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  • View in gallery

    MM5 and WRF forecast temperatures (°C) in the upper troposphere with aircraft temperature observations (°C) taken while ascending and descending between 39° and 59°N latitude en route from North America to southwest Asia in February 2009 and returning to North America in April 2009.

  • View in gallery

    Difference in upper-troposphere combined MM5 and WRF temperature forecasts and aircraft observed temperatures as a function of lateral distance deviation from MM5 and WRF model tracks (R = 0.1).

  • View in gallery

    Difference in upper-troposphere combined MM5 and WRF temperature forecasts and aircraft observed temperatures compared with forecast vertical velocity within 100-km lateral distance deviation from MM5 and WRF modeled flight tracks (R = 0.4).

  • View in gallery

    WRF upper-troposphere vertical cross-sectional forecast on 14 Feb 2009 for the planned route of flight between England and Romania. Model grid spacing is defaulted to 45 km. Shown are temperature (°C; dotted horizontal contour lines), wind direction (barbs, north at top of page), wind velocity [kt (1 kt ≈ 0.5 m s−1); barb flags], cloud prediction (dark solid line), and vertical velocity (μbar s−1; vertical dotted lines). Forecast initiation was for England (label a), with termination in Romania (label c) and midpoint in the Czech Republic (label b), as depicted by the map inset at top right. Latitude (°N) and longitude (°W/E) are displayed at bottom. Altitude is displayed on the left scale [mb (=hPa)], and pressure altitude is shown on the right scale in flight levels (FL) equating to thousands of feet (160 = 16 000 ft; 1 ft ≈ 0.3048 m).

  • View in gallery

    Radiosonde station locations, land surface types and surface elevation profile in meters above sea level for MM5 and WRF modeled flight tracks, and actual aircraft observation flight tracks during February and April 2009. Chart adapted from the HWSD (Fischer et al. 2011).

  • View in gallery

    Upper-troposphere aircraft temperature observations and WRF temperature forecasts over land compared with temperature error and forecast vertical velocity coupling ().

  • View in gallery

    As in Fig. 6, but over water ().

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Upper-Troposphere MM5 and WRF Temperature Error and Vertical Velocity Coupling

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  • 1 Department of Earth and Atmospheric Sciences, University of Houston, Houston, Texas
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Abstract

The fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the Weather Research and Forecasting Model (WRF) have been employed to predict troposphere temperatures for atmospheric study and operational decision making with positive results. Temperature bias in MM5 and WRF has been noted in previous troposphere studies through radiosonde vertical profile comparison; however, long-range horizontal in situ temperature observations have never been utilized to assess MM5 and WRF upper-troposphere temperature prediction. This study investigates upper-troposphere temperature forecasting of MM5 and WRF utilizing long-range in situ observations linking temperature error to forecast vertical velocity within the upper troposphere over surface elevation changes and different surface types. Temperature observations were taken during flights over North America, Europe, and southwest Asia between 6000 and 7600 m above sea level and compared with MM5 and WRF upper-troposphere forecasts. Regression analysis indicated MM5 and WRF upper-troposphere temperature forecast errors were related to changes in forecast vertical velocities within 100 km laterally of the modeled flight tracks between 39° and 59°N latitude. Temperature error and forecast vertical velocity coupling occurred in MM5 and WRF forecasts over land, while no evidence of temperature error and forecast vertical velocity coupling in MM5 or WRF forecasts was found over water. Evaluation of MM5 and WRF forecasts displayed varying results of temperature error and forecast vertical velocity coupling between specific surface elevations above sea level, vegetative cover, and urban influences.

Corresponding author address: Kelly Soich, 4800 Calhoun Rd., Houston, TX 77004. E-mail: k.soich@att.net

Abstract

The fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) and the Weather Research and Forecasting Model (WRF) have been employed to predict troposphere temperatures for atmospheric study and operational decision making with positive results. Temperature bias in MM5 and WRF has been noted in previous troposphere studies through radiosonde vertical profile comparison; however, long-range horizontal in situ temperature observations have never been utilized to assess MM5 and WRF upper-troposphere temperature prediction. This study investigates upper-troposphere temperature forecasting of MM5 and WRF utilizing long-range in situ observations linking temperature error to forecast vertical velocity within the upper troposphere over surface elevation changes and different surface types. Temperature observations were taken during flights over North America, Europe, and southwest Asia between 6000 and 7600 m above sea level and compared with MM5 and WRF upper-troposphere forecasts. Regression analysis indicated MM5 and WRF upper-troposphere temperature forecast errors were related to changes in forecast vertical velocities within 100 km laterally of the modeled flight tracks between 39° and 59°N latitude. Temperature error and forecast vertical velocity coupling occurred in MM5 and WRF forecasts over land, while no evidence of temperature error and forecast vertical velocity coupling in MM5 or WRF forecasts was found over water. Evaluation of MM5 and WRF forecasts displayed varying results of temperature error and forecast vertical velocity coupling between specific surface elevations above sea level, vegetative cover, and urban influences.

Corresponding author address: Kelly Soich, 4800 Calhoun Rd., Houston, TX 77004. E-mail: k.soich@att.net

1. Introduction

a. Background

Atmospheric temperature prediction has improved escalating atmospheric modeling skill and provided high degrees of success in regional climate modeling. Prior to computer modeling, weather prediction methods utilized manual calculations to solve lengthy mathematical formulas forecasting atmospheric temperature on which to base operational decisions (i.e., optimal aircraft cruise altitude) (Zhu et al. 2002). Advancements in computer technology allow atmospheric models to quickly calculate atmospheric temperatures and rapidly assimilate sounding data, improving the skill of meteorological predictions (Ali 2004). Computer technology improvements in atmospheric model computations (i.e., processor speed) require continued testing and validation to ensure atmospheric temperature modeling skill is not degraded (Cheng and Steenburgh 2005; Knutti et al. 2010). Therefore, atmospheric temperature forecasts require comparison with in situ temperature measurements and other modeled physical parameters (i.e., forecast vertical velocity) to determine if temperature errors are exhibited in model prediction (Manning and Davis 1997).

Atmospheric model developments utilizing improved computer processing have introduced models such as the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) described by Grell et al. (1994), replacing time-consuming manual statistical computations exhibited by Cornett and Randerson (1977). The MM5 has enhanced lower-troposphere and stratosphere temperature prediction by utilizing model-to-model comparisons, in situ aircraft and radiosonde measurements exhibited in regional meteorological investigation by Chandrasekar et al. (2002), boundary layer study by Song et al. (2004), and tropical cyclone analysis by Pattanayak and Mohanty (2008). MM5 has been used in Antarctica to compare forecast temperature and radiosonde soundings from the surface to 700 hPa by Guo et al. (2003), aircraft and radiosonde soundings up to 400 m AGL in Greenland katabatic layer studies by Bromwich et al. (2001), and short-range forecast skill in the northeast United States by comparing model and observation network temperatures within 2 m AGL by Jones et al. (2007). Research using MM5 has provided insight into regional atmospheric temperature prediction from the surface to 700 hPa by identifying varying MM5 temperature forecast skill by each study. However, to our knowledge there has been no study addressing the upper-troposphere temperature forecasting capabilities of MM5.

With MM5 successfully used as a forecasting tool in the lower troposphere, the Weather Research and Forecasting Model (WRF) described by Skamarock et al. (2008) and discussed by Zhang et al. (2009) has been developed as a replacement for MM5. Previous WRF forecast assessments have proved comparable to MM5 with improved capability of rapid data assimilation and nudging in WRF allowing improvements in model skill over MM5 (Pattanayak and Mohanty 2008; Wang et al. 2008). Improved assimilation of in situ measurements and radiosonde soundings suggest WRF skill within the troposphere has improved prediction of future temperature conditions over populated areas such New England and western Europe (Hines and Bromwich 2008; Coniglio et al. 2010; Wilson et al. 2011, 2012). For unpopulated regions where assimilation data are sparse and no upper-atmospheric temperature measurements exist (i.e., Atlantic Ocean and southwest Asia), little evaluation of WRF upper-troposphere temperature prediction has been accomplished, suggesting an unverified condition of WRF temperature modeling (Cardinali and Isaksen 2003). For this reason, WRF upper-troposphere temperature forecasts require exploration to identify anomalies in upper-troposphere temperature prediction that may go undetected.

b. Motivation

To use MM5 and WRF forecasts with confidence, the capability to predict temperature within the upper troposphere requires thorough validation encompassing regions without radiosonde capability or frequent aircraft travel. MM5 and WRF are applied in areas where temperature biasing might place upper-troposphere forecast users (i.e., aircraft flight planners) in a vulnerable position (i.e., selection of aircraft cruise altitudes). Vulnerabilities to the upper-troposphere forecast user may include erroneous areas of turbulence or incorrect cloud moisture prediction resulting in unexpected ice accumulation on aircraft control surfaces, reducing safety for crew and passengers (Zhu et al. 2002). Scenarios similar to these must be reduced in order for upper-troposphere prediction users to safely alleviate unnecessary aircraft operating expenses and eliminate the potential for aircraft loss (Mass 2006). To assist in this goal, MM5 and WRF temperature forecasting was explored across the upper troposphere to include areas of sparse radiosonde or aircraft in situ measurement data since temperature is a key variable in calculations used to predict other physical parameters such as cloud development and vertical motion of the atmosphere.

This study began with operational testing of MM5 and WRF upper-troposphere forecasts for worldwide use by aircraft to identify any temperature forecast anomalies that may exist. Operational testing was accomplished on a series of transworld flights within the upper troposphere using predesignated flight routes between 39° and 59°N latitude. MM5 and WRF upper-troposphere multileg vertical cross-sectional temperature and vertical velocity forecasts were obtained prior to observation flights where upper-troposphere temperatures were recorded from aircraft navigation system displays by flight crews. MM5 and WRF temperature errors (i.e., difference between forecast and observed temperature) were determined and RMSE computed, yielding an RMSE of 1.8°C (Fig. 1). The RMSE of 1.8°C was initially thought to have been due to lateral distance deviation of the aircraft from the MM5 and WRF modeled flight tracks as a result of required course deviations by air traffic control or hazardous weather avoidance.

Fig. 1.
Fig. 1.

MM5 and WRF forecast temperatures (°C) in the upper troposphere with aircraft temperature observations (°C) taken while ascending and descending between 39° and 59°N latitude en route from North America to southwest Asia in February 2009 and returning to North America in April 2009.

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

A correlation test was accomplished between upper-troposphere combined MM5 and WRF temperature error and lateral distance deviation from the modeled flight tracks producing a correlation coefficient R of 0.1, suggesting lateral distance deviation was not the prime contributor to the temperature RMSE and indicating another cause (Fig. 2). MM5 and WRF upper-troposphere temperature errors were plotted in time series producing a similar signature as MM5 and WRF upper-troposphere forecast vertical velocity (Fig. 3). The similarity in signature between MM5 and WRF upper-troposphere temperature error and forecast vertical velocity prompted a correlation test producing an R = 0.4. An R = 0.4 suggests a relationship between MM5 and WRF upper-troposphere temperature error and forecast vertical velocity providing the motivation for this study and attempting to answer the following question:

  • 1) Is temperature error and forecast vertical velocity coupling an anomaly in MM5 and WRF upper-troposphere temperature forecasts?
Further examination of MM5 and WRF upper-troposphere temperature error (Fig. 1) suggests a variation of temperature error within 100 km of lateral distance deviation from modeled flight tracks between 39° and 59°N, leading to the following question:
  • 2) Is there a lateral distance deviation from upper-troposphere MM5 or WRF modeled tracks where temperature error and forecast vertical velocity coupling diminishes?
Additionally, studies on land–atmosphere coupling and land-cover changes affecting heat flux by Evans and Geerken (2004), Giorgi, (2006), Sheffield and Wood (2008), Pitman et al. (2009), Myoung et al. (2012), de Noblet-Ducoudré et al. (2012), and Boisier et al. (2012) prompted the following question:
  • 3) Is temperature error and forecast vertical velocity coupling in MM5 and WRF upper-troposphere temperature forecast related to or enhanced by geographical traits such as changes in surface elevation above sea level or surface types such as land, water, urban influences, or vegetation?
RMSE and regression analysis was performed on MM5 and WRF upper-troposphere temperature error data indicating associations between temperature error and forecast vertical velocity over different surface elevations above sea level and surface types such as land, water, urban, and vegetation (Jolliffe 2007). Evaluation of these parameters at upper-troposphere levels provided insight into an MM5 and WRF model anomaly shedding light into MM5 and WRF upper-troposphere temperature forecast performance (Cocke et al. 2006).
Fig. 2.
Fig. 2.

Difference in upper-troposphere combined MM5 and WRF temperature forecasts and aircraft observed temperatures as a function of lateral distance deviation from MM5 and WRF model tracks (R = 0.1).

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

Fig. 3.
Fig. 3.

Difference in upper-troposphere combined MM5 and WRF temperature forecasts and aircraft observed temperatures compared with forecast vertical velocity within 100-km lateral distance deviation from MM5 and WRF modeled flight tracks (R = 0.4).

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

2. Experiment design

a. Methodology overview

MM5 and WRF upper-troposphere temperature and vertical velocity forecasts were provided by the U.S. Air Force Weather Agency (AFWA) and temperature observations were taken using aircraft navigation systems during long-range cruise flights in the upper troposphere. Aircraft navigation system–displayed temperature was recorded by the flight crew and compared to MM5 and WRF forecast temperature to determine temperature error. Aircraft observation and radiosonde temperatures were compared when available ensuring anomalies were not present in aircraft systems, which could corrupt model testing. Datasets were stratified and tested utilizing RMSE and regression analysis to identify statistically significant temperature error and vertical velocity coupling relationships. Statistically significant data were tested to a 95% confidence interval confirming temperature error and vertical velocity coupling relationships in MM5 and WRF upper-troposphere forecasts.

b. Temperature observation collection

Aircraft type selection was critical to best accomplish upper-troposphere temperature observations (Cardinali et al. 2004; Wroblewski et al. 2010). Larger jet aircraft were unfavorable because of cruise altitudes above upper-troposphere levels, while smaller aircraft were unable to operate at the distances required for long-range observations (Moninger et al. 2003). Aircraft availability was considered, requiring upper-troposphere temperature observations to be accomplished concurrent with an already designated flight, easing the selection process. The aircraft of choice was the C-130 Hercules, which met all requirements of cruise altitude, observation recording feasibility, distance capability, and availability. The aircraft was provided with Wyoming Air National Guard cooperation and was supported by 187th Airlift Squadron flight crews.

Atmospheric temperature was provided by a single Goodrich 102A external probe mounted on the aircraft fuselage feeding data to the aircraft air data computer (ADC) and the total air temperature gauge (Goodrich Sensor Systems 2002a). The probe integrates protection against inlet blockage from dust, insects, or bird strikes and provides thermal protection to prevent inlet blockage from ice formation without degrading accuracy (Goodrich Sensor Systems 2002b). Total air temperature compressibility correction factors were applied to C-130 temperature gauge observations per aircraft operating procedures in agreement with findings by Khelif et al. (1999). Once aircraft capability was identified and found to be satisfactory, a spreadsheet for manual in-flight data recording was developed using Microsoft Excel. Upper-troposphere temperature data collection was then accomplished on predesignated flights while established at cruise altitude, reducing ADC and navigation solution errors by aircraft climb or descent (Cole and Jardin 2000).

Upper-troposphere temperature observations took place on one transoceanic and three transcontinental flights in February 2009 and three transcontinental flights in April 2009 between 39° and 59°N, totaling seven separate observation datasets. Upper-troposphere temperature observations were manually recorded in flight from aircraft navigation system displays and total air temperature gauge readings between 6000 and 7600 m above sea level every 5 min, resulting in 25-km intervals. Data recording included universal coordinated time (UTC), observation geographical coordinates, aircraft altimeter, , and aircraft navigation system–displayed ambient air temperature. Compressibility at the temperature probe intake required a correction factor of −10°C [Eq. (1)] (U.S. Air Force 2006) to all readings deriving observed upper-troposphere ambient air temperature and found to be equivalent when compared with ADC air temperature calculations (Goodrich Sensor Systems 2002a):
e1
Aircraft geographical position and altitude were plotted on printed MM5 and WRF forecast maps and corresponding MM5 or WRF upper-troposphere temperatures values were manually recorded into data logs.

c. Temperature observation and aircraft instrument system verification

Upper-troposphere radiosonde temperature records were retrieved postflight near the actual aircraft flight tracks when available using the University of Wyoming Upper Air Sounding Database (University of Wyoming 2012) and are shown in Table 1. Aircraft temperature observation altitudes are not shown on radiosonde data, requiring interpolation of rounded to the whole number corresponding to aircraft navigation system display temperature format. Here was corrected for atmospheric heating or cooling as a result of time through interpolation of between the 0000 and 1200 UTC soundings surrounding the time of aircraft passage near the sounding station. The term is compared with by
e2
yielding a temperature delta range from +2°C (12 February) to −3°C (4 April). The remained warmer during most flights in February 2009 while decreasing to a cooling trend for flights in April 2009 over varying lateral distance deviations between sounding locations and at aircraft observation heights. Although interpolation can introduce some uncertainty into the analysis, averaged of the seven sounding stations within 100 km of the aircraft indicated small delta values (Table 1). Here indicated an average value of −1.0°C (standard deviation of 1.2°C), suggesting no visible shift in measurements, which may be due to indicator malfunction or probe inlet blockage. Therefore, comparison of aircraft observations with radiosonde measurements promoted reasonable confidence in data purity similar to Moninger et al. (2003) and Benjamin et al. (2010).
Table 1.

Comparison of upper-troposphere radiosonde temperature soundings with aircraft observed temperature near actual observation aircraft flight tracks (University of Wyoming 2012). No reporting stations available for 13 Feb because of transoceanic flight.

Table 1.

d. Source of modeling data

Determining temperature error and vertical velocity coupling for MM5 and WRF within the upper troposphere required employment of model forecasts in a similar manner as a potential user (i.e., aviation flight planning). To simulate forecast user employment, access was obtained to use the AFWA Joint Air Force and Army Weather Information Network (JAAWIN) Interactive Grid Analysis and Display System (IGrADS) to run MM5 and WRF forecasts in which were compared (Telfeyan et al. 2005). At the time of study initiation, JAAWIN’s authorized computer model coverage was the MM5 for North America and version 3.0.1.1 of the WRF variational data assimilation (WRF-Var) for the Atlantic Ocean, Europe, and southwest Asia. The IGrADS interface allowed forecast users to select certain forecast physical parameters such as isotherms, lower and upper height boundaries, model route start and stop locations, a model route segment midpoint, and forecast start and stop times for the model route segments. MM5 and WRF physics packages and domain settings were configuration controlled by JAAWIN with no ability for modification by the IGrADS user serving as a limitation preventing physics package modification for testing.

JAAWIN’s forecast domains covered the landmasses of North America (MM5), Europe, and Asia (WRF). JAAWIN-controlled parent domains for MM5 and WRF were set at 45 km with 15-km nesting encompassing all modeled flight tracks. MM5 and WRF utilized the Rapid Radiative Transfer Model (RRTM) longwave radiation and simple shortwave radiation schemes with the Noah land surface model. The Medium-Range Forecast planetary boundary layer and Kain–Fritsch cumulus parameterization schemes were selected by JAAWIN for MM5 using fixed-sigma vertical layering and Multivariate Optimum Interpolation assimilation. MM5 utilized the upper-radiative-boundary conditions that were standard on the MM5 model, while JAAWIN employed vertical velocity and traditional Rayleigh dampening for WRF upper-boundary conditions. JAAWIN’s approved WRF physics packages consisted of the Yonsei University planetary boundary layer, new Kain–Fritsch cumulus parameterization, and WRF Single Moment Five (WSM 5) schemes employing floating sigma vertical layering and three-dimensional variational data assimilation (3DVAR). The vertical boundaries of the MM5 and WRF model runs were set to begin at the surface and terminate at a height of 9100 m. In between 500 and 400 hPa the models have five layers, each of them between 500 and 540 m thick.

Upper-troposphere temperature observation time periods were identified during February and April 2009 based on aircraft availability of flights over sparsely traveled or radiosonde deficient regions within the upper troposphere. Once flight routes were designated and flight planning completed, the MM5 and WRF multileg forecast route parameters were entered into JAAWIN’s online IGrADS user interface 3 h prior to flight departure and completed within 5 min of model route parameter entry. Although temperature observation flight routes used great circle courses, JAAWIN’s IGrADS user interface system operated in straight line courses requiring desired flight altitudes, initial starting point, midpoint, and termination point. The takeoff time at the start point, estimated time over the midpoint, and estimated landing time at the termination point were entered into the IGrADS user interface producing time accurate forecasts across the flight route requiring no additional time correction needed between aircraft observed and forecast temperature data. MM5 and WRF forecast outputs were printed for comparison with isotherms depicted in degrees Celsius, forecast vertical velocity depicted in microbars per second (1 μbar = 0.1 Pa), cloud formation profiles, altitude in thousands of feet, and latitude and longitude in degrees (Fig. 4).

Fig. 4.
Fig. 4.

WRF upper-troposphere vertical cross-sectional forecast on 14 Feb 2009 for the planned route of flight between England and Romania. Model grid spacing is defaulted to 45 km. Shown are temperature (°C; dotted horizontal contour lines), wind direction (barbs, north at top of page), wind velocity [kt (1 kt ≈ 0.5 m s−1); barb flags], cloud prediction (dark solid line), and vertical velocity (μbar s−1; vertical dotted lines). Forecast initiation was for England (label a), with termination in Romania (label c) and midpoint in the Czech Republic (label b), as depicted by the map inset at top right. Latitude (°N) and longitude (°W/E) are displayed at bottom. Altitude is displayed on the left scale [mb (=hPa)], and pressure altitude is shown on the right scale in flight levels (FL) equating to thousands of feet (160 = 16 000 ft; 1 ft ≈ 0.3048 m).

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

During flight, forecast (denoted by subscript F) upper-troposphere temperature and vertical velocity were extracted from the MM5 and WRF printed outputs. A grid was included on each printed MM5 and WRF output and used to plot aircraft position (latitude and longitude) on the x axis and aircraft altitude in thousands of feet on the y axis. Isotherms on the MM5 and WRF forecast outputs were in 4°C increments and isotherms were not always depicted at the intersection of aircraft position and altitude so was interpolated by
e3a
where is the aircraft observation altitude, is the matching isotherm altitude height below , is the matching isotherm height above , is the modeled isotherm corresponding to , and is the modeled isotherm corresponding to resulting in a computed rounded to the whole number corresponding to aircraft navigation system temperature format. The microbar gradients varied on the MM5 and WRF forecast outputs and microbars were not always depicted at the aircraft position and altitude intersection, therefore interpolation was accomplished by
e3b
where represents the latitude and longitude of the observation, is the latitude and longitude of the model depicted microbar intercept left of on the x axis, is the model depicted microbar intercept on the x axis to the right of , is the corresponding microbar value of , and is the corresponding microbar value of . Differences between the latitude and longitude points (, , and ) in Eq. (3b) represent distances in kilometers and were computed using global positioning system (GPS) software. Manual extraction of model values occurred three times with navigational plotting equipment capable of measuring in 1.0° angles and dividing spatial areas down to 1.5 cm. Interpolation presents a potential error for the analysis and was mitigated to the maximum extent possible by using the average of the three interpolated values suggesting the estimated error to be less than 0.5°C and 0.5 μbar s−1 based on the resolution of the model values.

e. Postflight processing

With lateral distance deviation from MM5 and WRF modeled tracks noted as insignificant () and and computational resolutions of 1.0°C, lateral corrections of to match MM5 and WRF modeled flight tracks were deemed unnecessary. Here were arranged by smallest to largest lateral distance deviation from the modeled flight tracks, and within 100 km of lateral deviation were used to provide representative data nearest the modeled flight tracks for analysis. Data was classified into 0–50- and 51–100-km datasets to determine a point where temperature error and coupling may no longer exist. Surface elevation above sea level was derived through charted GPS elevation data and classified into sets of 100-m increments ascending in height from 0 to 699 m above sea level. For heights >699 m in surface elevation above sea level, data points were combined into varying categories because of diminishing data populations n.

Upper-troposphere temperature observations were classified referencing the Harmonized World Soil Database (HWSD) depicted in Fig. 5 to determine if upper-troposphere temperature error and coupling favored a surface type (Fischer et al. 2011). The HWSD map is a compilation of six separate supplementary databases allowing surface type classification by land, water, grass/scrub brush, crops, forest, no vegetation, and urban development. The database map allowed category definition up to >75% vegetation type; however, interference by blending of the 50%–75% and >75% map categories caused difficulty declaring >75% coverage for all . Therefore the surface type was declared using >50% for vegetation cover type and >10% urban coverage. Snow cover was indicated by archived data over forest surface type on both MM5 flights over southeast Canada (from Quebec to Caribou; n = 7) and on both WRF flights between Regensburg, Germany, and the Czech Republic border (n = 4). All other surface types did not indicate snow cover (Montreal Weather Center 2012; National Weather Service 2012).

Fig. 5.
Fig. 5.

Radiosonde station locations, land surface types and surface elevation profile in meters above sea level for MM5 and WRF modeled flight tracks, and actual aircraft observation flight tracks during February and April 2009. Chart adapted from the HWSD (Fischer et al. 2011).

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

f. Analysis

RMSE was determined for each dataset measuring skill as a potential marker to highlight the presence of temperature error and coupling. The initial step was to determine the upper-troposphere temperature error between and defined as
e4a
RMSE was then computed for datasets by
e4b
where n represents the number of observations (Stull 2000). A regression analysis was performed on each dataset to establish a coupling relationship between and using a simple linear model detailed by Riggs (1985) and defined as
e5a
where the slope a of the linear equation is computed by
e5b
and the intercept b of the linear equation derived from
e5c
The coefficient of determination was used as a primary discriminator to assess the performance of the linear data fit calculated by
e6a
with representing the sum squares of deviation of from the experimental average error for each observation point j (1 ≤ jn):
e6b
and signified by the totals of sum square error and regression error depicted as
e6c
in which represents the sum square error of the residuals γ of j (Riggs 1985):
e6d
A standard error of regression was computed to further substantiate fit of regression through assessment of dataset accuracy (Riggs 1985). Here depicted the experimental accuracy related to along the regression line, expressed as
e7
The lower (denoted by subscript L) and upper (denoted by subscript U) bounded confidence interval (CI) of 0.95 was computed regarding using
e8a
In this definition t is the number resultant from the t statistic, and the p value P from the statistical significance test of and SE the standard error of :
e8b
where i is the number of independent variables (Riggs 1985).
The and coupling identification was accomplished using , rounded to one decimal place where demonstrates a perfect fit (Knutti et al. 2010). After was determined, CI was tested by
e9
where inclusion of zero (CI = 0) signifies rejection of and coupling qualifying determinations made by .

3. Results

a. MM5 and WRF upper-troposphere forecast temperature RMSE evaluation

RMSE scores were computed for all upper-troposphere MM5 and WRF data subcategories listed in Tables 26 and tested as markers to help identify and coupling prior to regression analysis. RMSE analysis indicated WRF exhibited good ( RMSE ≤ 2.0°C) skill (WRF 0–50-km land RMSE = 1.8°C; WRF 51–100-km land RMSE = 1.1°C) while MM5 displayed moderate (2.1° ≤ RMSE ≤ 5.0°C) skill (MM5 0–50-km land RMSE = 2.2°C; and MM5 51–100-km land RMSE = 2.4°C) in upper-troposphere forecasts over land between 0–50- and 51–100-km lateral distance deviation from modeled flight tracks (Table 2). MM5 and WRF exhibited good skill in upper-troposphere forecasts over water between 0- and 50-km lateral distance deviation from modeled flight tracks (MM5 and WRF 0–50-km water RMSE = 2.0°C) and improvement in skill by MM5 (MM5 51–100-km water RMSE = 1.5°C) and WRF (WRF 51–100-km water RMSE = 1.0°C) upper-troposphere forecasts over water between 51- and 100-km lateral distance deviation from modeled flight tracks.

Table 2.

RMSE (°C) and regression analysis results for temperature error (°C) and forecast vertical velocity (μbar s−1) coupling for lateral distance deviation from MM5 and WRF modeled flight track over land and water. Boldface figures indicate , and italicized figures indicate CI = 0.

Table 2.
Table 3.

RMSE (°C) and regression analysis results for upper-troposphere temperature error (°C) and forecast vertical velocity (μbar s−1) coupling over surface elevations ≤499 m above sea level. Boldface figures indicate , and italicized figures indicate CI = 0.

Table 3.
Table 4.

As in Table 3, but for surface elevations >499 m above sea level.

Table 4.
Table 5.

RMSE (°C) and regression analysis results for upper-troposphere temperature error (°C) and forecast vertical velocity (μbar s−1) coupling over land, water, crops, and grass/scrub brush surface types. Boldface figures indicate , and italicized figures indicate CI = 0.

Table 5.
Table 6.

As in Table 5, but for forest, no vegetation, urban, and nonurban surface types.

Table 6.

MM5 indicated good skill in upper-troposphere forecasts over surface elevations ≤299 m above sea level differing by a RMSE = 0.2°C (Table 3). MM5 exhibited moderate skill over surface elevations between 300 and 399 m (MM5 300–399-m RMSE = 3.4°C) and between 400 and 499 m above sea level (MM5 400–499-m RMSE = 3.7°C) (Table 3). WRF indicated moderate skill over surface elevations between 100 and 199 m above sea level (WRF 100–199-m RMSE = 2.8°C) improving in skill between 0 and 99 m (WRF 0–99-m RMSE = 1.3°C), 200 and 299 m (WRF 200–299-m RMSE = 0.8°C), 300 and 399 m (WRF 300–399-m RMSE = 1.2°C), and between 400 and 499 m (WRF 400–499-m RMSE = 1.5°C) surface elevation above sea level. MM5 was not utilized over surface elevations >499 m above sea level (Europe and southwest Asia) but WRF was used for upper-troposphere forecasts producing RMSE scores ranging between 0.7°C (good) and 2.9°C (moderate) over surface elevations >499 m above sea level indicating varied skill with increased surface elevation (Table 4).

MM5 and WRF upper-troposphere forecast exhibited moderate skill over grass/scrub brush (MM5 grass/scrub brush RMSE = 2.3°C; WRF grass/scrub brush RMSE = 2.4°C). WRF forecasts indicated good skill over crops (WRF crops RMSE = 0.9°C), while MM5 forecast skill remained moderate (MM5 crops RMSE = 4.1°C) (Table 5). MM5 and WRF upper-troposphere forecasts exhibited good skill over forest regions (MM5 forest RMSE = 0.8°C; WRF forest RMSE = 1.8°C) and urban areas (MM5 urban RMSE = 0.9°C; WRF urban RMSE = 1.5°C) (Table 6). MM5 showed moderate skill over nonurban areas (MM5 nonurban RMSE = 2.4°C) and nonvegetated areas were not used in MM5 so a RMSE score was not computed. WRF was utilized over nonvegetated areas indicating good skill (WRF no vegetation RMSE = 1.6°C) similar to upper-troposphere forecasts over areas of nonurban development (WRF nonurban RMSE = 1.3°C).

b. Lateral distance deviation from MM5 and WRF modeled flight track

MM5 and WRF upper-troposphere data within 100 km laterally of MM5 and WRF forecast modeled flight tracks were tested and results detailed in Table 2. Strong and coupling (R2 = 0.6–0.9) was indicated in MM5 upper-troposphere forecasts over land between 0–50- and 51–100-km lateral distance deviation from modeled flight tracks where MM5 0–50-km land and MM5 51–100-km land and confidence intervals were exclusive of zero (). The and coupling was rejected between 0–50- and 51–100-km lateral distance deviation from modeled flight tracks in MM5 upper-troposphere forecasts over water where MM5 0–50-km and MM5 51–100-km water (). WRF upper-troposphere forecasts exhibited moderate and coupling (R2 = 0.3–0.5) over land between 0- and 50-km lateral distance deviation from modeled flight tracks where WRF 0–50-km land () and no and coupling exhibited over water between 0- and 50-km lateral distance deviation from modeled flight tracks in WRF (WRF 0–50-km water ) upper-troposphere forecasts. Between 51- and 100-km lateral distance deviation from modeled flight tracks, WRF upper-troposphere forecasts continued to indicate moderate and coupling over land (WRF 51–100-km land ; ) with no indication of and coupling in WRF upper-troposphere forecasts over water (WRF 51–100-km water ).

c. Changes in surface elevation above sea level

MM5 and WRF surface elevation datasets were tested determining if and coupling in MM5 and WRF upper-troposphere forecasts is specific to surface elevation above sea level. Strong to moderate and coupling was exhibited by MM5 (MM5 300–399 m ) and WRF (WRF 300–399 m ) upper-troposphere forecasts over surface elevations between 300 and 399 m above sea level exhibited by MM5 and WRF 300–399-m (Table 3). No indication of and coupling was indicated in MM5 upper-troposphere forecasts over surface elevations between 0 and 99 m above sea level where MM5 0–99-m . MM5 and WRF upper-troposphere forecasts over surface elevations between 100–299 and 400–499 m above sea level indicated no and coupling and MM5 and WRF 100–299-m and 400–499-m CI = 0. Surface elevation datasets >499 m above sea level contained no MM5 upper-troposphere data; however, WRF upper-troposphere forecasts exhibited strong and coupling over surface elevations between 600 and 699 m (WRF 600–699-m ; ) and between 700 and 999 m (WRF 700–999 m ; ) above sea level with (Table 4).

d. Surface type

Upper-troposphere temperature error data were classified by surface type isolating and coupling in MM5 and WRF over land, water, vegetation, and urban surface type with findings displayed in Tables 5 and 6. Weak and coupling (R2 = 0.1 or 0.2) was indicated in MM5 (MM5 land ; ) and WRF (WRF land ; ) upper-troposphere forecasts over land, while and coupling was not present in MM5 and WRF upper-troposphere forecasts over water with MM5 and WRF water CI = 0. In MM5 upper-troposphere forecasts over grass/scrub brush, and coupling was not indicated; however, WRF upper-troposphere forecasts did indicate moderate and coupling over grass/scrub brush (WRF grass/scrub brush ; ) and weak to moderate and coupling was indicated in MM5 (MM5 crops ; ) and WRF (WRF crops ; ) upper-troposphere forecasts over crops (Table 5). In MM5 and WRF upper-troposphere forecasts over forest-covered surfaces with CI = 0, and coupling was not detected and there was no indication of and coupling in WRF upper-troposphere forecasts over nonvegetated areas (WRF no vegetation ). MM5 and WRF upper-troposphere forecasts indicated and coupling differently over urban influences, where MM5 upper-troposphere forecasts (MM5 nonurban ; ) indicated and coupling over nonurban influences and WRF upper-troposphere forecasts (WRF urban ; ) indicated and coupling over urban influences (Table 6).

4. Discussion

Regression analysis indicated significant statistical evidence supporting and coupling in MM5 and WRF upper-troposphere forecasts within 100-km lateral distance deviation from modeled flight tracks, over different surface type and surface elevations above sea level. An attempt was made to correlate RMSE with and coupling that posted an indicating RMSE is not a good indicator of and coupling presence in MM5 and WRF upper-troposphere forecasts. Rejection of RMSE as a and coupling indicator in MM5 and WRF upper-troposphere forecasts is a result of similar RMSE values where and coupling exists (i.e., WRF land RMSE = 1.5°C and ) and where and coupling is not present (i.e., WRF water RMSE = 1.8°C and ) (Table 5). Examination of Fig. 3 indicated positive and negative temperature biases that tend to mirror and initially pointed toward and coupling in MM5 and WRF upper-troposphere forecasts. When were arranged in the order of coldest to warmest a visual depiction of and coupling was displayed corresponding to noticeable fluctuations in (Fig. 6).

Fig. 6.
Fig. 6.

Upper-troposphere aircraft temperature observations and WRF temperature forecasts over land compared with temperature error and forecast vertical velocity coupling ().

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

Figure 6 displays WRF and data over land illustrating and coupling where were arranged from coldest to warmest and is characteristic of MM5 and WRF upper-troposphere forecasts where and coupling is present (; ). Figure 6 suggests when TE ≥ 2.0°C a corresponding increase in magnitude is observed as exhibited by n = 25, n = 65, and n = 81.

Figure 7 displays WRF and data over water where were arranged from coldest to warmest and no and coupling present ( or CI = 0), which is representative for MM5 and WRF upper-troposphere forecasts that did not indicate and coupling ( or CI = 0). The increases in magnitude of displayed in Fig. 6 corresponding to TE ≥ 2.0°C were not displayed in Fig. 7 where changes in magnitude were independent of in MM5 and WRF upper-troposphere forecasts over water (n = 10, n = 36, and n = 44). Therefore appears to be the driver in erroneous events over land in MM5 and WRF upper-troposphere forecasts, which may result in erroneous cloud formation prediction causing incorrect forecasting of precipitation and turbulence.

Fig. 7.
Fig. 7.

As in Fig. 6, but over water ().

Citation: Journal of Applied Meteorology and Climatology 52, 5; 10.1175/JAMC-D-12-092.1

Since and coupling in MM5 (MM5 land ; ) and WRF (WRF land ; ) upper-troposphere forecasts occurs over land rather than over water (WRF and MM5 water or CI = 0) the possibility exists that differential heating and/or humidity may be a cause for MM5 and WRF upper-troposphere (Table 5). Where MM5 and WRF upper-troposphere forecasts have a cold bias, entrainment of air into areas of may actually be dryer and warmer than predicted, causing increased and overpredicting , which creates incorrect turbulence intensity (Fig. 6; n = 29, n = 69, and n = 97). Underforecasting of temperature in MM5 and WRF upper-troposphere forecasts may be tied to upwelling longwave radiation incorrectly parameterized over land in RRTM because of changes in upwelling longwave radiation angle and azimuth resulting from changes in slope at different surface elevations above sea level (Yang et al. 2012). MM5 and WRF upper-troposphere may possibly be forcing incorrect through changes in radiative flux as a result of land surface changes between urban and urban-free regions analogous to large cities surrounded by expanses of rolling hills and vegetation. The and coupling is not observed in MM5 and WRF upper-troposphere forecasts over water where water bodies do not experience land surface changes allowing for homogeneous radiative flux and decreases in occurrence of as depicted in Fig. 7.

A second mechanism for MM5 and WRF upper-troposphere instigating incorrect may be entrainment of more water vapor than predicted in areas of , which releases latent heat and warms the area surrounding , creating a larger and propagating an incorrect increase in . One possible cause for increased humidity is the disturbance of water runoff patterns causing soil to remain saturated and creating a source for increased humidity not captured in MM5 and WRF calculations. Evapotranspiration rates from croplands and urban vegetation irrigation may be greater than estimated over grass/scrub brush and nonurban regions releasing more moisture than predicted increasing humidity that is unaccounted for in MM5 and WRF. Snow cover was observed over a small subset of forest surface type (MM5 n = 7; WRF n = 4) but was not considered a factor since and coupling was not exhibited in general over forest surface type (Table 6). Incorrect evapotranspiration rates could be a result of deforestation and replacement with broadleaf vegetation such as aspen, corn, or grasses, which have higher evapotranspiration rates than traditional forest vegetation such as pine and/or leaf loss because of seasonal changes. This may explain why and coupling is observed in MM5 and WRF upper-troposphere forecasts over crop and grass/scrub brush regions while and coupling is not exhibited in MM5 and WRF upper-troposphere forecasts over forested areas.

Addressing the corrective factors within the physics packages used by AFWA for JAAWIN applications is beyond the scope of this study, but similarities in the physics packages used by MM5 and WRF may provide a starting point to address and coupling within the MM5 and WRF models. As detailed in section 3 (Tables 26), MM5 (MM5 land ; ) and WRF (WRF land ; ) upper-troposphere forecasts have indicated susceptibility to and coupling over land, suggesting the possibility this anomaly may exist in one or more shared physics packages. JAAWIN MM5 and WRF forecasts utilized the Noah land surface model governing physical processes in MM5 and WRF such as soil and vegetation mediums, evapotranspiration rates, and soil saturation properties, which may not be parameterized correctly (Chen and Dudhia 2001a,b; Hogue et al. 2005; LeMone et al. 2008; Wei et al. 2012). The new Kain–Fritsch cumulus parameterization scheme used by WRF (Table 5; WRF land ; ) saw reduced and coupling over the Kain–Fritsch cumulus parameterization scheme used by MM5 (Table 5; MM5 land ; ) but still may be inducing incorrect . This may be caused by the dry air minimum entrainment rate incorrectly applied if model humidity levels are biased low, resulting in latent heat flux in the cumulus parameterization schemes (Kain and Fritsch 1990; Siebesma and Holtslag 1996; Derbyshire et al. 2004; Kain 2004; Jonker 2005; de Rooy and Siebesma 2008).

If anomalies in the physics packages remain unaddressed, forecasting of vertical velocity may affect cloud and turbulence prediction decreasing the use of MM5 and WRF in upper-troposphere applications such as aircraft flight planning over sparsely populated regions (i.e., southwest Asia, the Atlantic Ocean, and likely others). If erroneous areas and intensities are allowed to be forecast along a route of flight an unnecessary lateral deviation to a less desired preplanned flight track may occur resulting in increased time and fuel expenditures. For example, if aircraft operating costs are $5000 per flight hour, an unnecessary deviation of 100 km to avoid areas of incorrectly forecast turbulence may result in a 300-km increase in travel distance and an additional expenditure of $2500 at a cruise speed of 556 km h−1. Working toward improving WRF and MM5 upper-troposphere temperature forecasts and eliminating forecast vertical velocity anomalies will help improve air transport operations by reducing unnecessary aircraft deviations resulting in possible economic savings and conservation of resources.

5. Conclusions

This study addressed temperature error and forecast vertical velocity relationships in the upper troposphere where regression analysis provided statistically significant evidence that MM5 and WRF exhibited coupling of temperature error and forecast vertical velocity. MM5 and WRF upper-troposphere temperature forecasts indicated temperature error and vertical velocity coupling between 39° and 59°N at lateral distance deviations up to 100 km from MM5 and WRF modeled flight tracks over land with temperature error and vertical velocity coupling absent over water. Regression analysis suggested different levels of temperature error and vertical velocity coupling in MM5 and WRF upper-troposphere temperature forecasts over different surface elevations above sea level, vegetative surface type, and urban development. Temperature error and vertical velocity coupling in MM5 upper-troposphere temperature forecasts was observed over crop-dominated regions, surface elevations between 300 and 399 m above sea level, and over nonurbanized areas. WRF upper-troposphere temperature forecasts exhibited temperature error and vertical velocity coupling between 0–99- and 300–399-m surface elevation above sea level, over grass/scrub brush, crop regions, and urban areas.

Temperature error and vertical velocity coupling analysis suggests temperature errors may be forcing artificial vertical motion in the MM5 and WRF upper-troposphere forecasts over land. Erroneous prediction of vertical motion by MM5 and WRF in upper-troposphere prediction may lead to incorrect cloud and turbulence forecasts negatively affecting the use of MM5 and WRF for operational decision making such as flight planning. Although the scope of this study was not intended to specifically address algorithms within the physics packages used by MM5 and WRF, it is possible the physics packages shared by MM5 and WRF may need adjustment since temperature error and vertical velocity coupling was observed in both models. Another physical parameter forecast by MM5 and WRF is horizontal wind velocity, which may be subject to forecast vertical velocity coupling resulting in erroneous wind forecasts used during flight planning which causes increased fuel use and increases operating costs. Research into the horizontal wind velocity physical parameter forecast by MM5 and WRF in the upper troposphere could be accomplished using methods explained in this study (e.g., long range in situ measurements, data stratification, and regression analysis) and could likely advance understanding of coupling relationships regarding forecast vertical velocity within MM5 and WRF modeling.

Acknowledgments

The authors thank the 187th Airlift and Wyoming Air National Guard for aircraft support; the Joint Air Force and Army Weather Information Network for model and forecasting access; Steven Rugg at the Air Force Weather Agency for model physics package information; the University of Wyoming for radiosonde database use; the International Institute for Applied Systems Analysis of Laxenburg, Austria, for use of the Harmonized World Soil Database; Fantine Ngan of the Cooperative Institute for Climate and Satellites, University of Maryland; and Xun Jiang and Max Shauck at the University of Houston.

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