with no estimate of the 

likely error. This case study examines the day-to-day persistence of forecast errors of basic surface weather parameters for four 

sites in northern Utah. Although exceptionally low or high forecast errors on one day are more likely to be associated with a 

similar quality forecast the following day, the relationship is not considered strong enough to provide beneficial guidance to 

users without meteorological expertise. Days resulting in average forecast errors showed no persistence in the quality of the 

subsequent day’s forecast. More sophisticated methods are needed to generate and portray weather forecast uncertainty 

information. 

15. SUBJECT TERMS

Weather Forecast Uncertainty; Forecast Errors; Error Persistence; WRF; MM5; Utah MesoWest 

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Barbara Sauter 

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iii 

Content 

List of Figures iv

List of Tables vi

Summary 1

1. Introduction 3

2. Methodology 3

2.1 Forecast Model Runs.......................................................................................................3

2.2 Surface Validation Stations.............................................................................................4 

3. Results 6

3.1 Case Study Considerations..............................................................................................6 

3.2 Background Information on Station Observed Weather and Forecast Errors.................6 

3.2.1 Observed Weather ...............................................................................................6 

3.2.2 Forecast Errors ....................................................................................................8 

3.3 Forecast Error Persistence.............................................................................................10 

3.3.1 Detailed Error Persistence Case Study Results .................................................10 

3.3.2 Summary Error Persistence Results by Station.................................................23 

3.3.3 Summary Error Persistence Results by Weather Parameter..............................25 

3.3.4 Summary Error Persistence Results by Time of Day.......................................26 

3.3.5 Summary Error Persistence Results by Season................................................26 

3.3.6 Summary Error Persistence Results by Model.................................................27 

4. Conclusions 28

4.1 Overall Case Study Results ...........................................................................................28 

4.2 Recommendations .........................................................................................................29 

References 31

Appendix. Average Forecast Error Ranges 32

Acronyms 39
iv 

Distribution List 40 

List of Figures 

Figure 1. Surface station locations..................................................................................................5 

Figure 2. Observed temperatures most frequently occurred within the ranges shown for each 

station and time. Summer months depicted by a red line, winter months by a blue line...........7 

Figure 3. Observed dew-point temperatures most frequently occurred within the ranges 

shown for each station and time. Summer months depicted by a red line, winter months 

by a blue line..............................................................................................................................7 

Figure 4. WRF dew-point temperature forecasts compared to the observations at 2 a.m. for 

the summer months at station DVE. ........................................................................................10 

Figure 5. Mean temperature errors at DVE for summer nighttime forecasts. Data markers 

are coded in green (better), yellow (average), or red (worse)..................................................11 

Figure 6. Mean wind speed errors at DVE for summer daytime forecasts. Data markers are 

coded in green (better), yellow (average), or red (worse)........................................................13 

Figure 7. The number of days with the dew-point temperature forecast error category of 

better (green bars), average (yellow bars), and worse (red bars), given the previous oneday forecast error category on the left and the previous two-day forecast error category on 

the right, for PRP at 2 p.m. in the summer. .............................................................................15 

Figure 8. The daily dew-point temperature forecast error amounts for PRP at 2 p.m. in the 

summer.....................................................................................................................................16 

Figure 9. The daily temperature forecast error amounts at SNZ at 2 a.m. in the summer............18 

Figure 10. The number of days with the dew-point temperature forecast error category of 

better (green bars), average (yellow bars), and worse (red bars), given the previous oneday forecast error category on the left and the previous two-day forecast error category on 

the right, for WBB at 2 a.m. in the summer.............................................................................20 

Figure 11. The daily dew-point temperature forecast error amounts for WBB at 2 a.m. in the 

summer.....................................................................................................................................20 

Figure 12. WRF wind speed forecasts compared to the observations at 2 a.m. for the summer 

months at WBB........................................................................................................................21 

Figure 13. Daily temperature forecast error categories for the daytime winter forecasts for 

WBB. The marker labels indicate the forecast day in order from 1 through 60, equating 

to the forecast period of January 1 through February 29, 2004...............................................22 
v 

Figure 14. Each chart shows the combined results for all forecasts for stations (a) DVE, 

(b) PRP, (c) SNZ, and (d) WBB. The y-axis indicates the percentage of subsequent days 

with the forecast error category of better (green bars), average (yellow bars), and worse 

(red bars), given the previous day’s forecast error category, which is listed on the 

horizontal labels for the x-axis on the left half of each chart. The right half of each chart 

provides the same information, except the x-axis groupings are based on having two 

previous days in the same error category. ...............................................................................24 

Figure 15. Each chart shows the combined results for all forecasts for weather parameters (a) 

temperature, (b) dew-point temperature, (c) wind speed, and (d) wind direction. See 

figure 14 caption for chart details. ...........................................................................................25 

Figure 16. Each chart shows the combined results for (a) the nighttime forecasts and (b) the 

daytime forecasts. See figure 14 caption for chart details. .....................................................26 

Figure 17. Each chart shows all the forecast results for (a) the summer forecasts and (b) the 

winter forecasts. See figure 14 caption for chart details.........................................................27 

Figure 18. Each chart shows the all the forecast results for (a) the WRF and (b) the MM5. 

See figure 14 caption for chart details. ....................................................................................27 

Figure A-1. The range of absolute temperature errors used for the average error category is 

shown by the line for (a) MM5 summer forecasts, (b) WRF summer forecasts, (c) MM5 

winter forecasts, and (d) WRF winter forecasts. One-third of the forecasts in each 

category had errors greater than the highest value and one-third had errors less than the 

lowest value depicted by the line. The asterisk associated with each line is the average 

absolute error for the given station and time. ..........................................................................34 

Figure A-2. The range of absolute dew-point temperature errors used for the average error 

category is shown by the line for (a) MM5 summer forecasts, (b) WRF summer forecasts, 

(c) MM5 winter forecasts, and (d) WRF winter forecasts. One-third of the forecasts in 

each category had errors greater than the highest value and one-third had errors less than 

the lowest value depicted by the line. The asterisk associated with each line is the 

average absolute error for the given station and time..............................................................35 

Figure A-3. The range of absolute wind speed errors used for the average error category is 

shown by the line for (a) MM5 summer forecasts, (b) WRF summer forecasts, (c) MM5 

winter forecasts, and (d) WRF winter forecasts. One-third of the forecasts in each 

category had errors greater than the highest value and one-third had errors less than the 

lowest value depicted by the line. The asterisk associated with each line is the average 

absolute error for the given station and time. ..........................................................................36 

Figure A-4. The range of absolute wind direction errors used for the average error category 

is shown by the line for (a) MM5 summer forecasts, (b) WRF summer forecasts, (c) 

MM5 winter forecasts, and (d) WRF winter forecasts. One-third of the forecasts in each 

category had errors greater than the highest value and one-third had errors less than the 

lowest value depicted by the line. The asterisk associated with each line is the average 

absolute error for the given station and time. ..........................................................................37 
vi 

List of Tables 

Table 1. Surface station information...............................................................................................4 

Table 2. Average differences between WRF forecast and observed values. Observed wind 

data at SNZ is considered unreliable. ........................................................................................8 

Table 3. Percent of forecasts in each error category 24 hours later, given the previous day’s 

error category...........................................................................................................................28 

Table 4. Percent of forecasts in each error category on the third day, given a consistent error 

category over the previous two days........................................................................................29 
1

Summary 

Military and civilian activities affected by the weather require decision makers to rely on 

uncertain weather forecasts. Specific information on the amount of uncertainty associated with a 

forecast has historically been non-existent, or based on a human expert indicating a level of 

confidence. Organizations and individuals involved in producing or using weather forecasts are 

becoming more aware of the value of including information about the amount of uncertainty 

associated with a forecast. At the same time, information processes are becoming more 

automated, relying less on human expertise. 

Various organizations are investigating methods to automatically calculate and portray weather 

forecast uncertainty. One proposed method was to provide a “stoplight” chart indicating whether 

the validated model forecast, from either 24 or 48 hours earlier, had produced errors that were 

either better than, the same as, or worse than the average error for the particular model being 

used. Specifically, for each numerical weather prediction model available, the average error 

produced by that model over some historical period would be known. If the forecast validated 

the previous day produced a significantly lower than average error for a particular model, the 

Web link to that model output would be preceded by a green circle; whereas, if a model 

generated a typical error on the previous day relative to its own historical performance it would 

be preceded by a yellow circle, or if it produced a higher than average error it would be preceded 

by a red circle. Two color-coded circles would be presented if the previous two days’ results 

were considered. This case study looks at model forecast errors on consecutive days to 

determine how useful it might be for a user to be given a “better,” “average,” or “worse” marker 

based on the previous day’s forecast. 

This case study is based on forecast errors for both the Pennsylvania State University/NCAR 

Mesoscale Model Version 5 (MM5) and the Weather Research and Forecasting (WRF) model 

for four specific sites in the vicinity of Salt Lake City, Utah. Ranges of forecast error values 

were defined as better, average, or worse for single parameter forecasts at the same location, time 

of day, season, and model. The divisions between the error categories were based on the 

thresholds that would produce an equal number of forecasts in each category. The summer 

months included 54 days and the winter months included 57 days, resulting in approximately 

18-19 forecasts in each error category for each permutation of 4 stations, 4 weather parameters, 2 

times of day, 2 seasons, and 2 forecast models. 

A day-by-day analysis shows how frequently the error category persisted for consecutive days. 

The report provides many details of these analyses. Forecasts that were better or worse than the 

average range were more likely to be associated with forecasts in the same category the 

following day. These persistent better and worse error categories generally occurred on 40-50% 

of the following days, with about 25% of the following days falling in the opposite error 
2

category. The days with average forecast errors were equally likely to be followed by any of the 

three forecast error categories. The original suggestion that precipitated this effort is not being 

pursued. The results seen in this study provide further justification that a simple stoplight marker 

based on a previous day’s forecast error is not sufficient to allow weather forecast users to 

incorporate an appropriate level of uncertainty information into their decisions involving 

probability, risk, and benefits. 
3

1. Introduction 

Weather forecasters regularly use the term “persistence” to indicate non-changing weather from 

one day to the next. Experienced forecasters will also recall specific instances when a forecast 

model performed poorly, and suspect poor performance from that model when similar conditions 

occur. This case study examines the likelihood of a poor model forecast to persist from one day 

to the next, without consideration of the weather pattern influencing the area. 

In a previous study, two mesoscale forecast models were run over northern Utah (1). These 

models were the Pennsylvania State University/National Center for Atmospheric Research 

(NCAR) Mesoscale Model Version 5 (MM5) and the first version of the Weather Research and 

Forecasting (WRF) model, under development by NCAR, the National Oceanic and 

Atmospheric Administration, and several universities (2, 3). The results of those hourly model 

forecasts compared to surface observations at 50-70 sites showed some very large errors. In 

order to examine the model performance in more detail, and to investigate any patterns in the 

quality of the forecasts, this case study focuses on four of the surface stations at one time during 

the night and one time during the day. 

Although the goal of this study emphasizes the relative performance of the individual model at a 

specific site over a limited timeframe, many general error statistics are included. These 

individual error amounts do not accurately reflect the models’ capabilities to the degree indicated 

by the values given, since the surface sensors used for validation do not meet standard height or 

calibration requirements. The Utah MesoWest Cooperative provides error flags for questionable 

observations, but these flags were not available for this study (4). Only rudimentary errorchecking was performed on the observations to ensure they were within possible limits. 

2. Methodology 

2.1 Forecast Model Runs 

Both the MM5 and WRF models were initialized with Global Forecast System (GFS) model 

output data (5). The MM5 was run with a coarse domain and two nests on an Army High 

Performance Computing Resource Center’s Cray computer, while the non-nested version of the 

WRF was run on a U.S. Army Research Laboratory Major Shared Resource Center IBM system 

(6, 7). The model forecast data used for comparison with surface observations was based on 

5-km grid spacing for both models. Model runs were initialized at 1800 Greenwich Mean Time 

(GMT) for 28 days in July 2003, 26 days in August 2003, 28 days in January 2004, and 29 days 

in February 2004. The initial 6 hours were used for spin-up purposes, so that the WRF 

validation times of 0900 and 2100 GMT used in this study would be considered a 9- and 21-hour 
4

forecast. These times were 2 a.m. and 2 p.m. Mountain Standard Time (MST). Through an 

inconsistency in the handling of the WRF and MM5 validation files for this case study, the times 

available for the MM5 analysis were one hour later each day, valid at 3 a.m. and 3 p.m. MST. 

The forecast model parameters of temperature and dew-point temperature at 2 m and u- and 

v-wind components at 10 m were horizontally interpolated to the surface station locations. Wind 

speed and direction values have been calculated from the wind components and are used in the 

discussion of the results. 

2.2 Surface Validation Stations 

As mentioned in the introduction, this case study leverages an existing dataset. Four 

meteorological stations were selected for closer scrutiny based on their dew-point temperature 

errors for a single day, reflecting a wide range of forecast error amounts: 

• Promontory Point, UT (PRP): much worse than average 

• DV-Burns, UT (DVE): worse than average 

• WBB/U Utah, UT (WBB): better than average 

• Bountiful/F G House, UT (SNZ): much better than average 

That criterion is not consistent for all the days used in this study, but the four stations previously 

selected were kept for this analysis. Site information for these stations is listed in table 1. PRP 

is situated on a hill on a peninsula extending into the Great Salt Lake, while DVE is in the 

Wasatch Mountains. WBB and SNZ are in urban areas, with WBB on the roof of a University of 

Utah building in Salt Lake City and SNZ on a 3-m tower in the backyard of a house in the 

vicinity of Bountiful, Utah. All four stations are part of the SNOWNET mesonet. 

Table 1. Surface station information. 

ID Name Latitude 

(°N)

Longitude 

(°W)

Elevation 

(ft)

PRP Promontory Point 41.2575 112.4398 6926 

DVE DV - Burns 40.6228 111.4520 7333 

WBB WBB/U Utah 40.76623 111.84755 4910 

SNZ Bountiful/F G House 40.8754 111.8716 4760 

Figure 1 shows the location of the four stations on a map of the Great Salt Lake/Wasatch Front 

areas, highlighting the complex terrain of northern Utah. 
5

PRP 

DVE 

SNZ

WBB 

Figure 1. Surface station locations. 
6

3. Results 

3.1 Case Study Considerations 

Although an attempt was made to narrow the scope of the thousands of results from the previous 

model output study, the resulting subset of data from two models, four stations, two times per 

day for two seasons still poses difficulties in analyzing and describing meaningful results. The 

primary goal of the analysis is to determine how often the quality level of a numerical model 

forecast persisted from one forecast to the following day’s forecast. Some definition of a 

persistent error must be used. In order to accomplish this, the forecasts are classified as “better” 

(the third of the forecasts with the lowest errors), “average” (the third in the middle), or “worse” 

(the third with the highest errors). This grouping results in approximately equal numbers of 

forecasts in each classification. If no correlation exists between the quality of a forecast on a 

preceding day and the quality of the forecast on the subsequent day, each preceding day 

classification category would result in approximately 33% of each classification on the next day. 

The sample size may be too small to obtain statistically significant results, and the classification 

groupings occasionally place forecasts with very small error differences in adjacent groups. 

With these limitations in mind, the following sections describe some of the results seen relating 

to the persistence of forecast errors from one forecast to the forecast 24 hours later. 

3.2 Background Information on Station Observed Weather and Forecast Errors 

3.2.1 Observed Weather 

Within each season, the individual stations’ temperatures most frequently fell within a 10-12 °C 

range over the two-month period, with occasional observations above or below that range. 

Figure 2 highlights these prevailing ranges, providing the summer temperatures with a red line 

and winter temperatures with a blue line. SNZ showed the highest daytime temperatures, but 

was cooler than the other urban station, WBB, at night during the summer. 

The most frequently observed dew-point temperatures were typically within a 10-15 °C range. 

As expected, the dew-point temperatures were significantly lower than the temperatures in the 

summer months, but were usually quite close to the temperatures in the winter months. 
7

-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

DVE PRP SNZ WBB DVE PRP SNZ WBB

2:00 a.m. 2:00 p.m.

Prevailing Temperatures (°C)

-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

DVE PRP SNZ WBB DVE PRP SNZ WBB

2:00 a.m. 2:00 p.m.

Prevailing Dew-Points (°C)

Figure 2. Observed temperatures most frequently occurred within the ranges shown for each station 

and time. Summer months are depicted by a red line, winter months by a blue line. 

Figure 3. Observed dew-point temperatures most frequently occurred within the ranges shown for each 

station and time. Summer months are depicted by a red line, winter months by a blue line. 
8

Wind speeds were predominantly light. Wind direction was only analyzed for this study for 

observations with corresponding wind speeds greater than 1 m/s. The nighttime winds at DVE 

were usually below 2 m/s, with primarily southerly winds in the summer and no determinant 

direction in the winter. DVE’s daytime wind reports were slightly stronger, concentrated 

between 0 and 4 m/s, and most frequently occurred from either a northerly or south to 

southwesterly direction. The other high elevation station, PRP, reported somewhat higher wind 

speeds, generally between 1 and 7 m/s. The summertime wind came from all directions during 

the night, while winds with a westerly component were most frequent during the day. Southerly 

winds were most common at PRP during the winter; however, all wind directions occurred a 

significant portion of the time. SNZ almost always reported wind speeds below 1 m/s. In 

addition to suspecting the observations were not reliable, SNZ did not report for ten days in 

mid-August. No analyses of the SNZ wind data will be provided. WBB showed both diurnal 

and seasonal variations in observed winds. During the summer months, wind speeds were 

generally between 1 and 6 m/s, but the direction varied from predominantly north to east at night 

and south to northwest during the day. The winter reports reflected wind speeds below 2.5 m/s 

from all directions during the night, with somewhat stronger winds, up to 5 m/s, from southwest 

to northwest during the day. 

3.2.2 Forecast Errors 

A summary of the average WRF model forecast errors is provided in table 2. 

Table 2. Average differences between WRF forecast and observed values. Observed wind data at SNZ is 

considered unreliable. 

 Summer Winter 

 2 a.m. 2 p.m. 2 a.m. 2 p.m. 

 Mean 

Error 

Absolute 

Error 

Mean 

Error 

Absolute 

Error 

Mean 

Error 

Absolute 

Error 

Mean 

Error 

Absolute 

Error 

T (°C) -2.1 2.6 0.3 1.3 1.1 1.9 2.6 2.9 

DP (°C) 8.6 8.6 7.1 7.1 3.2 3.3 2.6 3.0 

DVE 

WS (m/s) 2.6 2.6 1.2 1.7 2.8 2.9 2.8 3.0 

WD (°) 32 40 -31 65 21 66 -2 69 

T (°C) -1.4 2.4 4.9 4.9 4.3 4.4 7.0 7.0 

DP (°C) 11.0 11.0 8.3 8.4 5.4 5.4 4.3 4.8 

PRP 

WS (m/s) -1.1 2.1 -1.3 1.6 -0.2 1.8 0.4 1.6 

WD (°) -6 46 -54 65 -14 61 25 54 

T (°C) -1.0 2.2 -5.0 5.3 1.5 2.9 1.4 3.4 

DP (°C) 5.1 5.2 1.9 2.9 0.6 2.4 -0.8 2.5 

SNZ 

WS (m/s) 4.3 4.3 2.6 2.6 2.7 2.7 3.5 3.5 

WD (°) -5 6 11 49 71 71 26 27 

T (°C) -5.9 6.0 -2.6 3.0 0.5 2.4 3.4 4.2 

DP (°C) 8.2 8.2 5.3 5.4 1.4 2.2 1.4 2.8 

WBB 

WS (m/s) 0.6 2.0 -1.1 1.6 0.5 1.1 1.4 1.9 

WD (°) 32 61 4 52 9 71 11 50 

NOTE: Shading indicates unreliable data. 
9

Positive values for temperature, dew-point temperature, and wind speed mean errors indicate the 

forecasts were higher than the observations. When the mean error listed for wind direction is 

positive, the forecast wind was from a direction clockwise from the observed direction. 

The WRF exhibited a warm bias for all four stations during the winter, which was most 

pronounced at PRP, which is situated on a peninsula extending into the Great Salt Lake. The 

WRF forecasts for summertime temperatures were often too low, while the dew-point 

temperature forecasts at the same place and time were much too high, resulting in extremely 

overestimated relative humidity. 

Average wind speed forecasts typically reflected a bias 2-3 m/s too high at DVE, with smaller 

(or even low) biases at the other stations, excluding SNZ. Average wind direction absolute 

errors consistently ranged between 40o and 70o. 

The MM5 forecasts were valid one hour after the WRF forecasts. Most of these forecasts 

revealed average error trends similar to those seen in the WRF forecasts. The appendix provides 

the mean absolute errors for both the MM5 and WRF forecasts by season, station, and time of 

day. These charts in the appendix also highlight the range of errors categorized as “average” in 

the forecast error persistence analysis. 

The purpose of this study is not to evaluate the forecast model performance in detail; however, 

the simple face validations of plots of forecast and observed data points, as shown in figure 4, 

strongly suggest the model forecasts contain some skill, even when the bias error is significant. 

The Pearson correlation coefficient for these summer dew-point temperature forecasts and 

observations is 0.74. 
10

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

7/3

7/10

7/17

7/24

7/31

8/7

8/14

8/21

8/28

Summer Dates 2 a.m.

Dew-Point (°C)

forecast

observed

Figure 4. WRF dew-point temperature forecasts compared to the observations at 2 a.m. for the 

summer months at station DVE. 

3.3 Forecast Error Persistence 

The following sections provide the results of this case study on the day-to-day persistence of 

model forecast errors. Initial discussions provide some of the details seen at each of the four 

stations. Following those discussions, the findings are summarized by station, weather 

parameter, time, season, and forecast model. Whenever the forecast model is not explicitly 

named, the information is based on the WRF outcomes. 

3.3.1 Detailed Error Persistence Case Study Results 

3.3.1.1 DV-Burns (DVE) 

DVE is situated several miles southeast of Park City, Utah. Although, at over 7000-ft elevation, 

it is the highest station used in this case study, higher mountain peaks are found both to the west 

and east of the site. 

For the summer temperature forecasts valid at 2 a.m., a better result was only slightly more likely 

to be followed by a better result 24 hours later, as opposed to either an average or worse result. 

While more frequent than either of the other categories alone, the probability of the better 

forecast error category repeating was still less than 50%, which was almost always the case. An 

average forecast day was also only slightly more likely to be associated with an average forecast 

the subsequent day, rather than a better forecast, but was unlikely to be followed by a worse 

forecast. On the other hand, days when the 2 a.m. temperature forecast proved to be worse than 

usual were significantly followed by another worse temperature forecast the next day. 
11

-6.0

-4.0

-2.0

0.0

2.0

4.0

7/3 7/10 7/17 7/24 7/31 8/7 8/14 8/21 8/28

Summer Dates 2:00 a.m.

Temperature Errors (°C)

The categories of better, average, and worse are based strictly on absolute error amounts. 

Figure 5 highlights the mean temperature errors, with the absolute error category for each day 

displayed by a green, yellow, or red data marker. Wide day-to-day variations exist, but 

noticeable trends appear, including a majority of worse forecasts during the first half of July and 

primarily better forecasts during the second half of July. More variations are seen in the August 

results. The summer nighttime temperature forecast biases were predominantly too cold. 

The 2 p.m. summer temperature forecasts were significantly more likely to be in the same or 

adjacent category than in the opposite category from the previous day. Out of the 14 days with 

better afternoon temperature forecasts, the following afternoon included a better forecast on 

7 days, an average forecast on 5 days, and a worse forecast on 2 days. The days after an average 

afternoon temperature forecast were pretty evenly divided between better, average, and worse 

forecasts. The typical July temperature warm bias of about 2 °C in the afternoon was often 

found in the opposite direction as the nighttime bias, but was not as large. This study does not 

investigate correlations between the nighttime and daytime errors on the same date, but a cursory 

inspection of the DVE temperature forecasts seems to show little correlation between these 

errors. 

 Figure 5. Mean temperature errors at DVE for summer nighttime forecasts. Data markers are coded 

in green (better), yellow (average), or red (worse). 

The summer dew-point temperature forecasts for DVE included a very large warm bias, with 

average mean errors of 8.6 °C for the 2 a.m. forecasts and 7.1 °C for the 2 p.m. forecasts. Every 

nighttime forecast was too high, and all but one daytime forecast was too high. The actual 

amount of the forecast error frequently changed from one day to the next in the nighttime 
12

forecasts, but worse forecasts were much more likely to be followed by worse forecasts again the 

following day. Of the 18 days in the worse category, 13 of the subsequent days also displayed 

worse forecast errors. This is one of the highest percentages of error persistence, and is due to 

dew-point temperature forecast errors greater than 10 °C on all but one day during the first two 

weeks in July. A single 3-day period from July 4-6 showed errors close to 15 °C each day, while 

a 4-day period from July 25-28 contained daily errors of approximately 2 °C each day. 

Otherwise, the errors differed by over 2 °C almost every day. Significant changes, by 5 °C or 

greater from one day to the next, occurred for 11 out of the 47 days with data available for 

consecutive days. The worse dew-point temperature forecasts valid at 2 p.m. were somewhat 

concentrated in the first half of July, like the 2 a.m. forecasts, but were more spread out over the 

rest of July and August with a weaker pattern of persistent errors. 

Wind speed observations were frequently missing for station DVE at the 2 a.m. validation time. 

Almost all of the existing validations showed wind speed forecasts to be too high, with an 

average mean error of 2.6 m/s. It’s also possible that the consistently very low wind speed 

observations at these times were not accurate, but other DVE reports from the same general 

timeframe do include higher wind speeds so the sensor was not stuck at low readings. Although 

few consecutive days are available, the nighttime wind speed error amounts seem to jump around 

fairly randomly. Most of the daytime reports for these summer dates were available including 

wind observations. The average mean error at 2 p.m. was 1.2 m/s with an average absolute error 

of 1.7 m/s. As shown in figure 6, no strong pattern exists in the persistence of absolute error 

category from one day to the next. The wind speed forecasts exhibit a consistent bias of too high 

in July, continuing but becoming less dominant in August. 
13

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Summer Dates 2 p.m.

Wind Speed Errors (m/s)

Figure 6. Mean wind speed errors at DVE for summer daytime forecasts. Data markers are coded 

in green (better), yellow (average), or red (worse). 

Wind direction evaluations are only considered for observations with wind speed greater than 

1 m/s, in order to lessen the impact of variable wind cases. Therefore, the summer dates at 

2 a.m. provided too few wind direction observations to analyze. The 2 p.m. observations 

reflected no pattern in the amount of wind direction forecast errors for better or average forecast 

days, though the worse forecast days appeared less likely to be followed by a better forecast day. 

The winter months included an even smaller error persistence relationship for nighttime 

temperature forecasts, which had only been evident in the worse category for the summer 

months. The persistence of the temperature forecast error category was stronger in the daytime 

for the summer months, and that pattern was repeated to the same or to a slightly greater degree 

in the winter months. The dew-point temperature forecast error averages were much smaller in 

the winter than in the summer months. The winter average mean and absolute errors were 

approximately 3 °C for both the 2 a.m. and 2 p.m. forecasts. The nighttime dew-point 

temperature forecasts in the better and average categories were no more likely to be followed by 

the same category the following day than a different category. Those forecasts falling in the 

worse category were slightly more likely to be worse again the next day. The daytime forecasts 

repeated the same category for the better and average forecasts 7 out of 18 days, while the worse 

forecasts preceded another worse forecast 8 out of 17 days. The summer occurrence of many 

missing 2 a.m. wind observations was repeated in the winter. The 2 p.m. wind observations 

displayed a noticeable tendency for better forecasts to be followed by better forecasts, and for 

worse forecasts to be followed by worse forecasts. This trend seems primarily due to the 
14

changing pattern in wind speed forecast bias amounts, which are low or near zero in mid-January 

and late February. The remainder of the winter days reflected wind speed forecasts that were too 

high, but by varying amounts. Light winds or missing observations for the 2 p.m. forecasts 

provided very few consecutive days for wind direction in January. A pattern evidenced over 

several consecutive days in early February showed northerly observed winds associated with 

northwesterly forecast winds. Otherwise, the wind direction errors varied considerably from one 

day to the next in February. 

The MM5 error patterns are discussed relative to the WRF results described above for DVE: 

• The summer MM5 temperature forecast errors seemed to be slightly less persistent for the 

nighttime forecasts, and about the same for the daytime forecasts. 

• The summer MM5 dew-point temperature errors for both the 3 a.m. and 3 p.m. valid times 

showed a greater relationship between a better forecast one day being followed by a better 

forecast the next day than was seen in the WRF results. On the other hand, the persistency 

of the worse forecasts was evident but not to the degree found in the WRF results. 

Specifically, the MM5 results showed 9 out of 18 worse forecasts followed by another 

worse forecast, when the WRF results were 13 out of 18. 

• The winter MM5 temperature forecast errors didn’t exhibit strong persistence, but did show 

a slightly higher incidence of better forecasts after a previous better forecast at nighttime 

than seen in the winter WRF forecasts. The opposite occurred in the daytime forecasts, 

where the WRF error persistence was stronger, while the MM5 showed no relationship. 

• As was the case for WRF, the winter MM5 dew-point temperature forecast errors were not 

particularly persistent, with the strongest but still small relationship found in the worse 

category in the afternoon forecasts. 

• The summer and winter MM5 wind speed and wind direction results were similar to the 

WRF results. 

3.3.1.2 Promontory Point (PRP) 

PRP is the second highest station in this case study, at approximately a 6900-ft elevation. The 

site is complex not solely because of the hilly terrain, but also because of its location on a 

peninsula extending into the Great Salt Lake. 

The summer 2 a.m. WRF temperature forecasts included a negative bias of 1.4 °C that was 

strongest in July. The same forecast error category as the day before did not repeat most 

frequently, except for the better category, which resulted in another better category only one day 

more than an average result. Having an opposite category occur was infrequent, however. For 

16 nighttime temperature forecasts qualifying as a better result, only 3 of the following days 

were a worse result. Out of the 15 worse results, only 2 of the following days were a better 

result. The 2 p.m. temperature forecast errors were much larger than the nighttime errors, and 
15

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showed a stronger persistence from one day to the next. The mode for the second day was 

always the same category. In each category, about half of the subsequent days fell in the same 

category as the previous day. The two days with extremely high errors were each followed by 

days with smaller errors but still much higher than average. 

The summer dew-point temperature forecasts included extremely large biases of 11 °C at 2 a.m. 

and over 8 °C at 2 p.m. The individual categories encompassed large error ranges, and the 

forecast error value generally changed by several degrees on adjacent days. The largest errors in 

the nighttime forecasts were always followed by another larger than average error. The daytime 

forecasts showed a strong modal response of the second day falling in the same category as the 

preceding day. Figure 7 depicts this on the left side of the chart labeled “Previous Day.” For 

each daily forecast in the category of better, average, and worse, the bars show how many 

subsequent days fell in each of those categories. The right side of the chart shows the same 

information, except that the x-axis categories of better, average, and worse consist of cases where 

the two previous days were in the same category rather than just one previous day. This setup 

seems to display a considerable amount of persistence in the quality of the forecast. As seen in 

figure 8, however, there are still frequently very large variations in the dew-point temperature 

forecast error from one day to the next. 

Figure 7. The number of days with the dew-point temperature forecast error category of better 

(green bars), average (yellow bars), and worse (red bars), given the previous one-day 

forecast error category on the left and the previous two-day forecast error category on 

the right, for PRP at 2 p.m. in the summer. 
16

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Summer Dates 2 p.m.

Dew-Point Errors (° C)

Figure 8. The daily dew-point temperature forecast error amounts for PRP at 2 p.m. in the summer. 

The summer wind speed forecasts produced similar mean bias amounts of -1.1 m/s at 2 a.m. and 

-1.3 m/s at 2 p.m. However, the nighttime forecasts resulted in much more variation, including 

more frequent high errors in early July and late August and too low forecasts most of the rest of 

the time. The daytime wind speed forecasts had lower overall error amounts, with forecasts that 

were consistently too low. Neither the nighttime or daytime forecasts showed any persistence in 

the amount of absolute error from one day to the next. In fact, for the days with better or worse 

forecast results, the next day’s forecast was more likely to be the opposite category than the same 

category. 

The wind direction at PRP during the summer at 2 a.m. was predominantly out of the north. The 

WRF wind direction forecasts at these times did not show any bias and were often very accurate, 

with the wind direction forecasts categorized as average when the error was between 15 and 45o. 

Unlike the wind speed results, the nighttime wind direction errors reflected the common pattern 

of infrequent occurrence of the opposite category on days following a better or worse forecast. 

The observed wind directions were more variable at 2 p.m. The average forecast error category 

encompassed higher errors, ranging from 45o to 85o. As with the wind speeds, the daytime wind 

directions in the second day category were as likely or more likely to be the opposite than to be 

the same as the day before. 

The winter temperature forecast errors for PRP were higher than the summer errors for both 

validation times. The nighttime forecasts exhibited a higher persistence in error category than 

was seen in the summer months, while the daytime forecasts showed less persistence than in the 

summer. On the other hand, the dew-point temperature forecast errors were only about half as 
17

large in the winter, when compared to the 11 °C nighttime error and 8 °C daytime error 

experienced in the summer. The dew-point temperature errors showed some persistence from 

one day to the next. The nighttime pattern was similar to the summer results, but the daytime 

persistence was not as strong as seen in the summer. The wind speed errors were slightly more 

likely to show persistence between consecutive days in the winter than in the summer. The 

winter wind direction nighttime forecasts repeated the same category more frequently than either 

of the other categories the following day when the previous day fell in the worse category, but 

not when the previous day’s forecast fell in the better or average categories. As seen in the 

summer forecasts, the daytime wind direction forecasts were more frequently in the opposite 

category than in the same category. 

The MM5 error patterns are discussed relative to the WRF results described above for PRP: 

• Any persistence in the summer MM5 temperature nighttime forecast errors was weak, with 

the opposite category occurring more frequently than seen in the WRF results. The pattern 

of persistence was stronger in the daytime forecast, and is similar to the WRF pattern. 

• The summer MM5 dew-point temperature mean and absolute errors for both the 3 a.m. and 

3 p.m. valid times were approximately 8 °C. Both times reflected patterns showing 

persistence of error amounts from one day to the next, as seen in the WRF results. 

• The summer MM5 wind speed error categories mirrored the WRF findings of opposite 

category errors occurring more frequently than same category errors on subsequent days. 

• The MM5 wind direction nighttime errors were slightly higher than the WRF errors in the 

summer months. The persistence of the error category was also somewhat less, with only 

the better category forecast days most likely to be followed by a forecast in the same 

category. The MM5 wind direction forecasts shared similar daytime error amounts as well 

as the lack of persistence produced by WRF. 

• The bias in the winter MM5 temperature forecasts was generally in the same direction as 

the WRF forecasts, with similar or somewhat smaller absolute errors for the MM5. Both 

the MM5 and WRF nighttime results showed the repeat of average and worse forecasts to 

be more frequent than a different category, but this persistence still occurred in less than 

50% of the cases. Better nighttime MM5 forecasts were followed by another better 

forecast in 7 out of 16 days, compared to 12 out of 17 for the WRF forecasts. The MM5 

daytime temperature forecasts were even more likely to repeat an average or worse 

forecast; however, the better forecast days were followed by an equal distribution of each 

of the three categories. 

• The winter MM5 dew-point temperature errors exhibited no particular persistence pattern 

compared to a small persistence in the larger WRF forecast errors. 
18

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Summer Dates 2 a.m.

Temperature Errors (° C)

• The winter MM5 wind speed and wind direction forecasts also showed no persistence in 

the forecast error from one day to the next. 

3.3.1.3 Bountiful/F G House (SNZ) 

SNZ is the lowest station used in this case study, at a 4760-ft elevation. It is located in the 

backyard of a house in Bountiful, which is a city of about 40,000 just north of Salt Lake City. 

As mentioned previously, no analyses of the wind forecast data is included for SNZ. 

The summer temperature forecasts at SNZ at 2 a.m. encompassed a wide range of errors, as 

shown in figure 9. Several instances occurred with two or more consecutive days containing 

similar errors; however, there were just as many instances where the model produced wildly 

divergent errors on consecutive days. The temperature forecast bias was more consistently too 

low for the daytime forecasts, but no significant pattern appeared in the amount of the error from 

one day to the next. 

Figure 9. The daily temperature forecast error amounts at SNZ at 2 a.m. in the summer. 

The summer dew-point temperature forecasts for SNZ also contained large errors, and frequent 

sizeable day-to-day changes. However, both the nighttime and daytime dew-point temperature 

error categories were more likely to repeat the following day than the temperature error 

categories. 

The temperature and dew-point temperature forecasts for SNZ were much more accurate during 

the winter months. The only category exhibiting a significant persistence trend for temperature 
19

forecasts was the worse forecasts. Each category was slightly more likely to be followed by the 

same category for the dew-point temperatures. 

 The MM5 error patterns are discussed relative to the WRF results described above for SNZ: 

• The summer MM5 temperature mean errors were similar to those seen in the WRF. The 

daytime forecasts displayed strong persistence in the error amounts for one five-day period 

and another four-day period. 

• The summer MM5 nighttime dew-point temperature errors were smaller than the 

equivalent WRF errors, and showed no day-to-day pattern. The afternoon dew-point 

temperature errors were somewhat higher than the WRF errors, and also reflected the 

greater likelihood to repeat an error category the following day. 

• The winter MM5 temperature forecasts were less accurate than the WRF forecasts at night, 

but as accurate during the day. Both times shared the WRF pattern of the worse forecasts 

being most likely to be followed by another worse forecast. 

• The winter MM5 dew-point temperature forecast mean and absolute error amounts were 

very similar to those produced by the WRF. While the WRF forecasts showed persistence 

in the error categories for these dew-point temperature forecasts, the MM5 results showed 

no persistence. 

3.3.1.4 WBB/U Utah (WBB) 

WBB is located in the large urban area of Salt Lake City, slightly higher than SNZ at an 

elevation of 4900 ft. Whereas the SNZ sensors are on a mast in the backyard of a house, the 

WBB sensors are on the roof of a University of Utah building. 

The summer temperature forecasts at WBB displayed a large bias of -6 °C. With few forecasts 

accurate within 4 °C, the error categories incorporated ranges of 1-5 °C for the better forecasts, 

5-7 °C for the average forecasts, and 7-11 °C for the worse forecasts. Based on these relatively 

large ranges, each category was most likely to be associated with the repeat of the same error 

category the following day, but not by a high percentage. The afternoon temperature forecasts 

also contained a low bias, but only by about half as much as at night. These forecasts showed no 

persistence in the forecast error categories. 

The WBB summer dew-point temperature forecast errors were even greater than the temperature 

errors, with the opposite bias of forecasts much higher than observed values. The nighttime 

results are portrayed in figure 10, showing some of the highest persistence occurrences in this 

study. This occurrence is primarily due to the change in bias errors from extremely large values 

in July to smaller values in August, as seen in figure 11. This pattern is similar to the one for the 

summer dew-point temperature errors at PRP. The summer daytime dew-point temperature 

forecast errors were smaller than during the night, but the bias and persistence trends were the 

same as the nighttime results. 
20

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Summer Dates 2 a.m.

Dew-Point Errors (°C)

Figure 10. The number of days with the dew-point temperature forecast error category of better 

(green bars), average (yellow bars), and worse (red bars), given the previous one-day 

forecast error category on the left and the previous two-day forecast error category on 

the right, for WBB at 2 a.m. in the summer. 

Figure 11. The daily dew-point temperature forecast error amounts for WBB at 2 a.m. in the summer. 
21

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Wind Speed (m/s)

forecast

observed

The mean absolute error for the summer nighttime wind speed forecasts for WBB is just 2 m/s. 

However, figure 12 provides the forecast and observed values for each date, highlighting the lack 

of correlation between these data points. Their Pearson correlation coefficient is zero. With the 

lack of forecast skill, it is not surprising that the errors do not contain a pattern of persistence. 

The afternoon wind speed forecasts have a slightly positive correlation coefficient, but the days 

with better or worse forecast errors were more likely to be followed by the opposite category 

than the same category. 

Figure 12. WRF wind speed forecasts compared to the observations at 2 a.m. for the summer 

months at WBB. 

The summer wind direction forecasts had a mean absolute error of about 60o at 2 a.m. and 

slightly less at 2 p.m. Each time resulted in a slightly positive correlation coefficient. The better 

and worse categories were only slightly more likely to be followed by the same category the next 

day. 

Winter temperature forecasts at the 2 a.m. valid time contained smaller errors than the ones in the 

summer. The persistence trend was similar, though, with each category slightly more likely to be 

followed by the same category the following day. The 4 °C mean absolute temperature error in 

the winter 2 p.m. forecasts was somewhat higher than in the summer forecasts. These daytime 

temperature errors showed the most persistence of any sample of the case study. Of the better 

forecast days, 11 subsequent days were also better, 6 were average, and 0 were worse. The 

average days were followed by 5 better, 10 average, and 3 worse forecast days. The worse 

forecast days were associated with 2 better, 2 average, and 14 worse forecasts on the next day. 

Figure 13 depicts the order of the occurrences of all the forecast categories, starting with day 1 as 
22

1

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7 8

9 1011121314 161718192021222324

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30

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WRF Temperature Error Categories at 2:00 p.m. (Day 1-60 = Jan 1-Feb 29)

Avg

Better

Worse

January 1, 2004 and going through day 60 as February 29, 2004. The high rate of persistence is 

associated with a long period of 6-12 °C too high temperature forecasts from January 9 through 

January 24, followed by many days with forecast errors within 2 °C, and then with primarily 

2-4 °C error amounts, including both overforecast and underforecast days, during the last half of 

February. 

Figure 13. Daily temperature forecast error categories for the daytime winter forecasts for WBB. The marker 

labels indicate the forecast day in order from 1 through 60, equating to the forecast period of 

January 1 through February 29, 2004. 

The winter dew-point temperature forecast errors were considerably smaller than the errors seen 

in the summer months. There was a general trend for the high bias to decrease through the twomonth period, but many days deviated from the trend. The better and worse categories were 

slightly more likely to be followed by the same category for both the nighttime and daytime 

forecasts. 

As seen in the summer results, the winter wind speed forecast errors were usually quite small. 

The first week in January and the second week in February produced several 2 a.m. forecast 

errors higher than any other period, but they did not occur on consecutive days. The daytime 

forecasts did not show any persistence pattern. 

The winter wind direction forecasts produced mean absolute errors comparable to the summer 

errors. The wind direction errors do not display any persistence for either the nighttime or 

daytime. 

The MM5 error patterns are discussed relative to the WRF results described above for WBB: 

• The MM5 summer temperature forecasts produced larger errors at the nighttime than at the 

daytime, as was the case for the WRF, but the errors were smaller than those generated by 

the WRF. Only the worse category was most likely to repeat on consecutive days for the 

3 a.m. MM5 forecasts, and any persistence seen at 3 p.m. was very slight. 
23

• The MM5 summer dew-point error day-to-day persistence was not quite as frequent as the 

WRF dew-point errors, but was still fairly noticeable. 

• Summer MM5 wind speed errors were similar to the small WRF errors. Only the worse 

category in the nighttime forecasts showed any propensity to be followed by the same error 

category the next day. 

• The MM5 summer wind direction forecasts did not include any persistence pattern. 

• The MM5 winter temperature forecasts generated a more consistent warm bias than the 

WRF. The error categories showed some persistence but not to the extent evident in the 

equivalent WRF results. The MM5 nighttime worse category was repeated on 11 out of 17 

days, while better forecasts were most likely to be followed by average forecasts and 

average forecasts by better forecasts. Each category was most likely to repeat the same 

category the next day for the MM5 daytime temperature forecasts, but not as frequently as 

seen in the WRF results. 

• The MM5 winter dew-point temperature forecasts showed no persistence in the error 

categories. 

• The MM5 winter wind speed forecast errors were comparable to the generally small errors 

produced by the WRF. The only discernable pattern in the errors was that there was a 

greater likelihood for the better and worse categories to be the same or the adjacent 

category the following day than in the opposite category, particularly for the nighttime 

forecast. 

• The MM5 winter wind direction forecast errors were also similar in magnitude to the WRF 

errors, and did not display any persistence. 

3.3.2 Summary Error Persistence Results by Station 

Although the previous section provides many differences in the details of the forecast errors at 

the four station locations used in this case study, each station produced similar patterns for the 

error persistence, relative to that station. Nevertheless, the individual sites did produce different 

forecast error and bias amounts—the categories of better, average, and worse forecasts were 

determined separately for each seasonal grouping of forecasts for location, weather parameter, 

time, and forecast model. 

Unlike the charts shown in figures 7 and 10, the remaining bar charts (figures 14-18) are based 

on the percentage of total cases in a given category rather than on the raw numbers of days. 

Therefore, the axes are equivalent and the charts can be reasonably compared. 

Figure 14 shows the results for the DVE, PRP, SNZ, and WBB sites individually, based on the 

combined results for all weather parameters, both times, both seasons, and both forecast models. 

For each station, when the previous day had a forecast error in the better category, the following 
24

(a) DVE (b) PRP

(c) SNZ (d) WBB

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day had the highest percentage of better forecasts, as opposed to average or worse forecasts. 

WBB had the lowest percentage of repeating better days (39%), but the difference wasn’t 

substantial when compared to the highest at SNZ (44%). The differences were slightly 

accentuated when it was required that both of the previous two days were in the better category. 

In that circumstance, WBB showed a better forecast for the following day 37% of the time, while 

PRP fell in the better category 47% of the time. 

Figure 14. Each chart shows the combined results for all forecasts for stations (a) DVE, (b) PRP, (c) SNZ, and 

(d) WBB. The y-axis indicates the percentage of subsequent days with the forecast error category of 

better (green bars), average (yellow bars), and worse (red bars), given the previous day’s forecast 

error category, which is listed on the horizontal labels for the x-axis on the left half of each chart. 

The right half of each chart provides the same information, except the x-axis groupings are based on 

having two previous days in the same error category. 

The days with forecast errors falling in the worse category were also most likely to be in the 

same category the next day, and least likely to be in the opposite category. The percentage of 

repeating days was somewhat higher for the worse category than for the better category, ranging 

from a low of 42% at PRP to a high of 47% at SNZ. When the two previous days were both in 
25

(a) Temperature (b) Dew-Point Temperature 

(c) Wind Speed (d) Wind Direction

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(a) Temperature (b) Dew-Point Temperature 

(c) Wind Speed (d) Wind Direction

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the worse category, the lowest and highest percentage of subsequent days in the worse category 

rose to 45% at PRP and 51% at WBB. 

Days following an average forecast error were equally likely to produce a forecast error in any of 

the three categories at DVE and WBB. PRP generated a repeating average error the highest 

percentage of the time, at only 38%. 

3.3.3 Summary Error Persistence Results by Weather Parameter 

Figure 15 provides the same information as found in figure 14, except the individual charts total 

all the data by weather parameter rather than by station. 

Figure 15. Each chart shows the combined results for all forecasts for weather parameters (a) temperature, 

(b) dew-point temperature, (c) wind speed, and (d) wind direction. See figure 14 caption for 

chart details. 

The dew-point temperature errors were most likely to repeat the same error category on 

consecutive days. A better dew-point forecast was followed by a better forecast 47% of the time, 

an average forecast repeated 36% of the days, and a worse forecast was followed by another 

worse forecast 49% of the time. Temperature values were slightly lower, with 42% for the better 
26

(a) Nighttime 2-3 a.m. (b) Daytime 2-3 p.m. 

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forecasts, 37% for the average forecasts, and 47% for the worse forecasts. The instances with 

two preceding days in the better or worse forecast error categories resulted in even higher 

recurrences of the same category, reaching 57% for the worse dew-point temperature forecasts. 

The wind speed and wind direction forecasts show less persistence, with the same category 

repeating the following day 34-38% of the time. With regard to the wind forecast, having two 

previous days in the same category did not lead to the same category on the third day occurring 

more frequently than a different category. 

3.3.4 Summary Error Persistence Results by Time of Day 

As seen in figure 16, results grouped by the nighttime and daytime forecasts produced similar 

trends, with the better 2-3 a.m. forecasts repeated 40% of the time and the better 2-3 p.m. 

forecasts repeating 42% of the time. Both the nighttime and daytime forecasts repeated the 

worse forecast category 44% of the time. For the days with two previous days in the same 

forecast category, the repetition was 5% higher for the 2-3 a.m. better category and the 2-3 p.m. 

worse category. No persistence pattern emerges on days with average forecast errors. 

Figure 16. Each chart shows the combined results for (a) the nighttime forecasts and (b) the daytime 

forecasts. See figure 14 caption for chart details. 

3.3.5 Summary Error Persistence Results by Season 

The summer forecasts displayed greater error persistence than the winter forecasts, with the 

better and worse forecasts followed by the same category 44% and 45% of the time, as compared 

to 39% and 43% for the winter forecasts (figure 17). Days with average forecast errors were 

followed by another day with an average error 35% of the time for both the summer and winter 

months. The percentages of repeating better and worse category forecasts were similar for the 

summer and winter when the two preceding days were the same category, although the 

probability of an opposite category occurring was still higher in the winter than the summer. 
27

(a) Summer (b) Winter 

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Figure 17. Each chart shows all the forecast results for (a) the summer forecasts and (b) the winter forecasts. 

See figure 14 caption for chart details. 

3.3.6 Summary Error Persistence Results by Model 

Although the WRF and MM5 forecasts were for slightly different times, and the forecast errors 

between the two models were frequently quite different, the weak propensity for the error 

amount to persist from one day to the next was comparable for both models (figure 18.) A better 

forecast was followed by a better forecast 41% of the time and by a worse forecast about 25% of 

the time for both the WRF and MM5. A worse forecast was followed by a worse forecast 45% 

of the time for the WRF and 43% of the time for the MM5, and by a better forecast 24% of the 

time for both models. An average forecast was only very slightly more likely to be followed by 

another average forecast than by either a better or worse forecast. When two consecutive days 

were the same category of better or worse, the WRF model forecasts were about 5% more likely 

to repeat that category a third day than the MM5 forecasts. 

Figure 18. Each chart shows the all the forecast results for (a) the WRF and (b) the MM5. See figure 14 

caption for chart details. 
28

4. Conclusions 

4.1 Overall Case Study Results 

This case study examined the issue of using the quality of the previous one- or two-day 

numerical weather prediction model forecast to judge the quality of the following day’s forecast, 

in the absence of knowledge of the actual weather situation. Hundreds of forecasts were divided 

into equal categories of better, average, and worse forecasts within individual combinations of 

the following: 

• station location (four sites in northern Utah) 

• weather parameter (temperature, dew-point temperature, wind speed, wind direction) 

• time of day (2 a.m. and 2 p.m. for the WRF, 3 a.m. and 3 p.m. for the MM5) 

• season (summer: July-August, 2003, and winter: January-February, 2004) 

• forecast model (WRF and MM5) 

Table 3 provides the summary of all the results combined. The rows indicate the previous day’s 

forecast error category, with each row adding up to 100% of the forecasts for that given previous 

day’s category. The columns labeled subsequent day give the percent of the time the equivalent 

forecast 24 hours later fell into each of the three categories. Since one-third of the forecasts were 

in each category, a random result would lead to each subsequent day’s forecast category 

occurring approximately 33% of the time (rounding errors generate a slightly higher percentage 

in the subsequent day worse column than in the better column.) The cells where the forecast 

error persisted in the same category from one day to the next are shaded blue. The cells where 

the forecast error was in the opposite category are shaded peach. 

Table 3. Percent of forecasts in each error category 24 hours later, given 

the previous day’s error category. 

 SUBSEQUENT DAY 

 better average worse 

better 41 % 33 % 26 % 

average 33 % 35 % 32 % 

PREVIOUS 

DAY 

worse 24 % 32 % 44 % 
29

Table 4 is based on a subset of the data, considering only the days following occurrences when 

both the forecasts, 24 hours and 48 hours prior to the validation time, were in the same forecast 

error category. Since the validation days do not comprise the total dataset, these subsequent day 

results were not forced to be equally divided among the three categories, although it appears that 

the categories are evenly represented, with a few percent higher in the worse category than the 

average category. Again, the cells where the forecast error persisted in the same category from 

one day to the next are shaded blue. The cells where the forecast error was in the opposite 

category are shaded peach. 

Table 4. Percent of forecasts in each error category on the third day, 

given a consistent error category over the previous two days. 

 SUBSEQUENT DAY 

 better average worse 

better 43 % 34 % 23 % 

average 36 % 32 % 32 % 

PREVIOUS 

2 DAYS 

worse 21 % 31 % 48 % 

These results do support the theory that a forecast generating an exceptionally large or small 

absolute error amount will be more likely to be associated with a similar size error the following 

day. Although these repeating error categories are seen in more than 40% of the better and 

worse category forecasts, they occur less than half the time overall. Furthermore, they are 

followed by a forecast in the opposite category approximately one quarter of the time. An 

average forecast error is almost equally likely to be followed by an error in any of the categories 

the following day. 

As described in section 3.3.1, the results for a specific time and location could deviate 

substantially from these average results; however, many instances show similar percentages. In 

addition, the overall averages for each individual station, time of day, season, and model reflect 

comparable results. The only significant difference is seen in the overall averages based on the 

forecast weather parameters. The dew-point temperature forecast errors proved to be the most 

persistent, while the wind forecast errors contained little or no persistence from one day to the 

next. 

4.2 Recommendations 

Several organizations are addressing the requirement to provide weather forecast uncertainty 

information to users. Suggestions have been raised to base this guidance on the previous day’s 

accuracy of the numerical weather prediction model being used, or on a longer period of the 
30

historical statistical results of the model. In general, these ideas have been discarded in favor of 

relying on ensembles of models to produce a range of forecasts based on the specific conditions 

for the forecast of interest. Although running ensembles of multiple models or a single model 

with multiple initial conditions requires more time and/or computational power, this case study 

supports the conclusion that simply providing the error amount from the previous day or two 

does not provide sufficient uncertainty information for a user. Several analyses in this case study 

showed model bias trends lasting for a week or two, with exceptions even within the short 

timeframe. Calculating and correcting recent model biases should lead to lower forecast errors 

overall, but a statistical approach based on a single model run does not appear adequate to 

provide forecast uncertainty information beneficial to decision makers. 
31

References 

1. Sauter, B.; Henmi, T. Average Forecast Errors Using MM5 and WRF Over Complex 

Terrain: Utah, July/August 2003 and January/February 2004; ARL-MR-597; U.S. Army 

Research Laboratory: White Sands Missile Range, NM, October 2004. 

2. Grell, G.A.; Dudhia, J.; Stauffer, D.R. A Description of the Fifth-Generation Penn 

State/NCAR Mesoscale Model (MM5); NCAR/TN-398+STR; NCAR Tech. Note; 1995, 122. 

3. Michalakes, J.; Dudhia, J.; Gill, D.; Klemp, J.; Skamarock, W. Design of a Next-Generation 

Regional Weather Research and Forecast Model: Towards Teracomputing; World 

Scientific: River Edge, NJ, 1998, pp 117–124. 

4. Horel, J.; Splitt, M.; Dunn, L.; Pechmann, J.; White, B.; Ciliberti, C.; Lazarus, S.; Slemmer, 

J.; Zaff, D.; Burks, J. MesoWest: Cooperative Mesonets in the Western United States. 

Bulletin of the American Met. Soc. 2002, 83, 211–225. 

5. National Center for Environmental Prediction Global Forecast System: The GFS 

Atmospheric Model Home Page (status as of November 1, 2002). 

http://www.emc.ncep.noaa.gov/modelinfo/index.html (accessed November 2003). 

6. Army High Performing Computing Research Center Home Page. http://www.ahpcrc.org

(accessed December 2004). 

7. U.S. Army Research Laboratory Major Shared Resource Center Home Page. 

http://www.arl.hpc.mil/ (accessed December 2004). 
32

INTENTIONALLY LEFT BLANK. 
33

Appendix. Average Forecast Error Ranges 

This appendix is part of ARL-TR-3418, U.S. Army Research Laboratory, White Sands Missile 

Range, NM 88002-5501. 

The following charts depict the specific forecast error ranges categorized as average errors in this 

study. The range is specific for each forecast model (MM5 or WRF), each season (summer or 

winter), each station (DVE, PRP, SNZ, or WBB), and each forecast time (2 a.m. or 2 p.m. MST 

for WRF, or 3 a.m. or 3 p.m. MST for MM5, denoted as “am” and “pm” on the charts.) 

The chart data is as follows: 

• On each chart, the “high-low” line encompasses the average forecast absolute error values 

encountered in the middle third of all the forecasts for the given model, season, station, and 

time. 

• Forecast error values less than the lowest value of the “high-low” line comprise the third of 

the cases classified as better forecasts in this study. 

• Similarly, the third of the cases classified as worse forecasts in this study have absolute 

errors greater than the value at the high end of the line. 

• The simple average absolute error for all the forecasts in a category is shown by an asterisk. 

Most categories contain approximately 55 forecasts, with about 18 forecasts in each 

classification of better, average, and worse. Wind direction results are frequently based on a 

smaller number of forecasts, since wind direction errors were not included for any forecast with 

an observed wind speed less than 1 m/s. Any category without at least 10 forecasts in each 

classification was not used and will not have a line or asterisk plotted. 

Temperature, dew-point temperature, wind speed, and wind direction error plots are shown in 

figures A-1 through A-4, respectively. 
34

WRF Summer Temperature "Average" Absolute Errors

0

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am pm am pm am pm am pm

DVE PRP SNZ WBB

Temperature Errors (°C)

MM5 Winter Temperature "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Temperature Errors (°C)

WRF Winter Temperature "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Temperature Errors (°C)

MM5 Summer Temperature "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Temperature Errors (°C)

WRF Summer Temperature "Average" Absolute Errors

0

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MM5 Winter Temperature "Average" Absolute Errors

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WRF Winter Temperature "Average" Absolute Errors

0

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MM5 Summer Temperature "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Temperature Errors (°C)

Figure A-1. The range of absolute temperature errors used for the average error category is shown by the line for (a) MM5 

summer forecasts, (b) WRF summer forecasts, (c) MM5 winter forecasts, and (d) WRF winter forecasts. 

One-third of the forecasts in each category had errors greater than the highest value and one-third had errors 

less than the lowest value depicted by the line. The asterisk associated with each line is the average absolute 

error for the given station and time. 

(a) (b) 

(c) (d) 
35

MM5 Summer Dew-Point Temperature "Average" Absolute Errors

0

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Dew-Point Errors (°C)

WRF Winter Dew-Point Temperature "Average" Absolute Errors

0

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Dew-Point Errors (°C)

WRF Summer Dew-Point Temperature "Average" Absolute Errors

0

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Dew-Point Errors (°C)

MM5 Winter Dew-Point Temperature "Average" Absolute Errors

0

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Dew-Point Errors (°C)

MM5 Summer Dew-Point Temperature "Average" Absolute Errors

0

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WRF Winter Dew-Point Temperature "Average" Absolute Errors

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WRF Summer Dew-Point Temperature "Average" Absolute Errors

0

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Dew-Point Errors (°C)

MM5 Winter Dew-Point Temperature "Average" Absolute Errors

0

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14

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DVE PRP SNZ WBB

Dew-Point Errors (°C)

Figure A-2. The range of absolute dew-point temperature errors used for the average error category is shown by the 

line for (a) MM5 summer forecasts, (b) WRF summer forecasts, (c) MM5 winter forecasts, and (d) WRF 

winter forecasts. One-third of the forecasts in each category had errors greater than the highest value and 

one-third had errors less than the lowest value depicted by the line. The asterisk associated with each line 

is the average absolute error for the given station and time. 

(a) (b) 

(c) (d) 
36

MM5 Summer Wind Speed "Average" Absolute Errors

0

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6

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DVE PRP SNZ WBB

Wind Speed Errors (m/s)

WRF Summer Wind Speed "Average" Absolute Errors

0

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Wind Speed Errors (m/s)

MM5 Winter Wind Speed "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Wind Speed Errors (m/s)

WRF Winter Wind Speed "Average" Absolute Errors

0

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DVE PRP SNZ WBB

Wind Speed Errors (m/s)

MM5 Summer Wind Speed "Average" Absolute Errors

0

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Wind Speed Errors (m/s)

WRF Summer Wind Speed "Average" Absolute Errors

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Wind Speed Errors (m/s)

MM5 Winter Wind Speed "Average" Absolute Errors

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Wind Speed Errors (m/s)

WRF Winter Wind Speed "Average" Absolute Errors

0

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Wind Speed Errors (m/s)

Figure A-3. The range of absolute wind speed errors used for the average error category is shown by the line for (a) MM5 

summer forecasts, (b) WRF summer forecasts, (c) MM5 winter forecasts, and (d) WRF winter forecasts. 

One-third of the forecasts in each category had errors greater than the highest value and one-third had errors 

less than the lowest value depicted by the line. The asterisk associated with each line is the average absolute 

error for the given station and time. 

(a) (b) 

(c) (d) 
37

MM5 Summer Wind Direction "Average" Absolute Errors

0

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80

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120

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Wind Direction Errors (deg)

WRF Summer Wind Direction "Average" Absolute Errors

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120

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Wind Direction Errors (deg)

WRF Winter Wind Direction "Average" Absolute Errors

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120

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Wind Direction Errors (deg)

MM5 Winter Wind Direction "Average" Absolute Errors

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Wind Direction Errors (deg)

MM5 Summer Wind Direction "Average" Absolute Errors

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am pm am pm am pm am pm

DVE PRP SNZ WBB

Wind Direction Errors (deg)

WRF Summer Wind Direction "Average" Absolute Errors

0

20

40

60

80

100

120

am pm am pm am pm am pm

DVE PRP SNZ WBB

Wind Direction Errors (deg)

WRF Winter Wind Direction "Average" Absolute Errors

0

20

40

60

80

100

120

am pm am pm am pm am pm

DVE PRP SNZ WBB

Wind Direction Errors (deg)

MM5 Winter Wind Direction "Average" Absolute Errors

0

20

40

60

80

100

120

am pm am pm am pm am pm

DVE PRP SNZ WBB

Wind Direction Errors (deg) 

Figure A-4. The range of absolute wind direction errors used for the average error category is shown by the line for (a) MM5 

summer forecasts, (b) WRF summer forecasts, (c) MM5 winter forecasts, and (d) WRF winter forecasts. Onethird of the forecasts in each category had errors greater than the highest value and one-third had errors less than 

the lowest value depicted by the line. The asterisk associated with each line is the average absolute error for the 

given station and time.

(a) (b) 

(c) (d) 
38

INTENTIONALLY LEFT BLANK. 
39

Acronyms 

DVE Meteorological station identification letters for DV-Burns, UT 

GFS Global Forecast System 

GMT Greenwich Mean Time 

MM5 Pennsylvania State University/NCAR Mesoscale Model Version 5 

MST Mountain Standard Time 

NCAR National Center for Atmospheric Research 

PRP Meteorological station identification letters for Promontory Point, UT 

SNZ Meteorological station identification letters for Bountiful/F G House, UT 

WBB Meteorological station identification letters for WBB/U Utah, UT 

WRF Weather Research and Forecasting 
40

Distribution List 

 Copies 

HEADQUARTERS DEPT OF ARMY 1 

DAMI POB WEATHER TEAM 

1000 ARMY PENTAGON ROOM 2E383 

WASHINGTON DC 20310-1067 

 

US ARMY RESEARCH LAB 1 

AMSRD ARL D 

2800 POWDER MILL ROAD 

ADELPHI MD 20783 

 

US ARMY RESEARCH LAB 1 

AMSRD ARL CI E 

BATTLEFIELD ENVIR DIV 

ADELPHI MD 20783-1197 

 

US ARMY RESEARCH LAB 1 

AMSRD ARL CI EM 

BATTLEFIELD ENVIR DIV 

WSMR NM 88002-5501 

US ARMY RSRC OFC 1 

ATTN AMSRD ARL RO E DR BACH 

PO BOX 12211 

RTP NC 27009 

US ARMY DUGWAY PROVING GROUND 1 

STEDP MT 

DUGWAY UT 84022 

 

US ARMY FIELD ARTILLERY SCHOOL 1 

ATSF TSM TA 

FT SILL OK 73503-5600 

 

US ARMY TOPO ENGR CTR 1 

CETEC ZC 1 

FT BELVOIR VA 22060-5546 

 

WSMR TECH LIBRARY BR 1 

STEWS IM IT 

WSMR NM 88002 

 

 Copies 

HQ AFWA/DNX 1 

106 PEACEKEEPER DR STE 2N3 

OFFUTT AFB NE 68113-4039 

AFRL TECH LIB 1 

29 RANDOLPH RD 

HANSCOM AIR FORCE BASE, MA 01731-3010 

AFCCC/DOR TECH LIB 1 

151 PATTON AVE., ROM 120 

ASHEVILLE, NC 28801-5002 

 

NAVAL RESEARCH LAB 1 

MARINE METEOROLOGY DIVISION 

7 GRACE HOPPER AVENUE STOP 2 

MONTEREY, CA 93943-5502 

 

NCAR LIBRARY SERIALS 1 

NATL CTR FOR ATMOS RSCH 

PO BOX 3000 

BOULDER CO 80307-3000 

 

US ARMY RESEARCH LAB 3 hard copies 

AMSRD ARL CI EM 

B SAUTER 

WSMR NM 88002 

 

US ARMY RESEARCH LAB 1

ATTN IMNE AD IM DR 

MAIL & RECORDS MGMT 

ADELPHI MD 20783-1197

ADMNSTR 1 

DEFNS TECHL INFO CTR 

ATTN DTIC OCP ELECT CPY V MADDOX 

8725 JOHN J KINGMAN RD STE 0944 

FT BELVOIR VA 22060-6218 

 

US ARMY RESEARCH LAB 2 

AMSRD ARL CI OK TL 

2800 POWDER MILL ROAD 

ADELPHI MD 20783-1197 

 

TOTAL 21