Assimilating Tropospheric Airborne Meteorological Data 

Reporting (TAMDAR) Observations and the Relative Value 

of Other Observation Types 

by Brian P Reen and Robert E Dumais Jr 

ARL-TR-7022 August 2014 

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Army Research Laboratory 

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ARL-TR-7022 August 2014 

Assimilating Tropospheric Airborne Meteorological Data 

Reporting (TAMDAR) Observations and the Relative Value 

of Other Observation Types 

Brian P Reen and Robert E Dumais Jr 

Computational and Information Sciences Directorate, ARL 

Approved for public release; distribution unlimited. 
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Assimilating Tropospheric Airborne Meteorological Data Reporting

(TAMDAR) Observations and the Relative Value of Other Observation Types

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Brian P Reen and Robert E Dumais Jr

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US Army Research Laboratory 

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14. ABSTRACT 

The Weather Research and Forecasting model is applied here to domains centered over southern California in early 2012 to investigate how 

to best assimilate single-level, above-surface observations (e.g., aircraft-based observations) as well as the relative value of various 

observation types. 

Various configurations of observation nudging are applied to a single case day to assimilate aircraft-based observations on a 3-km horizontal 

grid-spacing domain nested in a 9-km domain in order to determine the best nudging configuration. These results are then used to configure 

model experiments on 5 case days that investigate the value of the aircraft data, a local rawinsonde, and more dense surface observations. 

These experiments indicate substantial day-to-day variability in the forecast improvements due to inclusion of observations. Overall, the 

inclusion of aircraft data improves temperature and water-vapor predictions, but degrades short-term (1–6 hours [h]) wind forecasts. The use 

of local rawinsonde data improves short-term temperature and wind forecasts, but degrades water-vapor forecasts. Ingesting denser surface 

observations improves surface forecasts of temperature, moisture, and wind, but above the surface the results may be degraded. Further 

experimentation is necessary to refine the results found in this study. 

15. SUBJECT TERMS 

WRF, data assimilation, observation nudging, TAMDAR 

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Brian P Reen 

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iii

 Contents 

List of Figures v

List of Tables ix

Acknowledgments x

1. Introduction 1

2. Model Description and Configuration 3

3. Case Description 5

4. Methodology 12

4.1 Observation Preparation ................................................................................................12

4.2 Observation Nudging ....................................................................................................13

5. Exploring Observation-Nudging Parameters for TAMDAR Assimilation 14

5.1 Experimental Design .....................................................................................................14

5.2 Results ...........................................................................................................................17

5.2.1 Noise ..................................................................................................................17

5.2.2 Verification ........................................................................................................18

5.2.3 Data-Assimilation Benefit vs. Degradation .......................................................27

5.3 Summary and Conclusions ............................................................................................30

6. Exploring the Value of Various Observational Data Sources 31

6.1 Experimental Design .....................................................................................................31

6.2 Results ...........................................................................................................................33

6.2.1 Value of TAMDAR Observations .....................................................................33

6.2.1.1 Three-kilometer Domain .................................................................................34

6.2.1.2 One-kilometer Domain ....................................................................................40

6.2.2 Value of Local Rawinsonde ..............................................................................46

6.2.3 Value of Denser Surface Observations .............................................................60

6.3 Summary and Conclusions ............................................................................................66

6.3.1 TAMDAR ..........................................................................................................66
iv

6.3.2 Local Rawinsonde .............................................................................................67

6.3.3 Denser Surface Observations ............................................................................68

7. References 69

List of Symbols, Abbreviations, and Acronyms 72

List of Variables 74

Distribution List 75
v

List of Figures 

Fig. 1 Map of the 9-, 3-, and 1-km horizontal grid-spacing WRF domains ..................................3

Fig. 2 Plots of the number of TAMDAR observations within the 3-km WRF domain for 

each of the 5 case days. Time series of the number of all observations between 0 and 

12,000-m AGL are shown for a) temperature observations, c) dewpoint observations, and 

e) wind observations. Profiles of all observations from 12 UTC on the case day until the 

end of the WRF simulation at 12 UTC on the next day are shown for b) temperature 

observations, d) dewpoint observations, and f) wind observations. ..........................................7

Fig. 3 Location of TAMDAR observations between 1131 and 1800 UTC inclusive for a) 7 

February, b) 9 February, c) 16 February, d) 1 March, and e) 5 March. The extent of the 

plot matches the extent of the 9-km domain, and the 3-km domain is the white square 

labeled “d02” while the 1-km domain is the red square labeled “d03”. ....................................9

Fig. 4 Locations where a rawinsonde is available for at least one of the case days during the 

data-assimilation period (specifically 1131–1800 UTC). Note that KEDW has a 

rawinsonde during these cases only for 9 February and 16 February, and that KNSI only 

has a rawinsonde for these case days for 1 March. ..................................................................10

Fig. 5 Map of all surface mesonet and non-mesonet observations available within the 

MADIS database for the 3 WRF domains. The area covered by the figure is coincident 

with the area of the 9-km domain. The 3-km domain is the white square labeled “d02” 

and the 1-km domain is the red square labeled “d03”. ............................................................11

Fig. 6 Map of all surface mesonet and non-mesonet observations available within the 

MADIS database for the 1-km WRF domain ..........................................................................12

Fig. 7 Time series showing the percentage of the error at time 0 that is still extant at a given 

time. This assumes that the only factor affecting the field is the nudging term. .....................15

Fig. 8 Time series of 3-km domain’s average tendency of perturbation dry air mass (dmu/dt) 

relative to the experiment with no data assimilation for all experiments with an obs_rinxy

of 60 km for 1 March 2012. A 100-point centered average was applied to smooth out the 

high-frequency variability. .......................................................................................................18

Fig. 9 Temperature MAE (K) for the experiments in Table 1: for 19–00 UTC (1–6-h 

forecast; a, c, e) and for 01–12 UTC (7–18-h forecast; b, d, f); at 2-m AGL (e, f), at 0–

1,000-m AGL (c, d), and at 0–12,000-m AGL (a, b). The x-axis indicates the nudging 

strength (Gq) of the experiment and the symbols indicate the obs_rinxy setting used to 

determine horizontal radius of influence. ................................................................................20

Fig. 10 Dewpoint temperature MAE (K) for the experiments in Table 1: for 19–00 UTC (1–

6 h-forecast; a, c, e) and 01–12 UTC (7–18-h forecast; b, d, f); at 2-m AGL (e, f), at 0–

1,000-m AGL (c, d), and at 0–12,000- m AGL (a, b). The x-axis indicates the nudging 

strength (Gq) of the experiment and the symbols indicate the obs_rinxy setting used to 

determine horizontal radius of influence. ................................................................................22

 
vi

Fig. 11 Wind-speed MAE (m/s) for the experiments in Table 1: for 19–00 UTC (1–6-h 

forecast; a, c, e) and for 01–12 UTC (7–18-h forecast; b, d, f); at 10-m AGL (e, f), at 0–

1,000-m AGL (c, d), and at 0–12,000-m AGL (a, b). The x-axis indicates the nudging 

strength (Gq) of the experiment and the symbols indicate the obs_rinxy setting used to 

determine horizontal radius of influence. ................................................................................24

Fig. 12 Wind-direction MAE (degrees) for the experiments in Table 1: for 19–00 UTC (1–6 

h-forecast; a, c, e) and for 01–12 UTC (7–18-h forecast; b, d, f); at 10-m AGL (e, f), at 0–

1,000-m AGL (c, d), and at 0–12,000-m AGL (a, b). The x-axis indicates the nudging 

strength (Gq) of the experiment and the symbols indicate the obs_rinxy setting used to 

determine horizontal radius of influence. ................................................................................25

Fig. 13 The percentage of observations against which the model verifies non-negligibly 

better as compared to the no-nudging experiments (a, c), and of the subset of observation 

against which the model verifies non-negligibly differently the percentage for which the 

change is an improvement (PCI; b, d). These are plotted for all experiments for the 0–

1,000-m AGL level for 19–00 UTC for both temperature (a, b) and dewpoint (c, d). ............28

Fig. 14 The percentage of observations against which the model verifies non-negligibly 

better as compared to the no-nudging experiments (a, c), and of the subset of observations 

against which the model verifies non-negligibly differently than the no-nudging 

experiments, the percentage for which the change is an improvement (PCI; b, d). These 

are plotted for all experiments for the 0–1,000-m AGL level for 19–00 UTC for both 

wind speed (a, b) and wind direction (c, d). .............................................................................30

Fig. 15 WRF 3-km domain MAEs for Exp. C, T, S, and TS from Table 3 verified against 

non-surface observations in the 0–1,000-m AGL layer for 19–00 UTC for a) temperature, 

b) dewpoint, c) wind speed, and d) wind direction. The x-axis indicates the experiment’s 

name and the symbols indicate the case day of the experiment. .............................................35

Fig. 16 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 2 m, 0–1,000-m AGL, 

and 0–12,000-m AGL on the 3-km domain for a) temperature and b) dewpoint. Positive 

values indicate Exp. T performs better than Exp. C and that Exp. TS performs better than 

Exp. S, respectively. A point is plotted for each case day as well as the mean of all of the 

case days, as noted in the figure legend. ..................................................................................37

Fig. 17 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 10 m, 0–1,000-m AGL, 

and 0–12,000-m AGL on the 3-km domain for a) wind speed and b) wind direction. 

Positive values indicate Exp. T performs better than Exp. C and that Exp. TS performs 

better than Exp. S, respectively. A point is plotted for each case day as well as the mean 

of all of the case days, as noted in the figure legend. ..............................................................38

Fig. 18 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 01–12 UTC for, 0–1,000-m AGL on the 

3-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind direction. 

Positive values indicate Exp. T performs better than Exp. C and that Exp. TS performs 

better than Exp. S, respectively. A point is plotted for each case day as well as the mean 

of all of the case days, as noted in the figure legend. ..............................................................40

 
vii

Fig. 19 WRF 1-km domain MAE for experiments C, T, S, and TS from Table 3 verified 

against non-surface observations in the 0–1,000-m AGL layer for 19–00 UTC for a) 

temperature, b) dewpoint, c) wind speed, and d) wind direction. The x-axis indicates the 

experiment’s name and the symbols indicate the case day of the experiment. ........................42

Fig. 20 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 2 m, 0–1,000-m AGL, 

and 0–12,000-m AGL on the 1-km domain for a) temperature and b) dewpoint. Positive 

values indicate Exp. T performs better than Exp. C and that Exp. TS performs better than 

Exp. S, respectively. A point is plotted for each case day as well as the mean of all of the 

case days, as noted in the figure legend. ..................................................................................43

Fig. 21 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 10 m, 0–1,000-m AGL, 

and 0–12,000-m AGL on the 1-km domain for a) wind speed and b) wind direction. 

Positive values indicate Exp. T performs better than Exp. C and that Exp. TS performs 

better than Exp. S, respectively. A point is plotted for each case day as well as the mean 

of all of the case days, as noted in the figure legend. ..............................................................44

Fig. 22 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 01–12 UTC for 0–1,000-m AGL on the 

1-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind direction. 

Positive values indicate Exp. T performs better than Exp. C and that Exp. TS performs 

better than Exp. S, respectively. A point is plotted for each case day as well as the mean 

of all of the case days, as noted in the figure legend. ..............................................................45

Fig. 23 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) and 

between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 19–00 UTC for 2 m, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature and b) 

dewpoint. Positive values indicate Exp. S performs better than Exp. SK and that Exp. TS 

performs better than Exp. TSK, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. ..........................................47

Fig. 24 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) and 

between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 19–00 UTC for 10 m, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) wind speed and b) wind 

direction. Positive values indicate Exp. S performs better than Exp. SK and that Exp. TS 

performs better than Exp. TSK, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. ..........................................48

Fig. 25 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) and 

between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 01–12 UTC for 2 m, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature and b) 

dewpoint. Positive values indicate Exp. S performs better than Exp. SK and that Exp. TS 

performs better than Exp. TSK, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. ..........................................50

Fig. 26 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) and 

between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 01–12 UTC for 10 m, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) wind speed and b) wind 

direction. Positive values indicate Exp. S performs better than Exp. SK and that Exp. TS 

performs better than Exp. TSK, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. ..........................................51
viii

Fig. 27 Vertical profiles of temperature MAE (excluding surface observations) for 19–00 

UTC for Exp. SK and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 

March, and e) 5 March. Panel f is a vertical profile of the number of observations used to 

construct the MAE in panels a–e. ............................................................................................53

Fig. 28 Vertical profiles of dewpoint MAE (excluding surface observations) for 19–00 UTC 

for Exp. SK and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 March, and 

e) 5 March. Panel f is a vertical profile of the number of observations used to construct 

the MAE in panels a–e. ............................................................................................................54

Fig. 29 Vertical profiles of wind-speed MAE (excluding surface observations) for 19–00 

UTC for Exp. SK and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 

March, and e) 5 March. Panel f is a vertical profile of the number of observations used to 

construct the MAE in panels a–e. ............................................................................................55

Fig. 30 Vertical profiles of wind-direction MAE (excluding surface observations) for 19–00 

UTC for Exp. SK and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 

March, and e) 5 March. Panel f is a vertical profile of the number of observations used to 

construct the MAE in panels a–e. ............................................................................................56

Fig. 31 Differences in MAE between Exp. S and Exp. TSK for 19–00 UTC for surface, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature, b) 

dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. TSK 

performs better than Exp. S. A point is plotted for each case day as well as the mean of 

all of the case days, as noted in the figure legend. ...................................................................58

Fig. 32 Differences in MAE between Exp. S and Exp. TSK for 01–12 UTC for surface, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature, b) 

dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. TSK 

performs better than Exp. S. A point is plotted for each case day as well as the mean of 

all of the case days, as noted in the figure legend. ...................................................................59

Fig. 33 Differences in MAE between Exp. S and Exp. SM for 19–00 UTC for surface, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature, b) 

dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. SM 

performs better than Exp. S. A point is plotted for each case day as well as the mean of 

all of the case days, as noted in the figure legend. ...................................................................61

Fig. 34 Differences in MAE between Exp. S and Exp. SM for 01–12 UTC for surface, 0–

1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) temperature, b) 

dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. SM 

performs better than Exp. S. A point is plotted for each case day as well as the mean of 

all of the case days, as noted in the figure legend. ...................................................................62

Fig. 35 Time series of the differences in MAE between Exp. S and Exp. SM on the 1-km 

domain for a) 2-m temperature, b) 2-m dewpoint, c) 10-m wind speed, and d) 10-m wind 

direction. Positive values indicate Exp. SM performs better than Exp. S. A time series is 

plotted for each case day, as noted in the legend. The vertical line at 18 UTC indicates the 

end of the preforecast period and the beginning of the forecast period during which no 

current observations are assimilated. .......................................................................................64

 
ix

Fig. 36 Time series of the differences in MAE between Exp. S and Exp. SM averaged over 

the 5 case days on the 1-km domain for a) 2-m temperature, b) 2-m dewpoint, c) 10-m 

wind speed, and d) 10-m wind direction. Positive values indicate Exp. SM performs 

better than Exp. S. The vertical line at 18 UTC indicates the end of the preforecast period 

and the beginning of the forecast period during which no current observations are 

assimilated................................................................................................................................65

List of Tables 

Table 1 List of WRF-ARW experiments exploring the assimilation of TAMDAR 

observations on 1 March 2012 using varying nudging strengths and horizontal radii of 

influence ...................................................................................................................................16

Table 2 Ranking of MAE values for the 4 experiments with the lowest MAE, with “1” 

being the best of the 4 experiments and “4” being the worst ...................................................26

Table 3 Experimental design for Section 6 indicating which observations are assimilated in 

each experiment (“Y” is yes) ...................................................................................................32
x

Acknowledgments 

AirDat LLC provided Tropospheric Airborne Meteorological Data Reporting observational data 

that expanded the above-surface data available for data assimilation and verification. This study 

was made possible in part due to the data made available to the National Oceanic and 

Atmospheric Administration by various providers for inclusion in the Meteorological 

Assimilation Data Ingest System (MADIS). The parallel Real-Time Mesoscale Analysis “use” 

and “reject” lists were provided by Steve Levine at the National Weather Service’s National 

Centers for Environmental Prediction – Environmental Modeling Center and greatly facilitated 

making full use of the MADIS observational data set. The madis2littler tool was provided by 

Ruifang Li (then) at the National Center for Atmospheric Research. Martin Kufus is 

acknowledged for his efforts as technical editor that improved the clarity of this manuscript and 

ensured it adhered to the proper format. 
1

1. Introduction 

Aircraft-based observations are a potentially promising data source for improving numerical 

weather prediction. Standard in situ observations above the surface are mostly limited to twicedaily rawinsondes at a limited number of locations (with an average spacing between 

rawinsondes of about 315 km over the United States) (Office of the Federal Coordinator for 

Meteorological Services and Supporting Research 1997). Compared to rawinsonde observations, 

there are many more surface observations available, especially over locations such as the 

continental United States. However, an individual surface observation is potentially less valuable 

for data assimilation than an individual above-surface observation; this is because of the less 

heterogeneous atmospheric conditions found above the surface and thus the greater errorcorrelation length scales above the surface as compared to at the surface. Aircraft-based 

observations have the potential to provide an additional source of above-surface observations and 

are neither limited to a specified number of locations nor to a twice-daily observation. 

There are many aircraft-based weather observations available, and they are referred to in general 

as aircraft meteorological data relay (AMDAR) reports. The data from the United States that are 

part of AMDAR are referred to as both Meteorological Data Collection and Reporting System 

(MDCRS) and by a system that is used to transmit some MDCRS observations, the Aircraft 

Communications Addressing and Reporting System (ACARS). A new network of aircraft-based 

observation called Tropospheric Airborne Meteorological Data Reporting (TAMDAR) (Daniels 

et al. 2004) has been introduced in recent years by AirDat, LLC. TAMDAR has several potential 

advantages compared to AMDAR. AMDAR observations are usually from larger aircraft; since 

larger aircraft tend to use larger airports, AMDAR observations are likely to be present below 

20,000 feet above ground level (AGL) only around major airports (Moninger et al. 2010). 

TAMDAR observations are generally on smaller commercial aircraft, which have the ability to 

use smaller airports than larger aircraft, and thus TAMDAR observations should have the 

potential to provide broader coverage below 20,000 feet than other aircraft observations. 

Additionally, TAMDAR observations measure water vapor while many AMDAR observations 

do not. Gao et al. (2012) estimated that TAMDAR errors are comparable to rawinsondes’ for 

temperature, slightly worse for winds <15 m/s, but slightly better for winds >15 m/s, and perhaps 

slightly better for moisture. 

TAMDAR observations are of interest for Army applications because they may provide a source 

of weather observations in environments where the available observations are very limited. An 

effort involving the US Army Research Laboratory, New Mexico State University’s Physical 

Science Laboratory’s Technical Analysis and Applications Center, and AirDat LLC developed a 

modified TAMDAR sensor referred to as TAMDAR-Unmanned Aerial System (TAMDAR-U) 

for use on an unmanned aerial system (UAS) (Passner et al. 2012). This sensor was tested on a 
2

UAS; the data produced were assimilated by the Advanced Research version of the Weather 

Research and Forecasting model (WRF-ARW) (Skamarock et al. 2008) using its observationnudging capability and nested domains with 3-km and 1-km horizontal grid spacing. Three case 

studies were used to show the sensitivity of the model forecast to the assimilation of these 

TAMDAR-U data. Their results suggest that model moisture forecasts were most affected by 

assimilation of the TAMDAR-U observations. The downstream propagation of changes due to 

the assimilation of TAMDAR-U data was shown. However, due to the limited availability of 

observations in the study region, no statistical verification was undertaken in that study to 

demonstrate improvement in the forecast due to the assimilation of the TAMDAR-U data. Since 

Passner et al. (2012) used a UAS the flight tracks are likely more representative of what could 

potentially be available on the battlefield via UAS than a study using all of the standard 

TAMDAR data available. 

Moninger et al. (2010) assimilate TAMDAR data in the 20-km horizontal grid spacing Rapid 

Update Cycle (RUC) model using three-dimensional variational (3DVAR) data-assimilation 

methods for approximately 4 years, and find that use of TAMDAR data results in improvements 

in temperature, moisture, and wind forecasts. Szoke et al. (2007) find that for specific 

precipitation events assimilating TAMDAR in RUC can be beneficial, apparently due to 

improvements in the model moisture fields. TAMDAR data have also been assimilated in WRFARW using both nudging (e.g., Zhang et al. 2011) and 3DVAR (e.g., Gao et al. 2012). Zhang et 

al. (2011) used nested 12- and 4-km horizontal grid-spacing WRF simulations with observation 

nudging to evaluate the impact of TAMDAR data for a 5-day case and found that moisture is 

generally improved, but the impact on temperature and wind is more mixed, especially on the 

4-km domain. 

Jonassen et al. (2012) assimilated observations from an unmanned aerial system over Iceland 

using observation nudging with 9-, 3-, and 1-km WRF-ARW nests for 2 case days. They 

investigated varying the size of the area over which a given observation was assimilated as well 

as the strength with which each observation affected the simulation. Their verification was 

purely against surface observations. 

In this study, we investigate the value of assimilating TAMDAR observations using WRF-ARW 

configured with nested 9-, 3-, 1-km horizontal grid-spacing domains using observation nudging. 

This differs from previous TAMDAR studies in that we include investigation into the size of the 

area over which each observation should be assimilated and the strength with which they should 

be assimilated. There are similarities between the current effort and that of Jonassen et al. (2012), 

but here we use all available TAMDAR observations instead of a single UAS, and we include 

above-surface observations to enhance our verification. 
3

2. Model Description and Configuration 

The WRF-ARW Version 3.4.1 (Skamarock et al. 2008) was configured with 9-, 3-, and 1-km 

horizontal resolution domains centered over southern California, as shown in Fig. 1, and with 56 

vertical layers (which implies there are 56 half levels and 57 full levels). For some experiments 

the 1-km domain was omitted. Depending on the experiment, the model was integrated from 12 

Coordinated Universal Time (UTC) to 12 UTC for one or all of the 5 case days described in 

Section 3. 

Fig. 1 Map of the 9-, 3-, and 1-km horizontal grid-spacing WRF domains 
4

The Global Forecast System (GFS) model’s 0.5° horizontal resolution output is used to create 

initial conditions and boundary conditions. Note that only GFS forecasts are utilized here (in 

contrast to analyses) so that we do not benefit from an observation type being included in the 

GFS analysis that a given model experiment is testing the exclusion of. For example, if we are 

testing the benefit of a specific rawinsonde and complete experiments both with and without that 

rawinsonde, but for both of these experiments use a GFS analysis for the initial conditions that 

includes this rawinsonde, we are not actually testing the effects of that local rawinsonde’s 

absence. A sea-surface temperature product with higher resolution than the GFS output is 

produced by the National Centers for Environmental Prediction’s Marine Modeling and Analysis 

Branch. Called the Real Time Global Sea Surface Temperature (Gemmill et al. 2007), it has 

1/12th degree horizontal grid spacing and was used to specify sea-surface temperatures for these 

simulations. Where available, GFS snow fields were replaced with 1-km snow fields from the 

SNOw Data Assimilation System (SNODAS) developed by the National Weather Service’s 

National Operational Hydrologic Remote Sensing Center (NOHRSC 2004). 

Obsgrid is part of the WRF software suite and can be used to create objective analyses and to 

quality-control the observations. Initial conditions for some experiments in this study are 

enhanced with observations using Obsgrid. Modifications to the methodology used to create 

these objective analyses are described in Reen et al. (2014b). As described in Section 4.1, we 

also use Obsgrid to perform quality control of the observations used for inclusion in the initial 

conditions and for data assimilation. 

The Mellor-Yamada-Janjić (MYJ) scheme (Janjić 2002) is used to parameterize the atmospheric 

boundary layer. This parameterization predicts turbulent kinetic energy (TKE) and is a MellorYamada Level 2.5 turbulence closure model. As in Lee et al. (2012) and Reen et al. (2014a), the 

background TKE is decreased to better simulate conditions with low TKE and the atmospheric 

boundary layer (ABL) depth diagnosis is altered. In preliminary experiments for this study, the 

standard MYJ scheme resulted in noisy TKE fields and thus noisy ABL depth fields over the 

water, and contributed to the formation of dry spots at the surface over land due to nudging. 

These were resolved using the altered version of MYJ. 

The WRF single-moment, 5-class microphysics parameterization (Hong et al. 2004; Hong and 

Lim 2006) and the Kain-Fritsch cumulus parameterization (Kain 2004) are utilized. For 

radiation, the Rapid Radiative Transfer Model (RRTM) (Mlawer et al. 1997) is used for 

longwave and the Dudhia scheme (Dudhia 1989) for shortwave. The Noah land surface model 

(Chen and Dudhia 2001) is used to represent land surface processes. 

The observation-nudging capability of WRF (Deng et al. 2009) is used to incorporate 

observations into the model via a 6-hour preforecast (12 to 18 UTC). During this preforecast, the 

model is gradually nudged toward observations of temperature, moisture, and wind. 
5

3. Case Description 

Five 24-hour periods in early 2012 over the southwestern United States were modeled with each 

starting at 12 UTC: 7 February, 9 February, 16 February, 1 March, and 5 March. The case days 

were chosen to include days with active weather and those with more benign weather. On 7 

February a trough moved onshore and led to widespread precipitation in the region. More 

quiescent weather was in place for the 9 February case with a 500-hPa ridge centered over 

central California at 12 UTC. On 16 February, an upper-level low was near the 

California/Arizona border with Mexico at 12 UTC bringing precipitation to that portion of the 

domain. The area of low pressure and the associated precipitation moved to the south and then 

east as the case day progressed. For 1 March, a weak shortwave trough at the beginning of the 

period resulted in precipitation in northern California that spread to Nevada and then moved 

southward and decreased in coverage. There was widespread high-level cloudiness for the 5 

March case due to weak, upper-level low pressure but very limited precipitation. 

Observations from the Meteorological Assimilation Data Ingest System (MADIS) database (at 

madis.noaa.gov) as well as TAMDAR (e.g., Gao et al. 2012) observations are available for these 

cases. The MADIS data include standard surface observations as well as mesonet data, maritime 

observations, profiler data, aircraft data, and rawinsondes. Note that although TAMDAR 

observations were in the past available via MADIS, as of the time of the case days studied here, 

TAMDAR observations were not available via MADIS. The TAMDAR observations were 

obtained directly from AirDat LLC. The MADIS database does include other aircraft-based 

observations, namely, ACARS observations. 

The temporal and vertical distribution of TAMDAR observations available in the 3-km WRF 

domain for the 5 case days is plotted in Fig. 2. The 3-km WRF domain is plotted here because 

there are very few TAMDAR observations within the 1-km domain, and the 3-km domain is the 

focus of the TAMDAR data-assimilation experiments. 

There is a clear temporal signal (Fig. 2a, 2c, 2e) with few TAMDAR observations between 09 

and 15 UTC (0200–0800 Pacific Daylight Savings Time). In general, it is expected that there 

will be fewer TAMDAR observations overnight because there will generally be fewer 

commercial aircraft airborne. There is also substantial day-to-day variability in the diurnal 

variation of the number of TAMDAR observations among the case days. For example, the 

number of TAMDAR temperature observations available at 16 UTC is ≈20 for 9 February and 5 

March but ≈85 for 16 February. 

Over the entire WRF-ARW simulation period (1200 to 1200 UTC) more TAMDAR observations 

are in the lowest 1,000 m AGL than in any other layer (Fig. 2b, 2d, 2f), with notably fewer in the 

1,000–2,000-m AGL layer compared to the 0–1,000-m AGL layer. The number of TAMDAR 
6

observations per 1,000-m band gradually decreases with height in the layers above 2,000 m 

AGL. The substantial variability in the number of TAMDAR observations among cases seen 

temporally (Fig. 2a, 2c, 2e) is also seen vertically. For example, in the lowest 1,000 m AGL, 1 

March has ≈300 temperature TAMDAR observations (Fig. 2d) whereas 5 March only has ≈115 

TAMDAR temperature observations. 

 
7

Fig. 2 Plots of the number of TAMDAR observations within the 3-km WRF domain for each of the 5 

case days. Time series of the number of all observations between 0 and 12,000-m AGL are 

shown for a) temperature observations, c) dewpoint observations, and e) wind observations. 

Profiles of all observations from 12 UTC on the case day until the end of the WRF simulation at 

12 UTC on the next day are shown for b) temperature observations, d) dewpoint observations, 

and f) wind observations. 

 

5 March

1 March

16 February

9 February

7 February

Number of TAMDAR Dewpoint Obs

Time (UTC)

5 March

1 March

16 February

9 February

7 February

Number of TAMDAR Temperature Obs

Time (UTC)

5 March

1 March

16 February

9 February

7 February

Number of TAMDAR Wind Obs

Time (UTC) Number of TAMDAR Wind Obs

11000-12000

10000-11000

9000-10000

8000-9000

7000-8000

6000-7000

5000-6000

4000-5000

3000-4000

2000-3000

1000-2000

0-1000

Height AGL (m)

5 March

1 March

16 February

9 February

7 February

11000-12000

10000-11000

9000-10000

8000-9000

7000-8000

6000-7000

5000-6000

4000-5000

3000-4000

2000-3000

1000-2000

0-1000

Height AGL (m)

Number of TAMDAR Dewpoint Obs

5 March

1 March

16 February

9 February

7 February

5 March

1 March

16 February

9 February

7 February

Number of TAMDAR Temperature Obs

11000-12000

10000-11000

9000-10000

8000-9000

7000-8000

6000-7000

5000-6000

4000-5000

3000-4000

2000-3000

1000-2000

0-1000

Height AGL (m)

a) b)

c) d)

e) f)
8

The horizontal distribution of TAMDAR observations for the time period during which they are 

assimilated for some experiments is shown in Fig. 3. The plots show all TAMDAR observations 

between 1131 and1800 UTC inclusive. Although TAMDAR observations prior to 1130 UTC 

may be used in the data assimilation if they are within the temporal window, here we include 

only those observations after 1130 UTC since the model begins integrating at 1200 UTC. For all 

of the case days, there is a greater concentration of TAMDAR in the vicinity of San Francisco’s 

airport (located in the northwest portion of the 9-km domain) and in the vicinity of the Los 

Angeles airport (located in the northwest portion of the 3-km domain). There are also TAMDAR 

observations in Mexico on the 9-km domain on each case day that appear to be related to the 

airport in Hermosillo, Sonora, Mexico. On 7 February and 1 March, it appears that one of these 

flights uses the airport in Mexicali, Baja California, Mexico (just south of the California border). 

Note that there are no TAMDAR observations on the 1-km domain during this time period. 
9

Fig. 3 Location of TAMDAR observations between 1131 and 1800 UTC inclusive for a) 7 February, b) 9 

February, c) 16 February, d) 1 March, and e) 5 March. The extent of the plot matches the extent of 

the 9-km domain, and the 3-km domain is the white square labeled “d02” while the 1-km domain is 

the red square labeled “d03”. 

a) b)

c) d)

e)
10

Rawinsondes are available at various locations within the model domains, as indicated in Fig. 4. 

Note that rawinsondes are not available during the data-assimilation time period for KEDW 

(Edwards Air Force Base, CA) and KNSI (San Nicolas Island, CA) on all days. The KNKX 

rawinsonde (Marine Corps Air Station Miramar in San Diego, CA) is the only rawinsonde 

available within the 1-km domain. 

Fig. 4 Locations where a rawinsonde is available for at least one of the case days during the data-assimilation 

period (specifically 1131–1800 UTC). Note that KEDW has a rawinsonde during these cases only for 9 

February and 16 February, and that KNSI only has a rawinsonde for these case days for 1 March. 

The locations with at least one surface observation available on at least one of the case days 

during the approximate data assimilation period (1131–1800 UTC) are plotted in Fig. 5 for all 3 
11

domains. The fact that mesonet stations are much more prevalent than non-mesonet stations is 

clearly evident, as is the clustering of observations in certain areas. Figure 6 also shows the 

locations of surface observations but shows only the 1-km domain. In general, there is fairly 

good coverage of mesonet stations over land except in Mexico, where very few observations are 

available. The apparent presence of mesonet stations just offshore is likely due to the reported 

locations of some mesonet stations being slightly inaccurate or imprecise. 

Fig. 5 Map of all surface mesonet and non-mesonet observations available within the MADIS 

database for the 3 WRF domains. The area covered by the figure is coincident with the area 

of the 9-km domain. The 3-km domain is the white square labeled “d02” and the 1-km 

domain is the red square labeled “d03”. 
12

Fig. 6 Map of all surface mesonet and non-mesonet observations available within 

the MADIS database for the 1-km WRF domain 

4. Methodology 

4.1 Observation Preparation 

The first step of quality control on the observations was applying use/reject lists from a nonoperational version of the Real-Time Mesoscale Analysis (RTMA) (De Pondeca et al. 2011; 

Levine et al. 2011; Levine et al. 2012; Pondeca et al. 2012) to filter the mesonet data. Universal 

reject lists as well as separate day/night reject lists are used for temperature and moisture. For 

wind, mesonet observations are rejected unless they are on the universal accept list or the 

observed wind direction is within a wind-direction bin that is listed as acceptable for that station. 

The use of these use/reject lists is designed to maximize the positive impact of mesonet 

observations while minimizing the potential negative impact of mesonet observations that may 

not accurately reflect the actual meteorological conditions for the desired vertical location and 

spatial area due to issues such as siting (e.g., wind observations at heights other than 10 m AGL 

or obstructions near the observation location). 
13

The majority of the quality control took place in the WRF component Obsgrid. The qualitycontrol component of Obsgrid includes checking observations for gross errors, comparing 

observations to nearby observations (“buddy check”), and comparing observations to a 

background field (here, GFS). For moisture observations, in addition to checking relative 

humidity, buddy checks and checks against the background field for dewpoint were applied as 

noted in Reen et al. (2014b) to allow overly dry observations to be removed more efficiently. For 

multi-level, above-surface observations (e.g., rawinsondes), Obsgrid interpolates the vertical 

profile to pressure levels where GFS data exist in order to enable the background check to occur. 

The Ungrib component of the standard version of the WRF preprocessing system (WPS) merely 

converts coarse grid model data (e.g., GFS) from Gridded Binary (GRIB) format to a WPS 

format. Here, we use a modified version of Ungrib provided by the National Center for 

Atmospheric Research (NCAR) that additionally interpolates the coarse grid model data to userspecified levels. This minimizes the interpolation of multi-level, above-surface observations 

needed to enable the background check to occur, and allows for a more detailed vertical structure 

to be maintained in high vertical-resolution observations. 

The standard version of Obsgrid will only effectively process single-level, above-surface 

observations if they are specific types of data. This is because of difficulties doing the 

background check of the observations: The single-level, above-surface observations are unable to 

be interpolated to a coarse-grid model pressure level (since they consist of a single level of data) 

and they are unlikely to fall exactly on a coarse-grid model pressure level. For observations 

labeled “FM-97 AIREP” and “FM-88 SATOB”, Obsgrid will attempt to create a new 

observation at the nearest coarse-grid model pressure level. It does this by adjusting temperature 

using a standard lapse rate, keeping the observed values of wind and discarding moisture. In 

order for the TAMDAR data and the MADIS aircraft data to be quality-controlled without doing 

these adjustments and discarding moisture, Obsgrid was modified to allow single-level, abovesurface observations to be quality-controlled against nearby coarse-grid model pressure levels, 

rather than requiring the observation to be exactly on the pressure level. Combining this with the 

version of Ungrib used here to interpolate the coarse-grid model data to additional vertical levels 

allows the aircraft data to have background-check quality control performed without any 

adjustments to the observation itself. 

4.2 Observation Nudging 

Observation nudging adds a non-physical term to the tendency equations, and is implemented in 

WRF as: 

  

      

  









 



 N

i

q

N

i

q o m i i i

q q

W i x y z t

W i x y z t q i q x y z t

x y z t F x y z t G

t

q

1

1

2

, , , ,

, , , , , , ,

, , , , , ,   (1) 
14

where q is the quantity being nudged (e.g., water-vapor mixing ratio); μ is the dry hydrostatic 

pressure; Fq represents the physical-tendency terms of q; Gq is the nudging strength for q; N is 

the total number of observations; i is the index to the current observation; Wq is the 

spatiotemporal weighting function; qo is the observed value of q; and qm(xi,yi,zi,t) is the model 

value of q interpolated to the observation location. The quantity qo–qm is the innovation. 

In WRF observation nudging, the effects of surface observations are spread horizontally along 

the model surface whereas the effects of above-surface observations are spread horizontally in 

pressure. This is based on the assumption that model error at the surface at point A is better 

correlated with model error at the surface at point B than with the model error at the model level 

with the same pressure at point B. Note that unlike the standard WRF observation-nudging code, 

surface observations reported as part of a sounding are treated as surface observations by the 

observation nudging rather than as part of the sounding. This allows these observations to be 

spread along the surface rather than being spread horizontally based on pressure. In areas where 

the terrain height differs, spreading surface observations along a constant-pressure surface may 

be problematic. 

5. Exploring Observation-Nudging Parameters for TAMDAR Assimilation 

5.1 Experimental Design 

In order to determine how to best assimilate TAMDAR observations, a series of model 

experiments utilizing the 9- and 3-km domains were completed for the 1 March 2012 case. These 

experiments assimilate TAMDAR observations only on the 3-km domain in order to better 

isolate the effects of various nudging configurations on this domain. Specifically, these 

experiments vary the strength with which observation nudging is applied and the size of the area 

over which the observation nudging applies corrections for a given observation. 

The nudging strength, Gq, determines how quickly the model value approaches the observed 

value. If one assumes that the nudging term is the only term in the tendency equation, the inverse 

nudging strength is the e-folding time of the model error. Therefore the error is divided by e (i.e., 

2.71828...) every time interval of 1/Gq. Figure 7 shows the decrease in error with time due to 

observation nudging and assuming that all other tendency terms are zero. Nudging strengths 

ranging from 1 × 10–4 to 128 × 10–4 s–1 are shown, which converts to e-folding times between 

≈167 minutes to ≈1.3 minutes. Note that although the larger nudging strengths should result in 

the model more closely matching the observation, with larger nudging strengths the physicaltendency terms are less likely to dominate and thus the dynamical consistency of the model will 

not necessarily be maintained. Also, by forcing the model very strongly toward a given 

observation, we are assuming that there is no observational error. Thus, the stronger nudging 
15

strengths can result in noise and overfitting. We investigate varying the nudging strength 

between 1 × 10–4 and 128 × 10–4 s

–1. 

Fig. 7 Time series showing the percentage of the error at time 0 that is still extant at a given time. This 

assumes that the only factor affecting the field is the nudging term. 

One component of the spatiotemporal weighting function, Wq, is the horizontal radius of 

influence, which is specified by the user using the option obs_rinxy. Between the surface and 

500 hPa, the user-chosen value is linearly increased with pressure to twice the chosen value, 

and remains at twice the chosen value above 500 hPa. For example, if one chooses obs_rinxy

= 60 km, then the radius of influence is 60 km just above the surface but increases linearly to 

120 km at 500 hPa, and remains 120 km above 500 hPa. For surface observations the user 

may choose to decrease the effective radius of influence via a factor, but our focus here is on 

TAMDAR observations, which are above the surface. The horizontal radius of influence 

represents the error-correlation length scale, i.e., the maximum distance from the observation 

at which errors are correlated with errors at the observation location. The actual horizontal 

weighting function is:	ܹ௫௬ ൌ ሺܴܫܰଶ െ ܫܦܵܶଶሻ/ሺܴܫܰଶ ൅ ܫܦܵܶଶሻ where RIN is the effective 

radius of influence for this observation (based on obs_rinxy and the vertical placement of the 

observation) and DIST is the distance between the observation and current model point where 

the innovation is being applied. If the horizontal radius of influence is too large, we would be 

using an observation to correct the model at locations where the error is not correlated with 

the error at the observation location, and thus the corrections will not necessarily improve the 

model. If the horizontal radius of influence we utilize is too small, then we will not be as 

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120

Percent of Error Remaining (%)

Time (minutes)

1.00E‐04

4.00E‐04

8.00E‐04

1.60E‐03

3.20E‐03

6.40E‐03

1.28E‐02

Nudging

Weight
16

effective in decreasing the model error as we could be. Here, we test varying the obs_rinxy

setting between 30 and 120 km. 

The model experiments for the 1 March 2012 case that test the strength of the nudging and the 

horizontal extent of the nudging are listed in Table 1. For verification we use all of the 

observations described in Section 4.1 during the forecast period (19–12 UTC); these include 

standard surface observations as well as mesonet data, maritime observations, profiler data, 

aircraft data (both TAMDAR and ACARS), and rawinsondes. 

Table 1 List of WRF-ARW experiments exploring the assimilation 

of TAMDAR observations on 1 March 2012 using varying 

nudging strengths and horizontal radii of influence 

obs_rinxy (km) 

Weight (x 10–4 s–1) 

None 1 4 8 16 32 64 

30 

X 

 X X X 

45 X X X 

60 X X X X X X 

90 X X X 

120 X X X 

As implemented in Reen et al. (2014b) we place a limit on negative water-vapor mixing ratio 

innovations when they are applied to locations where the model is drier than the model is at the 

observation location. Specifically, the magnitude of a negative moisture innovation applied to a 

location with less moisture than the location the innovation is calculated at is limited to be no 

more than the model water-vapor mixing ratio at the location the innovation is being applied to. 

In other words, when applying an observation q0(i) to (x,y,z,t) if: 

    qo    i  qm xi , yi ,zi ,t  0  qm x, y,z,t  qm xi , yi ,zi ,t (2) 

then the nudging equation becomes: 

  

          

  







 

 





N

i

q

N

i

q o m i i i m

q q

W i x y z t

W i x y z t q i q x y z t q x y z t

x y z t F x y z t G

t

q

1

1

2

, , , ,

, , , , max , , , , , , ,

, , , , , ,  

(3) 
17

5.2 Results 

5.2.1 Noise 

To evaluate the noise in the model solution, we examine the domain-average absolute value of 

the tendency of perturbation dry air mass (dmu/dt). The purpose of this is to look for rapid 

changes in pressure, which would indicate noise. It is difficult to evaluate the meaning of this 

variable alone, but we can look at its value relative to a control experiment. Here we investigate 

the noise added via various observation-nudging configurations and use a model experiment with 

no data assimilation as the control experiment. Figure 8 shows the noise of each experiment on 1 

March relative to the noise of the control experiment to show the added noise from data 

assimilation. As expected, the largest noise is seen in the experiment with the strongest nudging 

(Gq = 64 × 10–4 s–1). Data assimilation is applied at full strength through the first 6 h and then 

with linearly decreasing strength through the next hour. This is consistent with the added noise of 

data assimilation rapidly decreasing by 7 h. Also, note that most of the TAMDAR observations 

that were used for nudging were made between 4 and 6 h into the data assimilation (Fig. 2a, 2c, 

2e), consistent with the largest noise occurring during this time period. Besides a spike to about 

1.2 times the noise of the non-nudging experiment between 6 and 

7 h, the 8 × 10–4

 s

–1 experiment generally has low relative noise, and all experiments with Gq < 8 

× 10–4 s

–1 have very little noise compared to the experiment with strong nudging. This suggests 

that the optimal configuration should probably use Gq <16× 10–4

 s

–1. 
18

Fig. 8 Time series of 3-km domain’s average tendency of perturbation dry air mass (dmu/dt) relative to the 

experiment with no data assimilation for all experiments with an obs_rinxy of 60 km for 1 March 2012. 

A 100-point centered average was applied to smooth out the high-frequency variability. 

5.2.2 Verification 

The temperature mean absolute error (MAE) for each experiment for the first 6 h of the forecast 

(19–00 UTC) is shown in the left column of Fig. 9a, 9c, and 9e. Recall that a 6-hour (h) dynamic 

initialization using observation-nudging data assimilation precedes the beginning of the forecast. 

No observations during the forecast period are included in the data assimilation and so the 

evaluation here is against observations that were not used in the data assimilation. Also, note that 

verification was completed by horizontally interpolating the model to the observation location 

and vertically interpolating the model to the height above ground level of the observation. Figure 

9a indicates that the temperature MAE in the lowest 12,000-m AGL for the first 6 h of the 

forecast generally decreases with increasing Gq, consistent with stronger nudging being more 

able to bring the model into agreement with observations; thus it provides more accurate 

conditions for the start of the forecast period. There are exceptions, with the temperature MAE of 

the 90-km and 120-km experiments higher for Gq = 16 × 10–4 s

–1 than for Gq = 4 or 8 × 10–4

 s

–1. 

All experiments have lower 0–12,000-m temperature MAE than the control experiment with no 

2 4 6 8 10 12 14 16 18 20 22

1

1.2

1.4

1.6

1.8

2

2.2

Time (hours since model start)

Relative Domain Average dmudt (hPa/3h)

None

1x10−4s−1

4x10−4s−1

8x10−4s

−1

16x10−4s−1

32x10−4s−1

64x10−4s

−1
19

data assimilation. If one excludes experiments with Gq > 8 × 10–4 s

–1 due to the increased noise 

in those experiments, the best experiments are those with Gq of 4 or 8 × 10–4 s–1 and obs_rinxy of 

90 or 120 km. (Recall that obs_rinxy is the radius of influence just above the surface; the radius 

of influence increases linearly to twice this value at 500 hPa and remains at this value above 500 

hPa.) For the 0–1,000-m layer for 19–00 UTC (Fig. 9c)—the layer in Fig. 2 with the most 

TAMDAR observations—there is a similar pattern, with temperature MAE generally decreasing 

with increasing Gq. The magnitude of the improvement in temperature MAE is notably larger in 

the 0–1,000-m layer than the 0–12,000-m layer, with the difference between the no-nudging 

experiment and the strongest-nudging experiment (64 × 10–4 s

–1) ≈ 0.09 K for 0–12,000 m, but 

0.44 K for 0–1,000 m. As in the 0–12,000-m AGL layer, the best experiments with Gq ≤ 8× 10–4

s

–1 are those with Gq of 4 or 8 × 10–4 s–1 and obs_rinxy of 90 or 120 km. Note that the 0–1,000-m 

AGL layer plots do not include surface observations, since the surface observations for 19–00 

UTC are evaluated against the model 2-m AGL diagnostic temperature in Fig. 9e. For the surface 

observations there is a similar pattern of decreasing temperature MAE with increasing nudging 

strength, but the magnitude of the improvements due to nudging TAMDAR are quite small: 

0.03-K between the no-nudging experiment and the nudging experiment with the lowest 

temperature MAE in this time period. As in the 0–1,000-m and 0–12,000-m AGL layers for this 

time period, the temperature MAE for the experiments with Gq of 4 or 8 × 10–4

 s

–1 and obs_rinxy

of 90 km are among the 4 best experiments with Gq ≤ 8 × 10–4 s

–1; however, instead of the 

similar pair of experiments with an obs_rinxy of 120 km being part of the 4 best experiments, the 

pair of obs_rinxy = 60-km experiments constitute the 2 other experiments with the lowest 

surface-temperature MAE for this time period. This may suggest that nudging based on the 

above-surface TAMDAR observations with an obs_rinxy of 120 km spreads the influence of 

TAMDAR observations to areas where the surface-temperature error is not correlated with the 

error at the location of the TAMDAR observation. However, the very small magnitude of the 

differences in temperature MAEs among the experiments at the surface makes it difficult to 

make definite statements regarding the interpretation of the MAE differences. 
20

Fig. 9 Temperature MAE (K) for the experiments in Table 1: for 19–00 UTC (1–6-h forecast; a, c, e) and 

for 01–12 UTC (7–18-h forecast; b, d, f); at 2-m AGL (e, f), at 0–1,000-m AGL (c, d), and at 0–

12,000-m AGL (a, b). The x-axis indicates the nudging strength (Gq) of the experiment and the 

symbols indicate the obs_rinxy setting used to determine horizontal radius of influence. 

While the left column of Fig. 9 shows temperature MAE for the first 6 h of the forecast period 

(19–00 UTC; Fig. 9a, 9c, 9e), the right column shows the remaining portion of the forecast 0-12000 m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

a)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-12000 m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

b)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

d)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

c)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

2-m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

e)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

2-m Temperature MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

f)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64
21

period (01–12 UTC; Fig. 9b, 9d, 9f). Recall that the data assimilation only includes observations 

through the first 6 h (12–18 UTC) and the nudging of these observations is linearly decreased to 

zero by 19 UTC. One would expect that the benefits of the nudging would decrease with time 

and thus that the temperature MAE improvements for 01–12 UTC would be less than those for 

19–00 UTC. Consistent with this expectation, the range in temperature MAE among the 

experiments for 19–00 UTC (Fig. 9a, 9c, 9e) is indeed larger than for 01–12 UTC (Fig. 9b, 9d, 

9f). For the 01–12 UTC period, temperature MAE for experiments with Gq ≤ 8 × 10–4 s

–1 is 

lowest for those with Gq of 4 or 8 ×10–4 s–1 and obs_rinxy of 90 or 120 km. Unlike the 19–00 

UTC period, this is also true for surface temperature. 

Figure 10 contains the same format as Fig. 9 but plots the dewpoint MAE rather than the 

temperature MAE, and shows many similarities to the temperature MAE plots. As with 

temperature, dewpoint MAE generally decreases with increasing Gq, and data assimilation has a 

larger impact on MAE in the 0–1,000-m AGL layer than at the surface or throughout the lowest 

12,000 m. However, for the entire 0–12,000-m AGL layer for the first 6 h of the forecast (Fig. 

10a), dewpoint MAE increases with increasing Gq for Gq > 8 ×10–4

 s

–1. This may suggest that 

water vapor is more prone to overfitting and that there is more spatial variation in water vapor 

than temperature. However, consistent with temperature, the experiments with Gq ≤ 8 × 10–4

 s

–1

that perform the best are those with Gq of 4 or 8 × 10–4

 s

–1 and obs_rinxy of 90 or 120 km. 
22

Fig. 10 Dewpoint temperature MAE (K) for the experiments in Table 1: for 19–00 UTC (1–6 h-forecast; 

a, c, e) and 01–12 UTC (7–18-h forecast; b, d, f); at 2-m AGL (e, f), at 0–1,000-m AGL (c, d), 

and at 0–12,000- m AGL (a, b). The x-axis indicates the nudging strength (Gq) of the 

experiment and the symbols indicate the obs_rinxy setting used to determine horizontal radius of 

influence. 

 0-12000 m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-12000 m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

2-m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

2-m Dewpoint MAE (K)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

a) b)

c) d)

e) f)
23

The wind-speed MAEs in Fig. 11 and the wind-direction MAEs in Fig. 12 have patterns in the 

experiments that are similar to those of the dewpoint-temperature MAEs in Fig. 10. Consistent 

with temperature and dewpoint, wind speed and direction MAEs generally decrease with 

increasing nudging strength; however, similar to dewpoint MAE, wind speed and direction 

MAEs increase at large Gq for the first 6 h in the 0–12,000-m AGL layer (Fig. 11a and 12a). 

Consistent with temperature and dewpoint, the experiments with Gq ≤ 8 × 10–4 s

–1 that perform 

the best in wind MAE are generally those with Gq of 4 or 8 × 10–4 s

–1 and obs_rinxy of 90 or 120 

km. For the 0–12,000-m AGL level for 01–12 UTC, it is more difficult to determine which 

experiments performed best. The very small differences in MAE among many of the experiments 

make it likely that some of the differences are insignificant. 
24

Fig. 11 Wind-speed MAE (m/s) for the experiments in Table 1: for 19–00 UTC (1–6-h forecast; a, c, e) 

and for 01–12 UTC (7–18-h forecast; b, d, f); at 10-m AGL (e, f), at 0–1,000-m AGL (c, d), and 

at 0–12,000-m AGL (a, b). The x-axis indicates the nudging strength (Gq) of the experiment and 

the symbols indicate the obs_rinxy setting used to determine horizontal radius of influence. 

0-12000 m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-12000 m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

10-m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

10-m Wind Speed MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

a) b)

c) d)

e) f)
25

Fig. 12 Wind-direction MAE (degrees) for the experiments in Table 1: for 19–00 UTC (1–6 hforecast; a, c, e) and for 01–12 UTC (7–18-h forecast; b, d, f); at 10-m AGL (e, f), at 0–1,000-

m AGL (c, d), and at 0–12,000-m AGL (a, b). The x-axis indicates the nudging strength (Gq) 

of the experiment and the symbols indicate the obs_rinxy setting used to determine horizontal 

radius of influence. 

 0-12000 m Wind Direction MAE (degrees)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-12000 m Wind Direction MAE (degrees)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Direction MAE (degrees)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Direction MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

10- m Wind Direction MAE (m/s)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

10- m Wind Direction MAE (degrees)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

a) b)

c) d)

e) f)
26

In order to determine which of the 4 experiments performs best overall, a simple ranking was 

employed for each of the panels in Fig. 9–12. Thus, the ranking will consider MAE of 

temperature, dewpoint, wind speed, and wind direction for surface, 0–1,000-m AGL, and 0–

12,000-m AGL, and for the first 6 h of the forecast and the latter portion of the forecast. The 

rankings for wind speed and wind direction will be ranked with half as much weight as 

temperature and dewpoint because they are representing 2 aspects of the same field. This ranking 

is shown in Table 2. It indicates the overall ranking from best to worst among the overall 4 best 

experiments: 1) Gq = 8 × 10–4 s–1 and obs_rinxy = 120 km, 2) Gq = 8 × 10–4 s–1 and obs_rinxy = 

90 km, 3) Gq = 4 × 10–4 s

–1 and obs_rinxy = 120 km, and 4) Gq = 4 × 10–4

 s

–1 and obs_rinxy = 90 

km. This suggests that the best configuration for this case is Gq = 8 × 10–4 s

–1 and obs_rinxy = 

120 km. Note, however, that the Gq = 8 ×10–4 s–1 and obs_rinxy = 90 km experiment ranks very 

closely for temperature and wind direction. 

Table 2 Ranking of MAE values for the 4 experiments with the lowest MAE, with 

“1” being the best of the 4 experiments and “4” being the worst 

 Gq (s–1) 4 x 10–4 8 x 10–4

Field Time 

(UTC) Height (m AGL) obs_rinxy 

 (km) 90 120 90 120 

Temp. 

(K) 

19 - 00 0-12000 3 1 4 2 

01 - 12 4 2.5 2.5 1 

19 - 00 0-1000 3 4 1 2 

01 - 12 4 2.5 2.5 1 

19 - 00 2 2 4 1 3 

01 - 12 4 3 1 2 

Mean 3.33 2.83 2.00 1.83 

Dewpoint 

(K) 

19 - 00 0-12000 4 2. 3 1 

01 - 12 3.5 3.5 2 1 

19 - 00 0-1000 2.5 2.5 4 1 

01 - 12 3. 4 2 1 

19 - 00 2 3. 4 2 1 

01 - 12 4 3 2 1 

Mean 3.33 3.17 2.50 1.00 

Wind 

Speed 

(m/s) 

19 - 00 0-12000 4 3 2 1 

01 - 12 4 3 1 2 

19 - 00 0-1000 4 3 2 1 

01 - 12 4 2 3 1 

19 - 00 10 4 2 3 1 

01 - 12 4 3 2 1 

Mean 4.00 2.67 2.17 1.17 

Wind 

 Direction 

 (degrees) 

19 - 00 0-12000 3 4 2 1 

01 - 12 3 4 1 2 

19 - 00 0-1000 3.5 3.5 2 1 

01 - 12 2 4 1 3 

19 - 00 10 4 3 2 1 

01 - 12 4 1 3 2 

Mean 3.25 3.25 1.83 1.67 

Wind Wind Mean 3.63 2.96 2.00 1.42 

Mean Overall Mean 3.43 2.99 2.17 1.42 
27

5.2.3 Data-Assimilation Benefit vs. Degradation 

When assimilating data via observation nudging, a larger horizontal radius of influence may 

decrease the overall error, but do so by decreasing error near the observation while increasing 

error farther from the observation. To investigate this issue, we examined whether a given dataassimilation configuration improved, degraded, or caused no change in the verification of each 

individual observation and then determined how many observations fell into each category. “No 

change” was defined here as changes ≤0.1 K for temperature and dewpoint, ≤0.1 m/s for wind 

speed, and ≤1.0° for wind direction. Based on this information, plots are constructed of the 

percentage of observations where the data assimilation improved the model. Plots are also 

constructed that take the subset of observations where the data assimilation results in a nonnegligible change (either positive or negative) and find the percentage of these observations 

where the change was positive. This quantity is referred to here as the percentage changed 

improved (PCI). A value of PCI greater than 50% indicates that where the data assimilation is 

changing the solution, it is more often improving the solution than degrading the solution. 

For temperature in the 0–1,000-m AGL layer for 19–00 UTC, the percent of observation 

locations where the data assimilation improves the model solution (Fig. 13a) generally increases 

as nudging strength increases. This height layer and time period were chosen because the largest 

effects of nudging occur in these categories. Stronger nudging allows the data assimilation to 

more strongly affect the model at the grid points within the radius of influence; for temperature, 

this allows the nudging to benefit the model solution at an increasing number of observation 

points as Gq increases. The percent of observation locations where the model solution improves 

also increases with increasing obs_rinxy. This indicates that nudging over a larger area allows a 

larger number of model grid points to improve. Note, however, that this plot says nothing about 

the percentage of grid points at observation locations for which the assimilation degrades the 

solution. 
28

Fig. 13 The percentage of observations against which the model verifies non-negligibly better as compared to the 

no-nudging experiments (a, c), and of the subset of observation against which the model verifies nonnegligibly differently the percentage for which the change is an improvement (PCI; b, d). These are 

plotted for all experiments for the 0–1,000-m AGL level for 19–00 UTC for both temperature (a, b) and 

dewpoint (c, d). 

The PCI plot for temperature during this time period in the 0–1,000-m AGL layer (Fig. 13b) 

takes into account both the improvements and the degradations caused by the data assimilation. 

In general, the PCI decreases with increasing nudging strength, suggesting although nudging 

more strongly increases the number of grid points where the model solution improves, there is a 

stronger increase in the number of grid points where the model solution degrades. For the very 

strongest nudging (Gq ≥ 16× 10–4

 s

–1) the PCI increases; however, since there are only 

experiments for one obs_rinxy for these values of Gq and this is only one time period of one case 0-1000 m Temperature Pct Improved (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

a)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Temperature PCI (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

b)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Dewpoint PCI (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

d)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Dewpoint Pct Improved (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy c)

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64
29

at one height level, perhaps this is an anomaly. One might expect that PCI would decrease with 

increasing obs_rinxy, because with smaller obs_rinxy we will confine the changes due to 

nudging to a smaller area around the observation, and the error at the observation location is 

more likely to be correlated with error at correlations closer to the observation location. 

However, for temperature in this case, during this time period and vertical layer, this is not the 

case. There is not a clear relationship between obs_rinxy and PCI here. For Gq = 4 and 

16 × 10–4 s

–1

, an obs_rinxy of 90 km results in the best PCI, while at 8 ×10–4 s

–1 all but obs_rinxy 

= 30 km have a similar PCI. 

Unlike temperature, for dewpoint the percent of observation locations where the model improves 

(Fig. 13c) does not generally increase with increasing Gq or with increasing obs_rinxy. There is 

no obvious relationship between the Gq and the percent improved, but the larger values of 

obs_rinxy are generally associated with lower percentages of observation locations where the 

model improves. This suggests that increasing the area over which a moisture observation affects 

the solution can degrade the solution, at least for the larger of the values of obs_rinxy tested here. 

Comparing these results for moisture (Fig. 13c) to those for temperature (Fig. 13a) suggests that 

the horizontal error-correlation length scales for moisture may be smaller than those for 

temperature. 

For dewpoint PCI (Fig. 13d), we do see the increase in PCI with decreasing obs_rinxy that one 

might expect but that was not present for temperature. The largest dewpoint PCIs in this layer at 

this time are for the smaller values of obs_rinxy. At Gq = 4 × 10–4

 s

–1 the experiments with 

obs_rinxy = 30–60 km have very similar PCIs (≈80%), while the PCI for obs_rinxy = 90 km is 

≈73% and for obs_rinxy = 120 km the PCI is ≈69%. At Gq = 8 × 10–4 s

–1 the PCI for the 

experiments with obs_rinxy = 30, 45, 60, 90, and 120 km are approximately 82%, 77%, 71%, 

62%, and 69%, respectively. These results are consistent with the percent-improved statistics in 

Fig. 13c in suggesting that the horizontal error-correlation length scales are smaller for moisture 

than for temperature. 

Like dewpoint but unlike temperature, the percent of observation locations where the model 

wind speed (Fig. 14a) and direction (Fig. 14c) are improved by observation nudging does not 

show a general increase with Gq. However, similar to temperature, wind speed (and to a lesser 

degree, wind direction) generally indicates a larger percentage of model grid points coincident 

with observations are improved for larger values of obs_rinxy. This suggests that the errorcorrelation length scales of wind are perhaps more similar to those of temperature than those of 

water vapor. 

It is difficult to see a pattern in the wind speed and wind direction PCIs (Fig. 14b and 14d). 

Smaller values of obs_rinxy are generally associated with smaller PCIs (at least at Gq = 4 and 8 × 

10–4

 s

–1), which is in contrast to the opposite signal seen in dewpoint (Fig. 13c). This is also 

consistent with the wind error-correlation length scales perhaps being closer to those for 

temperature than moisture. 
30

Fig. 14 The percentage of observations against which the model verifies non-negligibly better as compared to the 

no-nudging experiments (a, c), and of the subset of observations against which the model verifies nonnegligibly differently than the no-nudging experiments, the percentage for which the change is an 

improvement (PCI; b, d). These are plotted for all experiments for the 0–1,000-m AGL level for 19–00 

UTC for both wind speed (a, b) and wind direction (c, d). 

5.3 Summary and Conclusions 

A set of observation-nudging experiments were completed to determine how to configure 

observation nudging for assimilating TAMDAR data. These were conducted for 1 March 2012 

for a region centered over southern California using 9-km and 3-km horizontal grid-spacing 

domains. The experiments vary the strength of the nudging (Gq) and the area over which an 

observation affected the model solution (obs_rinxy). Recall that obs_rinxy gives the radius of 0-1000 m Wind Speed Percent Improved (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Speed PCI (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Dir. Percent Improved (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

0-1000 m Wind Dir. PCI (%)

120 km

90 km

60 km

45 km

30 km

NA (Control)

obs_rinxy

Nudging Strength (x 10-4 s-1)

None 1 4 8 16 32 64

a) b)

c) d)
31

influence immediately above the surface but the radius of influence increases linearly with 

decreasing pressure until reaching twice the value of obs_rinxy at 500 hPa and above. 

Three methods were used to evaluate the experiments. First, the “noise” caused by the data 

assimilation was evaluated to determine which experiments contain unacceptable levels of model 

noise that suggest the data assimilation is degrading the model solution. This evaluation of the 

noise caused by the observation nudging indicates that in order to minimize noise, it is probably 

best to use experiments Gq ≤ 8× 10–4 s

–1. Second, the mean absolute errors of temperature, 

dewpoint, wind speed, and wind direction were evaluated during the model forecast (after the 

completion of the model preforecast). This evaluation indicated that the largest effects of 

observation nudging are in the first 6 h of the forecast (compared to the latter 11 h) and in the 

lowest 1,000 m of the atmosphere above the surface (compared to the surface and to the entire 0–

12,000-m AGL layer). The experiment with the best overall MAE is the experiment with Gq = 8 

× 10–4

 s

–1 and obs_rinxy = 120 km, with the next best experiment also with Gq = 8 × 10–4

 s

–1 but 

with obs_rinxy = 90 km. Third, we examined the relationship between the number of 

observations indicating the model forecast improved and the number of observations indicating 

the model forecast degraded. This analysis suggested that the error-correlation length scale of 

water vapor is likely smaller than that of temperature and wind. Due to this, it may be best to use 

the experiment found to have the second-smallest MAE because it has a smaller value of 

obs_rinxy than the experiment with the lowest MAE; namely, the experiment with Gq = 8 ×10–4

s

–1 and with obs_rinxy = 90 km. Future experiments exploring the ability to use a different 

horizontal radius of influence for different variables could result in further improvements in 

model forecasts. 

It is important to note that these results are from a single case day, and their generality is not 

known. The next section will include tests of using the Gq = 8 × 10–4 s

–1 and obs_rinxy = 90 km 

for 4 other case days. 

6. Exploring the Value of Various Observational Data Sources 

6.1 Experimental Design 

In order to determine the relative value of TAMDAR observations as well as other observations, 

a series of model experiments utilizing the 9-, 3-, and 1-km horizontal grid-spacing domains 

were completed for the 5 case days from 2012 (described in Section 3): 7 February, 9 February, 

16 February, 1 March, and 5 March. These experiments are designed to apply the lessons learned 

(in Section 5) assimilating TAMDAR observations on one case day on the 3-km domain to the 

task of creating the best possible model forecast. 

As noted in Table 3, there are 7 experiments for each case day. Experiment C is the control 

experiment and assimilates no observations via observation; it also used GFS data for initial 
32

conditions with no enhancement via observations. Experiment T uses observation nudging to 

assimilate only the TAMDAR observations; it also uses TAMDAR data to enhance the initial 

condition analysis from GFS. (Note that all experiments use initial conditions consisting of GFS 

data enhanced by the observations being assimilated in that experiment.) The value of 

assimilating “standard” observations is explored in Exp. S. There, standard observations refer to 

standard surface observations and rawinsonde observations (RAOBs). These are the observations 

included in the MADIS METAR (Aviation Routine Weather Report), maritime, and RAOB data 

sets. The METAR data set consists of stations reporting surface observations in the METAR 

format (including Automated Surface Observing System [ASOS], Automated Weather 

Observing System [AWOS], and non-automated stations). The maritime data set consists of 

reports from ships. The RAOB data set contains rawinsondes. The added value of TAMDAR 

observations compared to only using standard observations is demonstrated via comparing Exp. 

TS to Exp. S. 

Table 3 Experimental design for Section 6 indicating which 

observations are assimilated in each experiment (“Y” is yes) 

Exp. Name Observations Assimilated 

Standard KNKX TAMDAR Mesonet 

C 

T Y 

S Y Y 

TS Y Y Y 

SK Y 

TSK Y Y 

SM Y Y Y 

In order to determine the added value of having a local rawinsonde, an experiment using the 

standard observations but omitting the Miramar, CA, rawinsonde (KNKX), was completed (Exp. 

SK). A similar experiment was completed that also used the TAMDAR data to see if the 

TAMDAR data could serve as a replacement for the rawinsonde data. Finally, Exp. SM 

investigates the added value of more dense surface observations by using the MADIS mesonet 

data set in addition to the standard observations. 

For each experiment, observation nudging was applied on all 3 domains for observations no later 

than 18 UTC, 6 h into the model integration. The strength of the observation nudging of 

observations no later than 18 UTC was then linearly decreased to zero between 18 UTC and 19 

UTC (multiplied by the temporal weighting functions applied to the individual observations 

based on the difference between the observation time and the current model time). A Gq of 8× 

10–4 s–1 and an obs_rinxy of 90 km was used on the 3-km domain, based on the results in Section 

5. Note that although the obs_rinxy of 120 km led to lower overall MAE, there were indications 

that 120 km may be larger than the error-correlation length scale for water vapor. Therefore, the 

experiment with the second-best MAE was utilized here since it had a lower obs_rinxy, and thus 

will be less likely to spread the influence of water-vapor observations over too large of an area. 
33

The same nudging strength was also applied to the 9- and 1-km domains. Because the 

experiments in Section 5 did not utilize observation nudging on the 9- or 1-km domains, they do 

not provide direct guidance on the best obs_rinxy to apply on those domains. Therefore, we have 

used twice the obs_rinxy on 9-km domain than on the 3-km and one-half the obs_rinxy on the 1-

km as on the 3-km domain. This is designed to account for the smaller-scale features that are 

resolvable on finer-resolution model forecasts that may result in smaller error-correlation length 

scales. The horizontal radius of influence used for surface observations is 0.7 times obs_rinxy. 

Full weighting is given to the innovation based on an observation for a 90-minute period 

centered on the observation time, with weighting linearly decreasing to zero in the 45-minute 

period before and after the full weighting period. For surface observations this is decreased to a 

68-minute period centered on the observation time, with weighting linearly decreasing to zero in 

the ≈34-minute period before and after the full weighting period. 

Note that Exp. T is similar to the Gq = 8 × 10–4

 s

–1, obs_rinxy = 90 km experiment in Section 5 

but differs in a few potentially important ways. Here, the initial conditions at the beginning of the 

nudging period are enhanced by completing an analysis in Obsgrid that incorporates observations 

onto the GFS analysis, but in Section 5, the GFS analyses are used without enhancement. 

Another difference is that here we use data assimilation on all of the domains, whereas in Section 

5 data assimilation was used only on the 3-km domain. These 2 differences may potentially 

affect the 3-km solution in significant ways. Another difference is that here we include a 1-km 

nest, whereas in Section 5 only 9- and 3-km nests were utilized. We also do not use the 

observation-nudging modifications that ameliorate the creation of very dry conditions in these 

three-domain experiments. Note also that in Section 5 we only used model forecasts from one of 

the 5 case days, whereas here all 5 case days were simulated. 

6.2 Results 

6.2.1 Value of TAMDAR Observations 

In order to evaluate the value of TAMDAR observations, the control experiment with no data 

assimilation (Exp. C) will be compared to Exp. T, which nudges only TAMDAR observations; 

Exp. S, which nudges only standard observations; and Exp. TS, which assimilates both standard 

and TAMDAR observations. Comparing Exp. T to Exp C demonstrates the value of TAMDAR 

observations if there are no other observations available. Comparing Exp. TS to Exp. S 

demonstrates the added value of TAMDAR observations as compared to assimilating the 

standard observations. 

Since TAMDAR observations are not available on the 1-km domain during the data assimilation 

period, initial evaluation of the impacts of assimilating TAMDAR data will be completed using 

the 3-km domain. Following this an evaluation of the effects of TAMDAR data on the 1-km 

domain will be completed. These effects will occur entirely through differences in the lateral 

boundary conditions fed from the 3-km domain to the 1-km domain. 
34

6.2.1.1 Three-kilometer Domain 

Figure 15 shows the MAEs for the vertical layer (0–1,000-m AGL) and time period (19–00 

UTC, forecast h 1–6) likely to be most impacted from assimilating TAMDAR observations, 

given that there are more TAMDAR observations in this layer than in any other 1,000-m layer 

and that this time period immediately follows the end of data assimilation. The case day 

examined in Section 5 was 1 March. There is notable improvement on this case day in 

temperature from the inclusion of TAMDAR data; compare the square in the column for Exp. C 

with the square in the column for Exp. T in Fig. 15a. On 1 March, utilizing only standard data 

(compare Exp. S to Exp. C) actually degraded the model temperature forecast above the surface 

from 0–1,000 m during the first 6 h of the forecast. Adding the TAMDAR data to the standard 

data (Exp. TS) improves the solution compared to the standard-data-only solution and less so 

compared to the no-nudging experiment. The TAMDAR-only nudging experiment (Exp. T) best 

predicts temperature on this case day for this time and vertical bin. Looking at the other case 

days, the value of the TAMDAR observations for improving forecast temperature for this time 

and vertical bin is much less clear. In fact, on 3 case days assimilating only TAMDAR data 

slightly degrades the temperature forecast. That the forecast is unimproved via data assimilation 

is not limited to TAMDAR data: While assimilating only standard data results yields a clear 

improvement on 3 case days (7 February, 9 February, and 16 February), it degrades the forecast 

on one case day (1 March) and makes very little difference on another (5 March). The addition of 

TAMDAR data to standard data (Exp. TS compared to Exp. S) is a clear benefit on 2 days 

(1 March, 5 March), a slight benefit on one day (16 February), a slight degradation on one day 

(7 February), and a small degradation on the final day (9 February). 
35

Fig. 15 WRF 3-km domain MAEs for Exp. C, T, S, and TS from Table 3 verified against non-surface 

observations in the 0–1,000-m AGL layer for 19–00 UTC for a) temperature, b) dewpoint, c) wind speed, 

and d) wind direction. The x-axis indicates the experiment’s name and the symbols indicate the case day 

of the experiment. 

For dewpoint (Fig. 15b), the best improvement from TAMDAR data is once again on 1 March 

(the day examined in Section 5). Assimilating only TAMDAR data benefits 2 of the cases; 

however, only one of the 5 case days (16 February) indicates that nudging only TAMDAR data 

(Exp. T) performs worse than the assimilation of only standard observations. Similarly, adding 

TAMDAR data to the standard data only degrades one case day (5 March). 

Wind-speed and wind-direction MAEs for 0–1,000-m AGL for the first 6 h of the forecast (Fig. 

15c and 15d) show results similar to those of temperature and dewpoint. For both wind speed 

Experiment Name

0-1000 m Temperature MAE (K)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Dewpoint MAE (K)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Wind Speed MAE (m/s)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Wind Direction MAE (degrees)

7 February 

9 February

16 February

1 March

5 March

a) b)

c) d)
36

and direction, 1 March is the case day when assimilating only TAMDAR data is the most 

beneficial, while some case days indicate degradations from the use of TAMDAR data (whether 

alone or in concert with standard data). 

In order to more effectively analyze the potential benefits of TAMDAR-data assimilation, plots 

were created indicating the added value of assimilating TAMDAR data. Figures 16 and 17 

demonstrate the potential benefits of assimilating TAMDAR data based on the difference in 

MAE between experiments with TAMDAR data and those without TAMDAR data for the first 

6 h of the forecast period (19–00 UTC). If a column in these figures was labeled “A-B”, a point 

above the horizontal line indicating a zero MAE difference represents a case day when 

experiment B had a lower MAE than experiment A and thus experiment B performed better than 

experiment A. Figure 16a indicates that, averaged over the case days, the 1–6 h forecasts 

improve due to the assimilation of TAMDAR data compared to not nudging at all (Exp. C-T) 

and compared to nudging only standard data (S-TS), as seen by the mean value always being 

above the zero temperature MAE difference horizontal line. Note, however, that there is 

variation from day to day, with some days indicating small degradations due to nudging 

TAMDAR data for certain heights. The TAMDAR-data assimilation never increases the domainaverage MAE by more than 0.1 K, while it sometimes does cause improvements of more than 

0.1 K. For dewpoint (Fig. 16b), TAMDAR-data assimilation once again has, in general, a 

positive impact on dewpoint. As with temperature, there is notable variation from day to day. 

Perhaps the most striking variation is for the 0–1,000-m AGL layer, where the use of TAMDAR 

observations when compared to not doing data assimilation (Exp. C-T) decreased the dewpoint 

MAE by ≈1.2 K on 1 March, but increased the error by ≈0.2 K on 5 March. 
37

Fig. 16 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between Exp. 

S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 2 m, 0–1,000-m AGL, and 0–

12,000-m AGL on the 3-km domain for a) temperature and b) dewpoint. Positive values 

indicate Exp. T performs better than Exp. C and that Exp. TS performs better than Exp. 

S, respectively. A point is plotted for each case day as well as the mean of all of the case 

days, as noted in the figure legend. 

C−T S−TS C−T S−TS C−T S−TS −0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Temperature MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

2-m

C−T S−TS C−T S−TS C−T S−TS −0.2

0

0.2

0.4

0.6

0.8

1

1.2

Dewpoint MAE Difference (K)

0-1000 m AGL 0-12000 m AGL

a)

b)

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean
38

Fig. 17 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 10 m, 0–1,000-m 

AGL, and 0–12,000-m AGL on the 3-km domain for a) wind speed and b) wind 

direction. Positive values indicate Exp. T performs better than Exp. C and that Exp. TS 

performs better than Exp. S, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. 

 

C−T S−TS C−T S−TS C−T S−TS

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Wind Speed MAE Difference (m/s)

10-m 0-1000 m AGL 0-12000 m AGL

C−T S−TS C−T S−TS C−T S−TS

−12

−10

−8

−6

−4

−2

0

2

4

6

8

Wind Direction MAE Difference (degrees)

10-m 0-1000 m AGL 0-12000 m AGL

a)

b)

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean
39

Figure 17 indicates that, on average, assimilation of TAMDAR data degrades wind speed and 

wind direction in the first 6 h of the forecast (19–00 UTC). The 1 March case is a notable 

exception: Both wind speed and wind direction are improved for all height bins, both when 

comparing TAMDAR assimilation to no assimilation (C-T) and when comparing TAMDAR 

assimilation to assimilation of only standard observations. Because the average degradation 

caused in the wind fields is relatively small (≈0.1 m/s and ≈2°) these results may not be 

significant. 

We have been analyzing the model performance for the first 6 h of the forecast (19–00 UTC) 

which is the portion of the forecast period when the impacts of the nudging should be strongest; 

next, we investigate the impacts on the rest of the forecast period (01–12 UTC; 7–18-h forecast). 

Figure 18 shows the MAE difference caused by utilizing TAMDAR observations in the 0–1,000-

m AGL layer (excluding surface observations). For temperature (Fig. 18a) and dewpoint (Fig. 

18b) forecasts, using TAMDAR data on average resulted in small improvements: a decrease in 

case-day mean MAE of ≈0.1 K for temperature and ≈0.1 K for dewpoint when TAMDAR is 

added to standard observations; however, there is very little improvement in dewpoint when 

assimilating TAMDAR observations is compared to not assimilating any observations. For wind 

speed (Fig. 18c) there is a small improvement in the case-day mean MAE of ≈0.25 m/s when the 

use of TAMDAR data is compared to non-use of any observations (C-T) and ≈0.1 m/s when 

using TAMDAR data in addition to standard data (S-TS). For wind direction (Fig. 18d), the 

MAE differences due to the use of TAMDAR data averaged over the 5 cases days are very small 

(≤1°). For the 7–18-h forecast, the use of TAMDAR data, on average, results in small 

improvements. 
40

Fig. 18 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between Exp. S and Exp. TS 

(columns labeled S-TS) for 01–12 UTC for, 0–1,000-m AGL on the 3-km domain for 

a) temperature, b) dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. T 

performs better than Exp. C and that Exp. TS performs better than Exp. S, respectively. A point is plotted 

for each case day as well as the mean of all of the case days, as noted in the figure legend. 

Overall, assimilating TAMDAR data improved the 3-km forecast of temperature and dewpoint, 

especially during the first 6 h of the forecast, while the overall impact on wind was less clear. 

During the first 6 h of the forecast, assimilation of TAMDAR data degrades the case-day mean 

wind forecast; during the latter 11 h, the wind speed is improved while the case-day mean winddirection MAE is impacted very little by the TAMDAR data. It should be stressed that there is 

significant variability among the case days, in these results. 

6.2.1.2 One-kilometer Domain 

Since there are no TAMDAR observations available within the 1-km domain to assimilate, the 

impacts of TAMDAR observations will be through the lateral boundary conditions. Note that 

care should be taken when comparing the 1-km verification statistics against the 3-km 

verification statistics because the 1-km grid covers a small subset of the 3-km grid; thus the 

verifications of the 2 grids are over different areas. It may be that the verification statistics of the 

C−T S−TS −0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Dewpoint MAE Difference (K)

C−T S−TS −0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Temperature MAE Difference (K)

C−T S−TS −0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Wind Speed MAE Difference (m/s)

C−T S−TS −6

−4

−2

0

2

4

6

8

Wind Direction MAE Difference (degrees)

a) b)

c) d)

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean
41

2 domains would be more similar if the 3-km grid were verified only over the portion of the 3-

km domain coincident with the 1-km grid. 

Figure 19 shows the 1-km MAE for the 0–1,000-m AGL layer during the first 6 h of the forecast. 

This is similar to Fig. 15 but shows the verification for the 1-km domain instead of 3-km domain. 

The use of TAMDAR observations (Exp. T), compared to not using any observations (Exp. C), 

improves model forecast temperature (Fig. 19a) for this layer and time for 3 of the 5 cases, with 

the other 2 cases showing very slight degradations from the use of the TAMDAR data. Using 

TAMDAR observations in addition to normal observations (compare Exp. S to Exp. TS) 

indicates that temperature forecasts are improved in this layer for 2 case days (1 March and 5 

March), slightly improved in one case (16 February), slightly degraded in one case (7 February), 

and almost unchanged for the other case (9 February). For dewpoint (Fig. 19b) there does not 

appear to be a benefit compared to using no observations; when compared to assimilating only 

standard observations, however, there is a small benefit. Whether TAMDAR improves or 

degrades the wind is dependent on the specific case. The MAE differences will be plotted as with 

the 3-km domain in order to aid with the model analysis. 
42

Fig. 19 WRF 1-km domain MAE for experiments C, T, S, and TS from Table 3 verified against non-surface 

observations in the 0–1,000-m AGL layer for 19–00 UTC for a) temperature, b) dewpoint, c) wind speed, 

and d) wind direction. The x-axis indicates the experiment’s name and the symbols indicate the case day 

of the experiment. 

The case day’s mean temperature MAE difference (Fig. 20a) indicates that on average 

TAMDAR assimilation improves the 1-km temperature forecast for 19–00 UTC. As on the 3-km 

domain, there is notable variability among the case days. For dewpoint (Fig. 20b) the case-day 

mean MAE difference is positive for some measures and negative for others. This indicates that 

the TAMDAR-data assimilation neither clearly benefits nor clearly degrades the 1-km domain 

moisture field. The MAE difference for wind fields (Fig. 21) indicates that on average the 

TAMDAR assimilation has a slightly negative influence on the 1-km domain winds. 

Experiment Name

0-1000 m Temperature MAE (K)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Dewpoint MAE (K)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Wind Speed MAE (m/s)

7 February 

9 February

16 February

1 March

5 March

Experiment Name

0-1000 m Wind Direction MAE (degrees)

7 February 

9 February

16 February

1 March

5 March

a)

b)

c) d)
43

Fig. 20 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 2 m, 0–1,000-m AGL, 

and 0–12,000-m AGL on the 1-km domain for a) temperature and b) dewpoint. 

Positive values indicate Exp. T performs better than Exp. C and that Exp. TS performs 

better than Exp. S, respectively. A point is plotted for each case day as well as the 

mean of all of the case days, as noted in the figure legend. 

C−T S−TS C−T S−TS C−T S−TS

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Temperature MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

C−T S−TS C−T S−TS C−T S−TS

−1

−0.5

0

0.5

1

1.5

Dewpoint MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

a)

b)

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean
44

Fig. 21 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between 

Exp. S and Exp. TS (columns labeled S-TS) for 19–00 UTC for 10 m, 0–1,000-m 

AGL, and 0–12,000-m AGL on the 1-km domain for a) wind speed and b) wind 

direction. Positive values indicate Exp. T performs better than Exp. C and that Exp. 

TS performs better than Exp. S, respectively. A point is plotted for each case day as 

well as the mean of all of the case days, as noted in the figure legend. 

The latter portion of the model forecast (01–12 UTC; 7–18-h forecast) shown in Fig. 22 has 

significant variability among the case days. Averaged over the case days, the temperature MAE 

difference (Fig. 22a) indicates very small changes due to TAMDAR data (<0.1 K). For dewpoint 

C−T S−TS C−T S−TS C−T S−TS

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Wind Speed MAE Difference (m/s)

10-m 0-1000 m AGL 0-12000 m AGL

C−T S−TS C−T S−TS C−T S−TS

−10

−5

0

5

10

15

20

Wind Direction MAE Difference (degrees)

10-m 0-1000 m AGL 0-12000 m AGL

a)

b)

7 February 

9 February

16 February

1 March

5 March

Mean

7 February 

9 February

16 February

1 March

5 March

Mean
45

(Fig. 22b), adding TAMDAR observations (C-T) is a degradation when compared to not using 

any observations, whereas adding TAMDAR observations to standard observations (S-TS) has 

very little mean effect. Averaged over the case days, wind speed (Fig. 22c) for this period is 

improved by the addition of TAMDAR data especially compared to the use of no observations. 

While the individual case days’ wind direction is impacted by the TAMDAR data, the mean 

effect averaged over the case days is nearly zero (Fig. 22d). 

Overall, on the 1-km domain during the first 6 h of the model forecast, the use of TAMDAR 

observations improves the temperature forecast, has mixed effects on the dewpoint forecast, and 

degrades the winds slightly. During that latter portion of the forecast (01–12 UTC) the effects are 

mixed, with an improvement seen in wind speed. 

Fig. 22 Difference in MAE between Exp. C and Exp. T (columns labeled C-T) and between Exp. S and Exp. TS 

(columns labeled S-TS) for 01–12 UTC for 0–1,000-m AGL on the 1-km domain for a) temperature, b) 

dewpoint, c) wind speed, and d) wind direction. Positive values indicate Exp. T performs better than Exp. 

C and that Exp. TS performs better than Exp. S, respectively. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. 
46

6.2.2 Value of Local Rawinsonde 

To investigate a local rawinsonde’s value to the model forecast, we examine Exp. S, SK, TS, and 

TSK; also, we investigate whether TAMDAR data’s value can equal a local rawinsonde’s by 

examining Exp. S and TSK. Exp. S utilizes standard data (standard surface observations, ship 

reports, and rawinsonde) to both enhance the initial condition analysis from GFS as well as to 

assimilate into the model during a preforecast period. Exp. SK removes the KNKX/Miramar 

rawinsonde (Fig. 4) from the observations and is used to determine the value of the rawinsonde 

by comparing Exp. SK with Exp. S. Exp. TS and TSK are similar to Exp. S and SK but also 

include TAMDAR data; comparison between Exp. TS and TSK indicates the value of the 

rawinsonde if TAMDAR data is present. By comparing Exp. TSK to Exp. S, one can determine 

whether using TAMDAR data compensates for the lack of a local rawinsonde. 

The evaluation for this section will concentrate on the 1-km domain. This is because the 

rawinsonde is within this domain and because we are interested in the value of the local

rawinsonde and limiting our evaluation to the 1-km domain ensures that the rawinsonde remains 

more local than if we evaluated the larger 3-km domain. 

The KNKX rawinsonde removed for some experiments (Exps. SK and TSK) occurs at 12 UTC, 

at the beginning of the model integration, whereas the forecast begins at 18 UTC, and the 

verification at 19 UTC. Since the effects of assimilating an observation tend to fade with time, 

the benefits of the rawinsonde are likely to be less pronounced at that time than if they were 

evaluated closer to the time of the rawinsonde. However, since rawinsondes are often only 

available every 12 h, one will often not have any very recent rawinsondes available to assimilate, 

so the experimental configuration here is not inconsistent with real-world conditions. 

Figures 23 and 24 show the improvements on the 1-km domain during the first 6 h of the forecast 

(19–00 UTC) due to the inclusion of the local rawinsonde (Miramar, CA) in the initial conditions 

and data assimilation. The forecast’s surface-temperature, case-day mean MAE decreases with 

the use of the local rawinsonde (seen in Fig. 23a in the leftmost column, labeled 2-m SK-S, 

where the mean value is positive indicating that Exp. SK has larger temperature MAE than Exp. 

S), but only slightly and there is large case-day to case-day variability. The addition of the local 

rawinsonde to the experiment that included TAMDAR data in addition to the typical data of 

standard surface observations and rawinsondes (columns labeled TSK-TS) actually slightly 

degrades the case-day mean surface-temperature MAE. For the 0–1,000-m AGL layer, the 

addition of the local rawinsonde slightly improves the case-day mean MAE both with and 

without TAMDAR data. For the entire 0–12,000-m AGL layer, the case-day mean temperature 

MAE is nearly zero. The dewpoint forecast (Fig. 23b) is on average degraded through the 

addition of the local rawinsonde (by between ≈0.1 K and ≈0.5 K depending on the vertical level 

and whether TAMDAR data are utilized). The local rawinsonde generally improved the case-day 

mean wind-speed and wind-direction MAE, especially in the 0–1,000-m AGL layer (Fig. 24). 
47

Overall, the rawinsonde appears to have the greatest benefit in 0–1,000-m temperature and 

winds, and actually appears to degrade model forecast dewpoint. 

Fig. 23 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) 

and between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 19–00 UTC 

for 2 m, 0–1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) 

temperature and b) dewpoint. Positive values indicate Exp. S performs better than Exp. 

SK and that Exp. TS performs better than Exp. TSK, respectively. A point is plotted for 

each case day as well as the mean of all of the case days, as noted in the figure legend. 

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Temperature MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −2.5

−2

−1.5

−1

−0.5

0

0.5

1

Dewpoint MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

a)

b)

7 February

9 February

16 February

1 March

5 March

Mean

7 February

9 February

16 February

1 March

5 March

Mean
48

Fig. 24 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) 

and between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 

19–00 UTC for 10 m, 0–1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for 

a) wind speed and b) wind direction. Positive values indicate Exp. S performs better 

than Exp. SK and that Exp. TS performs better than Exp. TSK, respectively. A point is 

plotted for each case day as well as the mean of all of the case days, as noted in the 

figure legend. 

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −0.5

0

0.5

1

Wind Speed MAE Difference (m/s)

10-m 0-1000 m AGL 0-12000 m AGL

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −6

−4

−2

0

2

4

6

8

10

12

14

Wind Direction MAE Difference (degrees)

10-m 0-1000 m AGL 0-12000 m AGL

a)

b)

7 February

9 February

16 February

1 March

5 March

Mean

7 February

9 February

16 February

1 March

5 March

Mean
49

Looking further into the forecast (01–12 UTC; 7–18-h forecast), the local rawinsonde slightly 

degrades surface temperature but slightly improves the temperature forecast above the surface 

(Fig. 25a). The case-day mean effect on the dewpoint is very small, except in the lowest 1,000 m 

where the local rawinsonde improves the dewpoint forecast by about 0.3K for the experiment 

without TAMDAR and by about 0.6K for the experiment with TAMDAR (Fig. 25b). For wind 

(Fig. 26), the local rawinsonde on average degrades wind speed very slightly but has a mixed 

impact on the wind direction. In the 7–18-h forecast the greatest benefit from the local 

rawinsonde appears to be in temperature and moisture in the lowest 1,000 m. 

 
50

Fig. 25 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) 

and between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 

01–12 UTC for 2 m, 0–1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for a) 

temperature and b) dewpoint. Positive values indicate Exp. S performs better than Exp. 

SK and that Exp. TS performs better than Exp. TSK, respectively. A point is plotted for 

each case day as well as the mean of all of the case days, as noted in the figure legend. 

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Temperature MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

SK−S TSK−TS SK−S TSK−TS SK−S TSK−TS −1

−0.5

0

0.5

1

1.5

2

2.5

Dewpoint MAE Difference (K)

2-m 0-1000 m AGL 0-12000 m AGL

a)

b) 7 February

9 February

16 February

1 March

5 March

Mean

7 February

9 February

16 February

1 March

5 March

Mean
51

Fig. 26 Difference in MAE between Exp. SK and Exp. S (columns labeled SK-S) 

and between Exp. TSK and Exp. TS (columns labeled TSK-TS) for 

01–12 UTC for 10 m, 0–1,000-m AGL, and 0–12,000-m AGL on the 1-km domain for 

a) wind speed and b) wind direction. Positive values indicate Exp. S performs better 

than Exp. SK and that Exp. TS performs better than Exp. TSK, respectively. A point is 

plotted for each case day as well as the mean of all of the case days, as noted in the 

figure legend. 

The vertical profile of MAE is examined in order to determine whether there are any consistent 

signals in the vertical-error structure among the 5 case days. The 1-km domain vertical profile of 
52

temperature for the first 6 h of the forecast (19–00 UTC; 1–6-h forecast) is shown in Fig. 27 for 

Exp. S, which utilizes standard observations, and Exp. SK, which is the same as Exp. S but omits 

the local rawinsonde. If the use of the local rawinsonde improves the forecast, then the MAE for 

Exp. S will be smaller than the MAE for Exp. SK. For these cases, there does not appear to be a 

consistent day-to-day signal in the vertical distribution of the effects of using the local 

rawinsonde. It can be seen that the magnitude of the effect of the local rawinsonde on the MAE 

varies notably by case and within a specific case day by height. Note that the number of 

observations available for verification decreases with height (Fig. 27f). The limited number of 

observations at some heights (e.g., on 9 February there are 8 observations in the 7,000–8,000-m 

layer for this time period) calls into questions the statistical significance of the statistics at the 

upper levels. For dewpoint (Fig. 28) there also does not seem to be a consistent pattern across the 

case days in regard to the impact of the local rawinsonde. For example, while on 7 February the 

local rawinsonde lowers the dewpoint MAE in the 0–3,000-m AGL layer, on 5 March there is a 

significant degradation from the local rawinsonde in this layer. Note that the number of dewpoint 

observations available for verification (Fig. 28f) is notably less than for temperature (Fig. 27f); a 

very limited number of dewpoint observations is available for verification above 6,000-m AGL 

(Fig. 28f). For wind speed, there are again no clear patterns apparent in the vertical MAE profile; 

however, note that 7 February (Fig. 29a) does demonstrate that sometimes the local rawinsonde 

can result in notable improvements, such as the 4,000–5,000-m AGL level here where windspeed MAE is decreased from 5.8 to 4.5 m/s. For wind direction (Fig. 30), the rawinsonde results 

in at least a small improvement in MAE in the lowest 1,000 m, except for one case day when the 

MAE changes less than 1°. Overall, it is difficult to ascertain clear patterns in the vertical MAE 

from day to day except for the near-surface improvement in wind direction. 
53

Fig. 27 Vertical profiles of temperature MAE (excluding surface observations) for 19–00 UTC for Exp. SK 

and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 March, and e) 5 March. Panel f is a 

vertical profile of the number of observations used to construct the MAE in panels a–e. 
54

Fig. 28 Vertical profiles of dewpoint MAE (excluding surface observations) for 19–00 UTC for Exp. SK and 

Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 March, and e) 5 March. Panel f is a vertical 

profile of the number of observations used to construct the MAE in panels a–e. 
55

Fig. 29 Vertical profiles of wind-speed MAE (excluding surface observations) for 19–00 UTC for Exp. SK 

and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 March, and e) 5 March. Panel f is a 

vertical profile of the number of observations used to construct the MAE in panels a–e. 
56

Fig. 30 Vertical profiles of wind-direction MAE (excluding surface observations) for 19–00 UTC for Exp. SK 

and Exp. S for a) 7 February, b) 9 February, c) 16 February, d) 1 March, and e) 5 March. Panel f is a 

vertical profile of the number of observations used to construct the MAE in panels a–e. 

 
57

To investigate whether TAMDAR observations could serve as a replacement for the local 

rawinsonde, we compare Exp. S, which assimilates standard surface data and rawinsondes, with 

Exp. TSK, which assimilates standard surface data, rawinsondes besides the local rawinsonde, 

and TAMDAR data. If the MAE of Exp. TSK is lower than the MAE of Exp. S, this indicates 

that use of the TAMDAR data was able to make up any accuracy lost with the loss of the 

rawinsonde data. Figure 31 shows this comparison for the first 6 h of the forecast (19–00 UTC). 

For temperature (Fig. 31a) and dewpoint (Fig. 31b) the case-day mean MAE difference is 

positive at the surface, in the 0–1,000-m AGL layer, and in the 0–12,000-m AGL layer. 

However, for wind speed (Fig. 31c) and wind direction (Fig. 31d) the case-day mean MAE 

difference is negative. This suggests that for the short-term forecast (0–6 h), TAMDAR data are 

sufficient to compensate for the lack of a local rawinsonde for temperature and dewpoint, but not 

so for wind. For the longer forecast (7–18 h), the case-day mean MAE difference for temperature 

is very small (Fig. 32a), while for dewpoint TAMDAR is unable to compensate for the loss of a 

local rawinsonde in the lower atmosphere (0–1,000-m AGL; Fig. 32b). During this time period 

the inclusion of TAMDAR data result in a slightly better wind-speed and slightly worse winddirection forecast above the surface than the inclusion of the local rawinsonde (Fig. 32c and 

32d). Overall, the TAMDAR data appear sufficient to compensate for the loss of a local 

rawinsonde for short-term (1–6 h) temperature and dewpoint forecasts, but not for wind 

forecasts. For the longer term (7–18 h), the interpretation is less clear. 
58

Fig. 31 Differences in MAE between Exp. S and Exp. TSK for 19–00 UTC for surface, 0–1,000-m AGL, and 0–

12,000-m AGL on the 1-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind 

direction. Positive values indicate Exp. TSK performs better than Exp. S. A point is plotted for each case 

day as well as the mean of all of the case days, as noted in the figure legend. 
59

Fig. 32 Differences in MAE between Exp. S and Exp. TSK for 01–12 UTC for surface, 0–1,000-m AGL, and 0–

12,000-m AGL on the 1-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind direction. 

Positive values indicate Exp. TSK performs better than Exp. S. A point is plotted for each case day as well 

as the mean of all of the case days, as noted in the figure legend. 

We investigated the effects of removing the local rawinsonde from the observations that are used 

to create the analysis used as initial conditions and from the observations used for observation 

nudging. The local rawinsonde in general improves the 1–6-h forecast of temperature and wind 

in the lowest 1,000 m, but degrades the forecast for dewpoint in this layer. For the longer-term 

forecast in the 0–1,000-m layer (7–18 h), temperature and dewpoint MAE are generally 

improved while wind-speed MAE is slightly degraded and wind direction almost unchanged. A 

similar comparison was completed using experiments that additionally used TAMDAR data. We 

also investigated the potential to use TAMDAR data in place of a local rawinsonde and found 

that for these cases TAMDAR is an effective replacement in terms of the accuracy of short-term 

temperature and dewpoint forecasts. 
60

6.2.3 Value of Denser Surface Observations 

To determine the value added by increasing the density of surface observations, we compare 

Exp. S, using standard surface observations and rawinsondes, with Exp. SM that additionally 

includes mesonet surface observations from the MADIS data set. The extent of the standard 

surface observations and the mesonet surface observations for all 3 WRF domains are shown in 

Fig. 5. The significantly enhanced spatial coverage provided by inclusion of the mesonet 

observations is clearly visible. (Figure 6 provides the same details but only for the 1-km 

domain.) 

Figure 33 shows the difference between Exp. S and Exp. SM in MAE for the first 6 h of the 

forecast (19–00 UTC). For temperature, dewpoint, and wind speed at the surface there is at least 

a slight improvement through the use of the mesonet observations when averaged over the case 

days. For temperature the MAE improves very slightly above the surface with the use of the 

mesonet observations; for dewpoint, wind speed, and wind direction above the surface, however, 

the case-day mean MAE difference indicates either a degradation or very little impact from the 

use of the mesonet observations. The improvement at the surface accompanied by degradation 

above the surface for temperature, dewpoint, and wind speed suggest that the vertical spreading 

of the influence of the surface observation may not be optimal. 

 
61

Fig. 33 Differences in MAE between Exp. S and Exp. SM for 19–00 UTC for surface, 0–1,000-m AGL, and 0–

12,000-m AGL on the 1-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind 

direction. Positive values indicate Exp. SM performs better than Exp. S. A point is plotted for each case 

day as well as the mean of all of the case days, as noted in the figure legend. 

For the longer-term forecast (01–12 UTC) the case-day mean effects of the mesonet data are 

generally fairly small (Fig. 34). Generally the case-day mean effects of the mesonet are at least 

slightly positive, although the 2-m temperature and 0–1,000-m dewpoint are degraded slightly by 

the introduction of mesonet data. 

S−SM S−SM S−SM −0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Temperature MAE Difference (K)

a) 7 February 

9 February

16 February

1 March

5 March

Mean

2-m 0-1000 m AGL 0-12000 m AGL

S−SM S−SM S−SM −6

−5

−4

−3

−2

−1

0

1

2

3

4

Wind Direction MAE Difference (degrees)

d) 7 February 

9 February

16 February

1 March

5 March

Mean

10-m 0-1000 m AGL 0-12000 m AGL

S−SM S−SM S−SM −0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Wind Speed MAE Difference (m/s)

c) 7 February 

9 February

16 February

1 March

5 March

Mean

10-m 0-1000 m AGL 0-12000 m AGL

S−SM S−SM S−SM −0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

Dewpoint MAE Difference (K)

b) 7 February 

9 February

16 February

1 March

5 March

Mean

2-m 0-1000 m AGL 0-12000 m AGL
62

Fig. 34 Differences in MAE between Exp. S and Exp. SM for 01–12 UTC for surface, 0–1,000-m AGL, and 0–

12,000-m AGL on the 1-km domain for a) temperature, b) dewpoint, c) wind speed, and d) wind 

direction. Positive values indicate Exp. SM performs better than Exp. S. A point is plotted for each case 

day as well as the mean of all of the case days, as noted in the figure legend. 

Since the largest impacts of utilizing surface observations are expected to be at the surface, and 

because observations at the surface are often available hourly (compared to above-surface 

observations, which may be every 12 h), we examine the time series of model error at the 

surface. Specifically, in Fig. 35 we look at the difference between the time series of MAE of 

Exp. S to that of Exp. SM, where a positive value indicates that Exp. SM has a lower MAE than 

Exp. S and thus that mesonet data benefit the model solution. For temperature (Fig. 35a), on 

most case days the inclusion of mesonet data results in an improvement at the very beginning of 

the simulation (12 UTC); this is due to the addition of the mesonet data to the initial condition 

analysis completed by Obsgrid. The experiments using the mesonet data have a lower MAE 

through the period in which new observations are assimilated (12–18 UTC). Recall in Section 

6.1 that observations up to 18 UTC are included in the assimilation, and the model may be 

nudged toward those observations up until 19 UTC as the data assimilation ramps down during 

S−SM S−SM S−SM −0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Temperature MAE Difference (K)

7 February 

9 February

16 February

1 March

5 March

Mean

2-m 0-1000 m AGL 0-12000 m AGL

a)

S−SM S−SM S−SM −1

0

1

2

3

4

5

6

7

Wind Direction MAE Difference (degrees)

7 February 

9 February

16 February

1 March

5 March

Mean

10-m 0-1000 m AGL 0-12000 m AGL

d)

S−SM S−SM S−SM −0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Wind Speed MAE Difference (m/s)

7 February 

9 February

16 February

1 March

5 March

Mean

10-m 0-1000 m AGL 0-12000 m AGL

c)

S−SM S−SM S−SM −0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Dewpoint MAE Difference (K)

7 February 

9 February

16 February

1 March

5 March

Mean

2-m 0-1000 m AGL 0-12000 m AGL

b)
63

this period. The benefit of using mesonet data on the model temperature solution notably 

decreases by 19 UTC for 7 and 16 February, the 2 case days when model temperatures improved 

most due to use of the mesonet data. For 9 February and 5 March, the benefit of mesonet data is 

decreasing by 17 UTC, and for 9 February this trend continues so that by 19 UTC there is 

basically no benefit from using the mesonet observations. For 1 and 5 March the reduction in 

MAE from the use of mesonet observations increases between 18 and 19 UTC as the nudging 

ramps down; while 5 March continues its trend of showing less benefit from mesonet 

observations as the simulation advances, 1 March indicates the benefit stays relatively constant 

for a few hours after the end of the data assimilation. The case-day mean temperature MAE 

difference’s time series is shown in Fig. 36. For temperature, Fig. 36a indicates a benefit in the 

initial conditions that increases until the end of the data assimilation and then decreases to about 

zero by ≈22 UTC. 

 
64

Fig. 35 Time series of the differences in MAE between Exp. S and Exp. SM on the 1-km domain for a) 2-m 

temperature, b) 2-m dewpoint, c) 10-m wind speed, and d) 10-m wind direction. Positive values indicate 

Exp. SM performs better than Exp. S. A time series is plotted for each case day, as noted in the legend. 

The vertical line at 18 UTC indicates the end of the preforecast period and the beginning of the forecast 

period during which no current observations are assimilated. 

12 18 0 6 12

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 7 February

9 February

16 February

1 March

5 March

Time (UTC)

Temperature MAE Difference (K)

a)

12 18 0 6 12

−20

−10

0

10

20

30

7 February

9 February

16 February

1 March

5 March

Wind Direction MAE Difference (degrees)

Time (UTC)

12 18 0 6 12

0

0.5

1

1.5

2

2.5

7 February

9 February

16 February

1 March

5 March

Time (UTC)

Dewpoint MAE Difference (K)

12 18 0 6 12

−0.2

0

0.2

0.4

0.6

0.8

1

1.2 7 February

9 February

16 February

1 March

5 March

Time (UTC)

Wind Speed MAE Difference (m/s)

b)

c) d)
65

Fig. 36 Time series of the differences in MAE between Exp. S and Exp. SM averaged over the 5 case days on 

the 1-km domain for a) 2-m temperature, b) 2-m dewpoint, c) 10-m wind speed, and d) 10-m wind 

direction. Positive values indicate Exp. SM performs better than Exp. S. The vertical line at 18 UTC 

indicates the end of the preforecast period and the beginning of the forecast period during which no 

current observations are assimilated. 

For dewpoint (Fig. 35b), the mesonet data generally either have little effect or improve the initial 

conditions. The experiment using the mesonet data has lower dewpoint MAE throughout the 

data-assimilation period, although the magnitude of the improvement widely varies among the 

case days: ≈0.1K for 1 March to ≈2.9 K for 5 March. After the assimilation ends, the benefit of 

the mesonet data decreases, such that by 21–22 UTC there is very little benefit from the mesonet 

data (and perhaps a degradation due to the use of these observations). The case-day mean time 

series of MAE difference for dewpoint (Fig. 36b) shows improvements due to mesonet data 

reaching near zero at 21 UTC and shows small degradation, 0.1–0.2 K, for 22–01 UTC. 

While mesonet data generally improve wind speed (Fig. 35c) at the initial conditions and 

throughout the data-assimilation period, for wind direction (Fig. 35d) the results are more mixed, 

with the initial-condition wind direction at least slightly degraded by the mesonet data for each 

case. The domain’s mean wind-speed, MAE-difference time series (Fig. 36c) shows 

12 18 0 6 12

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time (UTC)

Temperature MAE Difference (K)

12 18 0 6 12

−0.1

0

0.1

0.2

0.3

0.4

0.5

Time (UTC)

Wind opeed MAE Difference (mgs)

12 18 0 6 12

−8

−6

−4

−2

0

2

4

6

8

Wind Directiwn MAE Difference (deSrees)

Time (UTC)

12 18 0 6 12 −0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Time (UTC)

De/ pwint MAE Difference (K)

a) b)

c) d)
66

improvements throughout the data-assimilation period, with the benefit decreasing to near zero at 

23 UTC. For wind direction, the case-day mean indicates a degradation of ≈9° in the initial 

conditions, but by 16 UTC an improvement of ≈8°; however, there is a slight degradation 

1 h later (17 UTC) and ≈7° improvement at 18 UTC, decreasing to near zero by 20 UTC. For 

wind direction at some times for some case days there is a lot of variability from hour to hour in 

the MAE difference between experiments. 

Overall, the mesonet data improve the surface forecasts, with the benefits on average extending 

to 21 UTC for temperature, 20 UTC for dewpoint, 22 UTC for wind speed, and 19 UTC for wind 

direction. For the 0–1,000-m AGL layer, the 19–00 UTC average MAE difference suggests that 

while the temperature is slightly improved, dewpoint and wind speed are degraded by the use of 

the mesonet data. 

6.3 Summary and Conclusions 

WRF-ARW experiments were carried out on 5 case days to investigate the impact of including 3 

types of data: TAMDAR, local rawinsonde, and mesonet surface observations. Each of these 

experiments utilizes the observations both to enhance the initial condition analysis from GFS and 

to observation nudge the model toward the observations. Observations valid up until 18 UTC are 

assimilated, with the nudging gradually decreasing to zero by 19 UTC, providing a 6-h 

preforecast period (12–18 UTC) before the 18-h forecast. To evaluate the value of these 

observations, we examined how well the model verified against observations for both the 

surface, the lowest 1,000-m AGL, and the 0–12,000-m AGL layer. 

The results reported here do not include tests of statistical significance. Inclusion of such tests 

could be beneficial in the future. 

6.3.1 TAMDAR 

Evaluation of the value of TAMDAR observations focuses on the 0-1,000-m AGL layer because 

this is the 1,000-m layer with the most TAMDAR observations. Positive impact is most 

prevalent for temperature, and then for dewpoint, while the impacts on wind are more mixed. 

The value of using TAMDAR data varies substantially from case day to case day. The 1 March 

case indicated the most benefit from using TAMDAR data for many measures, and this is the 

case day used to perform sensitivity experiments to determine the best nudging configuration for 

TAMDAR observations in Section 5. This raises the issue that the nudging configuration that 

worked best for 1 March may not be the nudging configuration that is best suited for the other 

case days. Sensitivity experiments varying the nudging configuration for the other case days 

would be helpful in determining if this is indeed the case. There are more TAMDAR 

observations available for assimilation on domain 2 (Fig. 2) for 1 March than some of the other 

case days, and this may have allowed the TAMDAR to be more effective on 1 March than on 

some of the other case days. 
67

The relative impacts on the different variables suggest that the wind observations from 

TAMDAR may be less valuable than the temperature and moisture observations. However, 

model experiments would be necessary to confirm this, especially because assimilating one 

variable can impact others. So, for example, it is possible that the assimilation of temperature is 

degrading model forecasts of wind speed. 

Because there were no TAMDAR observations within the 1-km domain during the dataassimilation period, we were unable to evaluate the horizontal radius of influence best used on 1-

km domains for above-surface observations. Thus, utilizing a 1-km domain covering an area that 

includes TAMDAR data would be beneficial toward investigating TAMDAR data assimilation 

on the 1-km domain. 

For application to the battlefield, the ability to prescribe flight paths based on what would most 

benefit the model forecasts could be very beneficial. During these 5 case days, on the 3-km 

domain the TAMDAR data are limited to the northwest quadrant of the domain on 3 of the days, 

and on the other 2 days there were also observations from a flight in the southeastern quadrant 

(Fig. 3). Presumably, the value of the TAMDAR observations may differ greatly depending on 

how the TAMDAR observations are distributed horizontally, vertically, and temporally. The 

potential to apply targeted-observations research to guide aircraft paths with TAMDAR 

observations on the mesoscale is an intriguing possibility that may have substantial benefits to 

forecast accuracy. 

6.3.2 Local Rawinsonde 

The presence of a local rawinsonde on the 1-km domain (at Miramar, CA) in general improves 

the 1–6-h forecast of temperature and wind in the lowest 1,000 m but degrades the forecast for 

dewpoint in this layer. For the longer-term forecast in the 0–1,000-m layer (7–18 h), temperature 

and dewpoint MAEs are generally improved, while wind-speed MAE is slightly degraded and 

wind direction almost unchanged. A similar comparison was completed using experiments that 

additionally used TAMDAR data. We also investigated the potential to use TAMDAR data in 

place of a local rawinsonde and found that, for these cases, TAMDAR is effective at this for 

temperature and dewpoint forecasts in the short term but not for wind. 

Since the local rawinsonde is available at 12 UTC, but the forecast period begins at 18 UTC and 

the evaluation period covers 19–00 UTC, the evaluation period is 7–12 h after the rawinsonde 

observation is made. The effect of the local rawinsonde may have been larger if the evaluation 

period was closer to the valid time of the rawinsonde. Additionally, other observations are being 

assimilated between 13 and 18 UTC, and the assimilation of these observations may very well be 

masking the potentially positive influence of the local rawinsonde. The length of the time period 

over which the rawinsonde was used for data assimilation and the horizontal radius of influence 

for this observation may not be optimal. Here, we apply the rawinsonde via observation nudging 

at full strength for a period of 1.5-h centered on the observation time (setting obs_twindo), and 

then ramp down the influence for 0.75-h before and after a full-strength nudging period. A 
68

longer time period may be appropriate for upper-air observations (e.g., 2 or 3 h at full strength 

instead of 1.5 h). The horizontal radius of influence for non-surface observations on the 1-km 

domain is set to 45-km at the surface, increasing as pressure decreases to 90-km at 500 hPa. This 

value may not be optimal for a 1-km WRF-ARW simulation. 

Having more frequent rawinsondes on the finest domain could greatly benefit efforts to evaluate 

the benefit of a local rawinsonde. The number of available above-surface observations on the 

1-km domain is limited and makes it difficult to evaluate the time evolution of the benefits of a 

local rawinsonde. Therefore, using a 1-km domain over an area completing a field experiment 

with frequent rawinsondes could be very beneficial. 

6.3.3 Denser Surface Observations 

The use of additional surface observations for enhancing initial conditions and observations was 

tested by adding the MADIS mesonet observations to the standard surface and upper-air 

observations. These observations were filtered using use/reject lists used in a test version of 

RTMA because there are known siting issues with mesonet observations. 

Overall, the mesonet data improve the 1-km domain surface forecasts, with the benefits on 

average extending to 21 UTC for temperature, 20 UTC for dewpoint, 22 UTC for wind speed, 

and 19 UTC for wind direction. For the 0–1,000-m AGL layer, the 19–00 UTC average-MAE 

difference suggests that while the temperature is slightly improved, dewpoint and wind speed are 

degraded by the use of the mesonet data. This suggests that the spreading of the effects of the 

surface observations may not be optimal. Vertically, the effects of assimilating surface 

observations is set to be spread throughout the planetary boundary layer during convective 

conditions and through the lowest 100 m during stable conditions. Reen and Stauffer (2010) 

demonstrate the benefits of such an approach. However, the influence in the boundary layer may 

be being spread across too large of an area. The horizontal radius of influence for above-surface 

observations was tested for 1 March for TAMDAR data on the 3-km, but no experiments were 

completed examining horizontal radii of influence for surface observations on any of the WRF 

domains. 

It could also be beneficial to examine the potential benefit of standard surface observations 

versus no surface observations. The experimental design examined the benefit of using no 

observations versus using standard surface and rawinsonde observations, so no experiment 

demonstrates the value of surface observations alone. However, surface observations are best 

assimilated in concert with rawinsondes: Assimilating the rawinsondes helps control the depth of 

the model’s atmospheric boundary layer, which is used to determine the depth through which 

surface observations are assimilated during convective conditions. 
69

7. References 

Chen F, Dudhia J. 2001. Coupling an advanced land surface-hydrology model with the Penn 

State-NCAR MM5 modeling system. Part I: model implementation and sensitivity. Mon Wea 

Rev. 129(4):569–585. 

Daniels TS, Murray JJ, Grainger CA, Zhou DK, Avery MA, Cagle MF, Tsoucalas G, Schaffner 

PR, Neece RT. Validation of tropospheric airborne meteorological data reporting 

(TAMDAR) temperature, relative humidity, and wind sensors during the 2003 Atlantic 

THORPEX regional campaign and the Alliance Icing Research Study (AIRS II). Paper 

presented at: 11th AMS Conference on Aviation, Range, and Aerospace; 2004 Oct 4–7; 

Hyannis (MA). 

Deng A, Stauffer D, Gaudet B, Dudhia J, Bruyere C, Wu W, Vandenberghe F, Lui Y, Bourgeois 

A. Update on WRF-ARW end-to-end multi-scale FDDA system. Paper presented at: 10th 

WRF Users’ Workshop, NCAR; 2009 Jun 23–26; Boulder (CO). 

De Pondeca MSFV, Manikin GS, Dimego G, Benjamin SG, Parrish DF, Purser RJ, Wu W, Horel 

JD, Myrick DT, Lin Y, et al. The real-time mesoscale analysis at NOAA’s National Centers 

for Environmental Prediction: current status and development. Wea Forec. 2011;26(5):593–

612. 

Dudhia J. Numerical study of convection observed during the winter monsoon experiment using 

a mesoscale two-dimensional model. J Atmos Sci. 1989;46(20):3077–3107. 

Gao F, Zhang X, Jacobs NA, Huang X, Zhang X, Childs PP. Estimation of TAMDAR 

observational error and assimilation experiments. Wea Forec. 2012;27(4):856–877. 

Gemmill W, Katz B, Li X. Daily real-time, global sea surface temperature–high-resolution 

analysis: RTG_SST_HR. NOAA/NWS/NCEP/MMAB Office Note 260. 2007 [accessed 

2013 Dec 6]. http://polar.ncep.noaa.gov/mmab/papers/tn260/MMAB260.pdf. 

Hong S-Y, Dudhia J, Chen S-H. A revised approach to ice microphysical processes for the bulk 

parameterization of clouds and precipitation. Mon Wea Rev. 2004;132(1):103–120. 

Hong S-Y, Lim J-O. The WRF single-moment 6-class microphysics scheme (WSM6). J Kor Met 

Soc. 2006;42(2):129–151. 

Janjić ZI. Nonsingular implementation of the Mellor-Yamada level 2.5 scheme in the NCEP 

meso model. NCEP Office Note. 2002;437:1–61. 
70

Jonassen MO, Olafsson H, Agustsson H, Rognvaldsson O, Reuder J. Improving high-resolution 

numerical weather simulations by assimilating data from an unmanned aerial system. Mon 

Wea Rev. 2012;140(11):3734–3756. 

Kain JS. The Kain-Fritsch convective parameterization: an update. J Appl Meteor.

2004;43(1):170–181. 

Lee JA, Kolczynski WC, McCandless TC, Haupt SE. An objective methodology for configuring 

and down-selecting an NWP ensemble for low-level wind prediction. Mon Wea Rev. 

2012;140(7):2270–2286. 

Levine SL, Lazarus SM, Splitt ME, Pondeca MSFV. The development and utility of a database 

of mesonet wind observations for use in the real-time mesoscale analysis (RTMA) system. 

Paper presented at: 15th AMS Symposium on Integrated Observing and Assimilation Systems 

for Atmosphere, Oceans, and Land Surface (IOAS-AOLS), 2011 Jan 24–27; Austin (TX). 

Levine S, Pondeca M, DiMego G. Improved quality control and metadata usage in the real time 

mesoscale analysis (RTMA) system. Paper presented at: 46th Annual CMOS 

Conference/21st AMS Conference on Numerical Weather Prediction/25th Conference on 

Weather Analysis and Forecasting; 2012 May 29 –Jun 1; Montreal (CA-QC). 

Mlawer EJ, Taubman SJ, Brown PD, Iacono MJ, Clough SA. Radiative transfer for 

inhomogeneous atmosphere: RRTM, a validated correlated-k model for the long-wave. J 

Geophys Res. 1997;102(D14):16663–16682. 

Moninger WR, Benjamin SG, Jamison BD, Schlatter TW, Smith TL, Szoke EJ. Evaluation of 

regional aircraft observations using TAMDAR. Wea Forec. 2010;25(2):627–645. 

[NOHRSC] National Operational Hydrologic Remote Sensing Center, 2004. Snow Data 

Assimilation System (SNODAS) data products at NSIDC. Boulder (CO): National Snow and 

Ice Data Center; [accessed 2013 Dec 6]. http://dx.doi.org/10.7265/N5TB14TC. 

 Office of the Federal Coordinator for Meteorological Services and Supporting Research (US), 

1997: Federal Meteorological Handbook No. 3: Rawinsonde and Pibal Observations. FCMH3-1997; [accessed 2014 May 14]. http://www.ofcm.gov/fmh3/fmh3.htm. 

Passner JE, Kirby S, Jameson, T. Using real-time weather data from an unmanned aircraft 

system to support the advanced research version of the weather research and forecast model. 

White Sands Missile Range (NM): Army Research Laboratory (US); April 2012. Report No.: 

ARL-TR-5950. 

 
71

Pondeca MSFV, Manikin G, Zhu Y, Levine S, DiMego G, Purser J, Parrish D, Keyser D, Vavra 

J. The third upgrade of NOAA’s National Centers for Environmental Prediction’s Real-Time 

Mesoscale Analysis. Paper presented at: 46th Annual CMOS Conference/21st AMS 

Conference on Numerical Weather Prediction/25th Conference on Weather Analysis and 

Forecasting; 2012 May 29–Jun 1; Montreal (CA-QC). 

Reen BP, Stauffer DR, Davis KJ. Land-surface heterogeneity effects in the planetary boundary 

layer. Boundary-Layer Met. 2014a;150(1):1–31. 

Reen BP, Dumais RE, Passner JE. Mitigating excessive drying from the use of observations in 

mesoscale modeling. Adelphi (MD): Army Research Laboratory (US); January 2014b. 

Report No.: ARL-TR-6775. 

Skamarock WC, Klemp JB, Dudhia J, Gill DO, Barker DM, Duda MG, Huang X-Y, Wang W, 

Powers JG. A description of the advanced research WRF version 3. Boulder (CO): National 

Center for Atmospheric Sciences (US); June 2008. Report No.: NCAR Tech. Note 

NCAR/TN-475+STR.

Szoke EJ, Benjamin S, Collander RS, Jamison BD, Moninger WR, Schlatter TW, Schwartz B, 

Smith TL. Effect of TAMDAR data on RUC short-term forecasts of aviation-impact fields 

for ceiling, visibility, reflectivity, and precipitation. Paper presented at: 13th AMS Conference 

on Aviation, Range and Aerospace Meteorology; 2008 Jan 21–24; New Orleans (LA). 

Zhang Y, Liu Y, Childs P, Huffman A, Nipen T. Evaluation of TAMDAR data impact on 4-km 

CONUS WRF-based RTFDDA simulations and warm-season convection prediction. Paper 

presented at: 15th AMS Symposium on Integrated Observing and Assimilation Systems for 

Atmosphere, Oceans, and Land Surface (IOAS-AOLS); 2011 Jan 24–27; Austin (TX). 
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List of Symbols, Abbreviations, and Acronyms 

3DVAR three-dimensional variational assimilation 

ABL atmospheric boundary layer 

ACARS Aircraft Communications Addressing and Reporting System 

AGL above ground level 

AMDAR Aircraft Meteorological Data Relay 

ASOS Automated Surface Observing System 

AWOS Automated Weather Observing System 

GFS Global Forecast System 

GRIB Gridded Binary 

h hour 

hPa hectopascal (=1 mb) 

KEDW Edwards Air Force Base, CA, rawinsonde location 

km kilometer 

KNKX Miramar Marine Corps Air Station, San Diego, CA, rawinsonde location 

KSNI San Nicolas Island, CA, rawinsonde location 

MADIS Meteorological Assimilation Data Ingest System 

MAE mean absolute error 

MDCRS Meteorological Data Collection and Reporting System 

METAR Aviation Routine Weather Report 

m/s meter per second 

MYJ Mellor-Yamada-Janjić turbulence parameterization 

NCAR National Center for Atmospheric Research 

NCEP-EMC National Centers for Environmental Prediction – Environmental Modeling 

Center 

PCI percentage changed improved 
73

RAOB rawinsonde observation 

RRTM Rapid Radiative Transfer Model 

RTMA Real-Time Mesoscale Analysis 

RUC Rapid Update Cycle 

SNODAS Snow Data Assimilation System 

TAMDAR Tropospheric Airborne Meteorological Data Reporting 

TAMDAR-U Tropospheric Airborne Meteorological Data Reporting - Unmanned Aerial 

System 

TKE turbulent kinetic energy 

UAS unmanned aerial system 

UTC Coordinated Universal Time 

WPS WRF Preprocessing System 

WRF-ARW Advanced Research version of the Weather Research and Forecasting model 

 
74

List of Variables 

μ = dry hydrostatic pressure 

DIST = distance between the observation and the current model point 

e = mathematical constant (sometimes known as Napier’s constant or Euler’s number) 

Fq = physical tendency terms of q 

Gq = nudging strength for q 

i = index to the current observation 

q = quantity being nudged 

qm= model value of q

qo = the observed value of q

N = total number of observations 

obs_rinxy = observation nudging radius of influence setting 

obs_twindo = observation nudging time window setting 

RIN = effective radius of influence 

Wq = spatiotemporal weighting function 

Wxy = horizontal weighting function 
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 (PDF) ATTN DTIC OCA 

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 B REEN 

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(PDF) A MALHOTRA