The Effect of Topographic Variability on Initial Condition Sensitivity of Low-Level Wind Forecasts. Part II: Experiments Using Real Terrain and Observations

Paul E. Bieringer National Center for Atmospheric Research, Boulder, Colorado

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Peter S. Ray The Florida State University, Tallahassee, Florida

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Andrew J. Annunzio National Center for Atmospheric Research, Boulder, Colorado

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Abstract

A study by Bieringer et al., which is Part I of this two-part study, demonstrated analytically using the shallow-water equations and numerically in controlled experiments that the presence of terrain can result in an enhancement of sensitivities to initial condition adjustments. The increased impact of adjustments to initial conditions corresponds with gradients in the flow field induced by the presence of the terrain obstacle. In cross-barrier flow situations the impact of the initial condition adjustments on the final forecast increases linearly as the height of the terrain obstacle increases. While this property associated with initial condition perturbations may be present in an analytic and controlled numerical environment, it is often difficult to realize these benefits in a more operationally realistic setting. This study extends the prior work to a situation with actual terrain, Doppler radar wind observations over the terrain, and observations from a surface mesonet for model verification. The results indicate that the downstream surface wind forecast was improved more when the initial conditions adjusted through the assimilation of Doppler radar data originated from areas with terrain gradients than from regions where the terrain was relatively flat. This result is consistent with the findings presented in Part I and suggests that when varying terrain elevation is present upstream of a target forecast area, a greater benefit (in terms of forecast accuracy) can be made by targeting additional observations in the regions containing variable terrain than regions where the terrain is relatively flat.

Corresponding author address: Paul E. Bieringer, National Center for Atmospheric Research, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: paulb@ucar.edu

Abstract

A study by Bieringer et al., which is Part I of this two-part study, demonstrated analytically using the shallow-water equations and numerically in controlled experiments that the presence of terrain can result in an enhancement of sensitivities to initial condition adjustments. The increased impact of adjustments to initial conditions corresponds with gradients in the flow field induced by the presence of the terrain obstacle. In cross-barrier flow situations the impact of the initial condition adjustments on the final forecast increases linearly as the height of the terrain obstacle increases. While this property associated with initial condition perturbations may be present in an analytic and controlled numerical environment, it is often difficult to realize these benefits in a more operationally realistic setting. This study extends the prior work to a situation with actual terrain, Doppler radar wind observations over the terrain, and observations from a surface mesonet for model verification. The results indicate that the downstream surface wind forecast was improved more when the initial conditions adjusted through the assimilation of Doppler radar data originated from areas with terrain gradients than from regions where the terrain was relatively flat. This result is consistent with the findings presented in Part I and suggests that when varying terrain elevation is present upstream of a target forecast area, a greater benefit (in terms of forecast accuracy) can be made by targeting additional observations in the regions containing variable terrain than regions where the terrain is relatively flat.

Corresponding author address: Paul E. Bieringer, National Center for Atmospheric Research, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: paulb@ucar.edu

1. Introduction

Recent advances in computational technology are making it possible to run numerical weather prediction (NWP) models at resolutions where many of the significant terrain features are now being well resolved. While terrain can be accurately specified, often the gradients in wind, temperature, and moisture fields associated with the higher-resolution terrain are not. As a result, initial conditions in complex terrain environments are often not adequately specified. Knowledge of terrain-related effects on observation impacts is important to consider when deploying a weather sensor network to support a regional scale NWP model. Knowledge of terrain-related model sensitivity to observations can provide an indication of which variables in the initial conditions have a significant influence on the forecast and where initial conditions need to be most accurate to minimize model forecast error.

Based on this concept, a sensor network can be designed to minimize initial condition errors by selectively deploying critical sensors in sensitive locations, thereby reducing forecast error without the costly deployment of a uniform high-density sensor network. This concept is essentially the targeted observation technique first suggested by Emanuel et al. (1995). Beginning in the late 1990s a series of targeted observation studies were conducted to evaluate the forecast accuracy improvements using this concept. Several examples of this kind of study are the Fronts and Atlantic Storm Track Experiment (FASTEX; Joly et al. 1997), the North Pacific Experiment (NORPEX; Langland et al. 1999), and work conducted by the Tropical Prediction Center (TPC; Aberson and Franklin 1999). In all of these experiments, targeted observations are taken in regions where initial condition errors are suspected to grow rapidly into significant forecast errors. While these studies indicate that this concept shows promise as a practical technique for reducing forecast errors in global, synoptic, and hurricane forecast models (Emanuel and Langland 1998; Aberson and Franklin 1999; Szunyogh et al. 1999), it was often logistically difficult to deploy observational resources in a timely manner to illustrate the benefit of the targeted observations (Langland et al. 1999). This study addresses this challenge by identifying areas of initial condition sensitivity that are linked to stationary features in the simulation such as the underlying terrain and targeting additional observational resources there.

NWP model forecast errors in mountainous areas are thought to be due to poorly resolved terrain, or to model physics that are not suited for use in a complex terrain environment. Flow over complex terrain and in particular mountains have been extensively studied. Most of the studies examined the sensitivity of the downstream flow to upstream conditions. Klemp and Lilly (1975) were among the first to demonstrate the ability to forecast downslope winds and that topography may enhance predictability. For example, Vosper (2004) examined the effects of an inversion and the formation of lee waves, lee-wave rotors, hydraulic jumps, and breaking waves, and found the Froude number was strongly correlated with downstream flow and that nonlinear effects were significant in predicting the magnitude of these phenomena. Pierrehumbert and Wyman (1985) examined upstream flow and concluded that in addition to the Froude number, the Rossby number was also a controlling parameter. Also germane to this study is the work by Reinecke and Durran (2009) and Doyle et al. (2007) who examined the sensitivity of downslope winds to initial conditions with numerous flow field simulations each with varying initial conditions. While similar in some respects (e.g., winds and terrain, use of adjoint models to understand initial condition sensitivity, etc.) this work differs from the studies cited above in that the focus here is not on the highly nonlinear blocked flow cases, but instead examines the efficacy of observations in improving a downwind forecast during the more commonly occurring cross-barrier flow situation.

This work is the second paper in a two-part study that examines the relative effects of the impact of forecast sensitivity in areas with elevated and flat terrain. The first part of this work, Bieringer et al. (2013, hereafter Part I), illustrated that sensitivity of the model to initial condition adjustments is related to the dynamics of the airflow over the terrain obstacle. Using the shallow-water equations they showed that when the bottom surface is flat and the fluid depth is constant, perturbations to the flow do not grow. However, perturbations to the flow made over the terrain grow or are amplified. The instability is not tied to the presence of an obstacle at the lower boundary, but to the gradients in the base-state fluid depth, and more importantly the base-state fluid velocity gradients created, in this case, from the presence of the obstacle. A negative velocity gradient or slowing of the base-state flow field causes convergence, resulting in growth of the perturbation amplitude. While the analysis utilizing the shallow-water equations does not include all of the dynamics present in mesoscale flows involving terrain, it provided insight on where one could expect increased initial condition sensitivity and why.

Because the shallow-water equations are highly idealized, Part I also investigated this problem within a modeling framework that more accurately describes the atmosphere. In that study they present a methodology for characterizing the relationship between the impact of observations and the underlying terrain. This characterization uses an adjoint model to identify initial condition sensitivity and the adjoint model to characterize the forecast impact of perturbations made to the initial wind conditions at these locations. Here an idealized terrain environment, wherein a single mountain was surrounded by “flat” terrain, is used to characterize the impact of the terrain-related initial condition sensitivity. The relative magnitudes and locations of initial condition sensitivity are derived from gradient computations using the adjoint of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). The adjoint sensitivity results give a preliminary indication of initial condition sensitivity and provided information regarding the locations where the surface wind forecast was sensitive to adjustments in the initial conditions. When compared to adjoint simulations where the terrain was removed, the results from simulations using the idealized terrain indicated an increase in adjoint initial condition sensitivity over the elevated terrain. Next this study uses these adjoint sensitivity results to define the perturbation of the initial condition fields in a series of forward simulations using the MM5. A positive 3 m s−1 perturbation is then made to the initial conditions for each of the forward MM5 simulations. Again, simulations using the idealized single mountain are compared to the simulations where the terrain had been removed. The impact of the initial condition perturbations are measured in terms of maximum differences and root-mean-square (RMS) differences in a target region. The results of this component of the Part I study also indicate that an initial perturbation made over elevated terrain where wind gradients were present had a larger impact on the forecast than comparable perturbations made to the initial analysis over flat terrain. These results were found to be insensitive to whether the simulations were from a “cold start” initialization of the model or the perturbations to the flow were made after the model was spun up for 60 min. The results were also shown to not be due to transients (such as gravity waves) moving through the model domain associated with the terrain.

A third component of the Part I study examined the question of whether the height of the terrain would influence the amplification of the initial condition perturbations. The impact of the initial condition adjustments increases linearly as the height of the terrain obstacle increases when the flow is cross barrier, and initial condition perturbations have a more dramatic effect when the flow field switches from cross barrier to partially blocked. Assuming that the inclusion of additional observations results in a positive adjustment to the initial analysis, the findings of this study suggest that targeted observations deployed over elevated terrain will result in a larger forecast improvement than comparable observations deployed in regions of homogenous terrain. Such findings are not only relevant for mesoscale flows over topography, but also in regions where topographic features influence the synoptic flow field, such as in coastal regions and regions with mountain chains.

While Part I demonstrated that the model is more sensitive to initial perturbations where gradients in the flow velocity are present due to the terrain, it is often difficult to translate this result into a tangible positive result (e.g., more accurate forecast) in a more operationally realistic setting. This study extends the prior work to a situation with actual terrain, Doppler radar wind observations over the terrain, and observations from a surface mesonet for model verification. Here, initial condition sensitivity is characterized for a case with weak synoptic-scale forcing using the unmodified terrain of the Hudson River valley region near Albany, New York. Level II data from the Albany (KENX) Weather Surveillance Radar-1988 Doppler (WSR-88D) are used to measure a vertical profile of the horizontal winds upwind of the forecast verification region and serve in this experiment as the surrogate targeted observations. The model forecasts are verified against an objective analysis of the surface winds, based on measurements taken from a network of surface mesonet stations located in the Greylock Valley near Williamstown, Massachusetts. While it is not possible to speak to the generality of the results from a single case study, it does demonstrate that it was possible to show that the results of an analytic solution and idealized numerical study were observed in a more complicated real-world scenario. Additional case study analyses would be required to determine the overall cost–benefit ratio of utilizing this concept to direct the deployment of weather sensing platforms.

This paper is organized as follows. Section 2 contains a brief description of the data collection effort designed to support this study. The NWP modeling tools and specifics of the particular dataset used in this study are described in section 3. Section 4 describes the experimental setup. The results from both the forward and adjoint simulations are presented in section 5. Section 6 contains a summary of the results and a brief discussion of their implications.

2. Experimental data

Three types of data were used in this study: model analysis from the Rapid Update Cycle (RUC) for initialization, observations from a surface mesonet for verification, and Doppler weather radar data for the supplemental observations.

a. Model initial conditions

This study is conducted using the terrain data and atmospheric measurements collected from the Berkshire Mountain region of western Massachusetts, eastern New York State, and southern Vermont. This region was chosen in order to capitalize on a small network of weather instruments located there and its proximity to the KENX WSR-88D. Figure 1 illustrates the terrain elevation in this region, the existing observational resources, and the target forecast region. The small rectangle in the right center of the image indicates the target forecast region located over the Greylock Valley. The Berkshire Mountains provide a complex topographic environment with valley to peak elevation variations of over 2500 ft (760 m).

Fig. 1.
Fig. 1.

A depiction of the terrain heights in western Massachusetts, southern Vermont, and eastern New York State. Terrain is given in meters above sea level. The ⊗ denotes the location of the KENX WSR-88D. The dots represent the locations of National Weather Service (NWS) or Federal Aviation Administration (FAA) surface observation sites and the triangle denotes the location of the NWS upper-air site. The small white rectangle indicates the target forecast region.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

The data used in this case were from 1600 to 1900 UTC 4 October 2001. This was a case with negligible synoptic-scale forcing and relatively uniform environmental flow. On this day, skies were mostly clear, winds were primarily out of the west-southwest at 10–15 kt (5.1–7.7 m s−1), and there was no significant precipitation in the region. The winds varied from southerly at 5 kt (2.6 m s−1) at the surface, to westerly at 20 kt (10.2 m s−1) at an elevation equivalent to the top of Mt. Greylock [~3500 feet (~1067 m) above mean sea level (MSL)]. One important characteristic of this case is that the flow in the lower model levels was nearly uniform (horizontally). This made it possible to use remotely sensed observations such as radar wind profiles to modify the background analysis over a larger horizontal area than would have been possible if the winds were more spatially variable. While it is understood that local terrain has an influence on a model forecast over a wide range of weather conditions, the dataset used in this study removes much of the forecast sensitivity that might be associated with a more complex weather pattern.

As described above, Part I found that the model sensitivity to initial conditions was related to the characteristics of the airflow over the terrain obstacle. The Froude number (Fr) [(1)] is a commonly used parameter to characterize atmospheric airflow over terrain:
e1

Here is the environmental wind speed, is the Brunt–Väisälä frequency, and is the mountain height (Durran 1990). The square of the Froude number is proportional to the ratio of kinetic energy in the environmental wind to potential energy required for the air to flow up and over the terrain barrier. In high Froude number flows where Fr > 1, the air has adequate kinetic energy to flow up and over the terrain obstacle and is often referred to as a cross-barrier flow scenario (Bluestein 1993). Using the Albany sounding from 1200 UTC 4 October 2001 an Fr ≅ 2.0 was computed for this case for the layer between the surface and 850 mb, implying cross-barrier flow.

The initial atmospheric conditions for the sensitivity study are based on the initial fields from the 20-km grid increment RUC model from this period. The RUC analysis was interpolated to a 19 vertical (sigma) level, 1-km horizontal grid increment, MM5 model domain using the MM5, version 3, REGRID and INTERPF data preprocessing programs. No additional observations are included in the MM5 initial conditions beyond those already present in the 20-km resolution RUC analysis. The initial conditions created by the MM5 data preprocessing software were then converted to the MM5, version 2, format to be ingested by the adjoint-modeling system. For a more in-depth discussion of the MM5 data preprocessing programs, the reader should refer to Dudhia et al. (2000).

b. Supplemental surface mesonet observation collection

Observations from the nine Berkshire mesonet stations provide surface wind measurements for the validation of the forecasts. This mesonet is located inside the rectangle in Fig. 1. The locations of the surface mesonet sensors deployed in the Greylock Valley of western Massachusetts are overlaid on an image of the local terrain in Fig. 2. These data are used in a separate objective analysis to generate a gridded surface wind analysis against which the accuracy of the surface wind forecasts are measured. Throughout most of the forecast period, five of nine mesonet stations were operational and reporting data; however, occasionally the operational station count fluctuated down to four and up to six stations.

Fig. 2.
Fig. 2.

A magnified map depicting the terrain heights near Williamstown in western Massachusetts, southern Vermont, and eastern New York State. Terrain is in meters above sea level. The circles denote the locations of the surface mesonet observation sites used in the verification. The mesonet sites include the following: Williamstown farm (FRM), Mt. Greylock summit (GLK), Harriman-West Airport (HWA), Mt. Ramier summit (MTR), Notch Road (NCH), Greylock School (SCH), Taconic Ridge (TCN), Williamstown landfill (WLL), and Williamstown water tower (WTR).

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

c. Supplemental Doppler weather radar observations

As discussed previously, WSR-88D wind data from the KENX radar in Albany were available for the case used in this study, and served as the surrogate-targeted observations. Between 1600 and 2100 UTC 4 October 2001 the KENX radar operated in the volume control pattern (VCP) 32, or clear-air mode (Fig. 3). Clear-air mode operations are preferred on days when there are no precipitating echoes within range of the radar because it typically allows the radar to better detect the low-altitude air motions (Williamson et al. 1991). Radar velocity estimates are quite accurate volume averages, typically better than 0.5 m s−1. However it is less clear how well a volume average represents the wind at a point, for that is dependent on the wind fluctuations within the sampling volume. That is why we chose a day with less complex, in time or space, weather conditions. Archived radar base data provide access to radial velocity, spectrum width, radar reflectivity, and all of the derived products at the radar sampling resolution. The ⊗ symbol in Fig. 1 denotes the location of the KENX WSR-88D.

Fig. 3.
Fig. 3.

Radial-velocity data from the KENX, Albany, NY, WSR-88D. The data were collected on 1601 UTC 4 Oct 2001 while the radar was operating in clear-air mode. The antenna was pointed at 0.5° elevation angle. The warm colors (reds) represent winds moving away from the radar while the cool colors (greens) represent wind motion toward the radar.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

3. Experimental design

This study is similar to Part I in that it uses both forward and adjoint-model simulations. It utilizes a case with weak synoptic-scale forcing (the same case used in the two sensitivity analyses examined in Part I). The primary differences are that the actual terrain elevations from the region are used, along with wind measurements from a Doppler weather radar and surface observations in a small mountain valley downwind of the Doppler wind measurements.

a. NWP models

The MM5 adjoint-modeling system is used in conjunction with the forward version of the MM5, version 3, to examine initial condition sensitivity and forecast accuracy. The adjoint model is based on a linearized version of the MM5, version 2, nonhydrostatic, limited-area model and is used to calculate the gradient of the forecast variables with respect to a prescribed forecast cost function. For additional information regarding the MM5 adjoint-modeling system, the reader should consult the detailed discussion provided in Zou et al. (1997, 1998). A more detailed description of the meteorological modeling applications of an adjoint model, including a discussion of its use in initial condition sensitivity studies like this one, can be found in Errico (1997), Giering and Kaminski (1998), and Zou et al. (1997).

The MM5, version 3, is a nonhydrostatic limited-area primitive equation model suitable for both atmospheric research and operational weather forecast applications. It is a flexible tool providing numerous options for physical-process parameterizations and initializations, and can be used for a wide range of model resolutions. Detailed descriptions of the MM5 can be found in Grell et al. (1994) and Dudhia et al. (2000).

As will be discussed in greater detail later in this section, the environmental conditions for the case used were dominated by a large-scale high pressure system. The models were configured to make short-duration forecasts of surface winds. The simulations do not use the cumulus or radiation parameterization packages, however, they do utilize explicit microphysics. A more simplistic two-layer planetary boundary layer (PBL) parameterization option was used in the adjoint model while the forward-model simulations used a more sophisticated Blackadar PBL parameterization scheme (Blackadar 1976, 1979; Grell et al. 1994). The reason for using the two-layer PBL parameterization option was because a more complex parameterization was not available in the adjoint model. The configuration of the models was nearly identical to that used in Part I. For additional details regarding the model configurations of both the forward and adjoint models, the reader is referred to this study.

b. Model domain

Both the adjoint- and forward-model components of the experiment are centered over the Hudson River valley in New York. Figure 4 depicts the model domain. The domain was designed such that the forecast verification region (where the cost function is defined and represented by the rectangle in Fig. 4) corresponds with the location of a surface mesonet. Because the environmental flow was west-southwesterly in this case, this configuration minimizes the domain size required to make a 4-h forecast during which the influence of the boundary conditions on the surface wind forecast in the Greylock Valley remain small.

Fig. 4.
Fig. 4.

The MM5 domain and terrain used in the real-data component of the study. The forecast verification region is located in the Greylock Valley and is designated by the white rectangle in the northeastern corner of the domain.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

c. Sensitivity analysis

In this study, the surface horizontal wind forecast is used as the metric by which this influence is measured. Surface winds are used for several reasons: 1) the u- and υ-wind components are state variables directly forecasted by the model, 2) wind speed and direction are among the more reliable measurements made by the Berkshire mesonet and therefore serve as a suitable variable against which model forecasts can be evaluated, and 3) the results presented in Part I can be used to help interpret the results of this study.

The adjoint model was used in this study to analyze the region where the forecast is most sensitive to perturbations in the initial conditions. When using an adjoint model for a sensitivity study, a cost function representing the forecast aspect of interest must be specified (Errico 1997; Giering and Kaminski 1998; Zou et al. 1997). This study used vorticity at the lowest model level as the cost function because it contains both the zonal and meridianal components of the surface horizontal winds. As in Part I we also used divergence as a cost function, but because of the similarities, only the results based on the vorticity cost function are shown here. The adjoint model computes the gradient of the cost function with respect to all of the model state variables at the initial time. It is reasonable to think of the gradient computations as an indication of initial condition sensitivity for each of the state variables in the model.

The vorticity cost function is evaluated for a series of adjoint simulations that use the same model domain and initial conditions of forecast lengths ranging from 5 to 210 min in 5-min increments. The location and valid time for the forecast are held constant for the adjoint sensitivity analysis. This is used to identify the locations of adjoint sensitivity and the corresponding terrain elevation below these regions. Each forecast length defines a region of maximum forecast sensitivity to the initial conditions, which is displaced upstream with increasing distance from the evaluation region. In their limited-area model studies, Vukićević and Errico (1990) found that model forecasts are sensitive to initial condition errors until the region of initial condition sensitivity coincides with the lateral boundaries. At this point, model forecast errors can be attributed primarily to the lateral boundary conditions.

Then, a series of two forward-model simulations (the control and experimental) of the same length were used to examine the forecast error for each forecast duration from 5 to 210 min in 5-min increments. The control simulation is based solely on the initial analysis derived from the 20-km RUC. The experimental simulation, demonstrating the effects of modifying the model initial conditions, is created by initializing the model with a 20-km RUC analysis that has been adjusted through an objective analysis that incorporates the radar wind observations. Control and experimental forecasts of surface wind all have the same verification time (although durations vary from 5 to 210 min).

Forecast error is determined by directly comparing the wind forecasts from the lowest model level to gridded analyses of surface winds that are based on the measurements collected every 5 min from the Berkshire mesonet. The adjoint sensitivity analysis provides the upstream location where the model is sensitive to initial conditions. By knowing this location it is possible to infer the degree to which terrain variability influences the impact that initial analysis adjustments made at that location have on the surface wind forecast accuracy in the verification region.

4. Analysis and results

There were four primary analyses conducted in this study. The first two were associated with the observational data used as targeted observations and as the verification data. The second two analyses were associated with the characterization of initial condition sensitivity and forecast accuracy. A description of the specifics of each of the analyses and the result of these analyses are provided below.

a. Doppler radar data analysis

The radar data from 4 October show no evidence of contamination by either ground clutter or biological targets (Fig. 3). A vertical profile of the horizontal winds was generated with the WSR-88D Algorithm Testing and Display System (WATADS), velocity azimuth display (VAD), and velocity wind profile (VWP) algorithms (WATADS 2000). This is one of several methods for defining horizontal winds from single Doppler radar radial-velocity data. It should be noted that the radar observations are not a point measurement, but a weighted volume average (with the maximum weight along the beam axis). The volume measured extends to the ground at even 0.5° elevation, even though the center of the beam is slightly above ground. The size of the volume increase with range as the beam spreads. The radar cannot “see” below the height of the radar or behind any obstacles. The analysis suggest that, at lower levels, the horizontal zonal winds exhibit a correlation of greater than 0.5 at ranges of 35–40 km downwind from the radar (Fig. 5). These results factor into the design of the objective analysis used later to incorporate the radar observations into the initial analysis of the experimental simulation.

Fig. 5.
Fig. 5.

Results from the discrete autocorrelation of the u winds in the control initial model analysis. The autocorrelation was computed at the radar's latitude, 42.6°N across a 175-point grid. The results suggest that the u-wind component of the winds in most of the lowest 10 sigma levels is positively correlated out to ranges of 35–40 km.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

Prior to defining the influence radius (the range away from the point of observation where the radial velocity is representative of the wind at that location) of the radar wind observations, a discrete autocorrelation analysis was performed on the horizontal winds from the 10 lowest sigma levels of the 1600 UTC control simulation initial analysis. The adjoint sensitivity analysis from Part I indicated that the initial condition sensitivity would be located west of the forecast verification region for this synoptic/mesoscale situation. Since the radar is located roughly due west of the verification region and that anticipated location where the targeted observations are desired, the autocorrelation analysis was confined to the u-wind component.

The radar-derived vertical profile of the horizontal wind from 1601 UTC was used to adjust the initial wind analysis used by the experimental MM5 simulation and the MM5 objective analysis preprocessing software was used to create the new initial wind analysis. This starts with a background analysis and then objectively incorporates any additional surface or upper-air observations. In this case, a successive-correction, Cressman objective-analysis technique was used to weight the adjustment of the background RUC wind analysis in the lower model levels by incorporating the radar-derived vertical profile of the horizontal wind. No variables other than the u and υ winds were modified by the objective analysis preprocessor. This successive-correction objective analysis was configured to use four influence radii: 50, 30, 20, and 10 km. The outer radius was based on the wind autocorrelation analysis that indicated that the winds were positively correlated out to 35–40 km combined with the fact that the radar observations are based on radial velocity measurements made at a 10–15-km slant range from the radar. The 50-km influence radius was large enough to adjust the winds over the Hudson River valley and the mountains on the New York–Massachusetts border that will serve as the targeted measurements in this study (Fig. 6). Because the adjusted analysis is based on the background RUC analysis, the new wind analysis is modified only at the altitudes and locations where the radar derived winds differ from the background (Figs. 6 and 7). Additional details regarding the MM5 objective analysis is described in Dudhia et al. (2000).

Fig. 6.
Fig. 6.

A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The blue arrows represent the wind analysis after the addition of the radar-derived horizontal wind observations. The blue contours represent the difference between the two u-wind analyses in m s−1, and illustrate the influence radius of the Cressman objective analysis. The ⊗ denotes the location where the vertical profile of the horizontal wind shown in Fig. 7 was taken.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

Fig. 7.
Fig. 7.

Vertical profile of the horizontal winds from the 1600 UTC initial wind analyses used in both the control and experimental simulations. The wind profiles are taken at the radar location and over the sloping terrain southwest of the Greylock Valley at 42.64°N, 73.46°W. The solid line represents the winds without the addition of any radar observations. The dashed line represents the wind profile after it was adjusted using the radar observations. The dotted–dashed line represents the observed wind profile from the radar VAD algorithm.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

b. Mesonet data analysis

Surface wind observations from the Berkshire mesonet are used to assess the accuracy of the surface wind forecasts. These data are used in a separate objective analysis that creates a gridded surface wind analysis. Here, the objective analysis uses the wind field from the RUC model, interpolated to the 1-km MM5 grid, as the background field and then utilizes a modified Cressman objective-analysis scheme to create the surface wind analysis. In this analysis scheme, the influence radii were set to 7, 5, 3, and 2 km. Wind analyses are generated from 1605 to 2100 UTC at 5-min intervals and used for the forecast verification. A visual inspection of the objective analyses indicate that they provide a reasonable depiction of the surface winds when compared to the station observations (e.g., Fig. 8).

Fig. 8.
Fig. 8.

The gridded surface wind analysis and surface wind observations from the Berkshire mesonet valid at 1630 UTC 4 Oct 2001. This gridded wind analysis is used as the ground truth against which the accuracy of the MM5 surface wind forecasts is measured. This image is characteristic of the surface wind analyses used. The dashed rectangle illustrates the forecast verification region used in the study.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

c. Adjoint sensitivity analysis

This analysis uses a vorticity cost function defined at the lowest model level in the forecast verification region. The u- and υ-wind sensitivity calculations from the adjoint model provide the geographic locations where the upstream winds will most strongly influence the surface wind forecast in the Greylock Valley. For short simulations, these adjoint sensitivity areas cover small areas and exhibit sharp gradients. As the adjoint-model simulation time increases, the sensitivity maximum decreases in magnitude and the sensitivity area increases. The simulation length was limited to 210 min to avoid conditions where it became difficult to identify a central location for the adjoint sensitivity. The adjoint sensitivity simulations used to provide the initial condition sensitivity results resemble that shown in Fig. 9 and the center locations for the regions of initial condition sensitivity are subjectively determined by reviewing these adjoint sensitivity results. Figure 10 depicts points that correspond to the location where the model is most sensitive to adjustments to the initial conditions. For the purpose of illustration, every other location identified by the adjoint analysis is depicted in Figs. 9 and 10.

Fig. 9.
Fig. 9.

A map of adjoint sensitivity for a 60-min simulation. Terrain is given in meters above sea level. The solid and dashed contours represent adjoint sensitivity of the u-wind component. The ⊗ denotes the location of the center of the adjoint sensitivity for the 60-min simulation and the dots denote the center locations of adjoint sensitivity for simulations ranging from 10 to 50 min in 10-min intervals.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

Fig. 10.
Fig. 10.

Center points of the adjoint initial condition sensitivity regions. The dots designate the center locations for the regions of adjoint sensitivity for the simulations ranging from 10 to 210 min in 10-min intervals. As the length of the adjoint simulation increases, the initial condition sensitivity tends to be located farther west of the Greylock Valley.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

d. Forecast sensitivity analysis

First, the forecast accuracy improvements are evaluated for the case where the largest area is adjusted (largest influence radius for the radar data) in the initial analysis of the experimental simulation. This encompasses the area within the outer-most contour in Fig. 6. Each of the forecast sensitivity analyses utilizes two model simulations. The first simulation uses only the RUC analyses to provide the initial and boundary conditions. This simulation provides the surface wind forecast that serves as the control against which improvements in all experimental forecast are measured. The initial and boundary conditions for the second simulation use the same RUC analyses as a background field for the incorporation of the radar-derived vertical profile of the horizontal wind to provide a presumably more accurate representation of the wind field at the time of model initiation. The accuracies of the surface wind forecasts from the experimental simulations are compared to the accuracies of the forecasts from the control simulation to assess the forecast improvement or degradation that results from the inclusion of the radar observations. The radar-derived observations influence the initial fields over a relatively large portion of the model domain, and cover the regions of sloping terrain directly west of the target forecast region in addition to the relatively flat terrain of the Hudson River valley (Fig. 6). The geographic locations of initial condition sensitivity (illustrated in Fig. 10) are used to determine where the model is sensitive to initial condition perturbations and relate this to the underlying terrain. As a result, it is possible to infer the relative influence that flat versus sloping/elevated terrain has on the impact that observations from these locations have on the forecast accuracy.

Forecast error is quantified by the root-mean-square errors in the wind forecast at the lowest model level compared to the gridded surface wind analysis. The forecasts are evaluated in the Greylock Valley inside the verification region illustrated by the rectangle in Fig. 8. This area not only exhibits local variability in the surface wind forecast, compared to the smoother background wind field, but it is also in the region strongly influenced by the objective analysis of the surface wind observations.

Surface wind observations were available every 5 min from 1600 to 2100 UTC. The gridded analyses of these observations (similar to the one shown in Fig. 8) were compared to corresponding surface wind forecasts from the control and experimental simulations. Both components of the wind were examined. Figure 11 illustrates the forecast error as a function of simulation length. Here the addition of the upstream radar observations is shown to decrease the error in the short-term surface wind forecasts in the Greylock Valley. In the majority of the simulations, the inclusion of the radar observations in the initial analysis results in a decrease in u-wind RMS forecast error. The RMS error in the υ-wind forecasts from the control and experimental simulations show little variation. The absolute value of the forecast improvements are relatively small, a possible consequence of the light environmental winds on this day; however, in relative terms, the accuracy improvements were on the order of 10%. Forecast improvements of this magnitude are consistent with other targeted observation studies that report forecast accuracy improvements that range from 10% to 20% (Szunyogh et al. 2002). Figure 11 also suggests that the amount of forecast error improvement may be linked to the presence of, or lack of, terrain gradient in the region of initial condition sensitivity.

Fig. 11.
Fig. 11.

RMS forecast error in the u and υ winds in the verification region as a function of simulation length. Terrain elevations are based on values that correspond to the centers of adjoint initial condition sensitivity illustrated in Fig. 10. The experimental forecast, based on an adjustment of the wind field at a single time, typically indicates improved u-wind forecast accuracy, while little or no improvement is evident in the υ-wind forecast.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

This is more evident in the differences between the RMS forecast errors of the control and experimental simulations, plotted versus the simulation length (Fig. 12). Forecast improvement is defined here as (RMS error in the control forecast minus the RMS error in the experimental forecast). The perturbations that impact the forecast at each time are from adjustments to the initial conditions made progressively farther upstream as the forecast length is increased and not from the initial condition perturbations closer to the verification region that would have indeed advected past the verification region. The perturbations that had the greatest impact originated from the locations that were over the higher terrain (as indicated by the adjoint sensitivity analysis). Their impact was felt at roughly the time it took them to advect to the verification region. The largest forecast improvement roughly coincides with areas of high terrain slope below the center of the adjoint sensitivity regions. From 160 to 210 min, the forecast error improvements again increase slightly, but the increase is not as pronounced as the shorter simulations. Within this time period the adjoint sensitivity regions are closest to the location of the KENX weather radar, with the 195-min simulation having an adjoint sensitivity region that was the closest to the radar. In spite of the fact that the initial condition modifications are larger in this area because this location is closer to the radar, the effect on the forecast accuracy is smaller. The forecast accuracy improvement is smaller here because the model sensitivity to initial conditions is weaker and spread over a larger area at the longer simulations.

Fig. 12.
Fig. 12.

RMS u-wind forecast improvement and the underlying terrain at the location of the adjoint sensitivity vs simulation length. RMS forecast improvement, defined as control RMS error minus experimental RMS error, illustrates the differences between the u-wind RMS error lines in Fig. 11. Terrain elevations are based on values corresponding to the locations identified as the centers of the regions of adjoint initial condition sensitivity illustrated in Fig. 10. The forecast improvement maxima and minima, based on the adjustment of the winds at a single time, suggest that terrain variability influences the impact of the additional wind observations included in the experimental simulations.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

The same analysis technique is used to examine the forecast sensitivity to the initial conditions for two variants of the radar-wind-adjusted analysis. All of the procedures described above are retained except for how the initial wind analysis is defined. One analysis is created by using the radar-adjusted winds only in the region where the vertically integrated, absolute value of the gradient sensitivity indicates a sensitivity greater than zero (referred to as the sensitive zone, Fig. 13). The other analysis uses the adjusted winds only from outside the sensitive zone (Fig. 14). The purpose is to quantify the contributions of the adjustments where the adjoint sensitivity analysis indicates that the model is more sensitive versus less sensitive. The forecast accuracy of these experimental simulations is then contrasted with the forecast accuracy of the control experiment.

Fig. 13.
Fig. 13.

A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The blue arrows represent the wind analysis in the sensitive zone after the addition of the radar-derived horizontal wind observations. The blue contours represent the difference between the two u-wind analyses in m s−1.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

Fig. 14.
Fig. 14.

A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The red arrows represent the adjusted wind analysis outside the sensitive zone after the addition of the radar derived horizontal wind observations. The red contours represent the difference between the two u-wind analyses in m s−1.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

The RMS forecast error improvement for the experimental forecasts using radar data either inside or outside the sensitive zone are compared to the forecast error computations from the control forecast without the radar data (Fig. 15). Forecast accuracy using only the winds from outside the sensitive zone show mixed results, with small forecast improvements occurring between 10 and 90 min and between 105 and 135 min, and a degraded forecast for the remainder of the simulation. The presence of both positive and negative forecast impact is likely due to the limitations of the tangent linear and corresponding adjoint to fully represent the sensitivity of the full nonlinear dynamical system. Consequently, the region of sensitivity is most likely larger than the “inside” mask used here, particularly at longer model integration times. This most likely results in the insertion of artificial gradients in the flow field along the edge of the mask. These gradients still alter the flow field inside the area of the maximum sensitivity when the observations outside the sensitive zone are used, resulting in unpredictable results due to the insertion of gradients in the sensitive zone. For this reason the forecast improvement results from the case where observations are added outside the sensitive zone are difficult to interpret. The model forecast of surface winds in the Greylock Valley is improved throughout most of the 3.5-h simulation when the simulation uses the radar-adjusted winds inside the sensitive zone. The peaks in forecast improvement coincide with the times when the centers of the adjoint sensitivity were over regions of terrain-elevation variation. Simulations exhibiting a minimum in forecast improvement coincide with the adjoint sensitivity located over the valley. The forecast improvement based on the use of radar data inside the sensitive zone exhibits a bimodal pattern (Fig. 15).

Fig. 15.
Fig. 15.

A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The black arrows represent the background wind analysis used in the control simulations. The white arrows represent the adjusted wind analysis outside the sensitive zone after the addition of the radar derived horizontal wind observations. The white contours represent the difference between the two u-wind analyses in m s−1.

Citation: Monthly Weather Review 141, 7; 10.1175/MWR-D-11-00055.1

5. Conclusions

There are a number of factors that contribute to the relative impacts that observations have on forecast accuracy. One factor is that forecast sensitivity to adjustments made to the initial analysis diminishes as the simulation length increases. Another factor is that the locations of the analysis adjustments and sensitivity may not coincide. Additional wind observations will on average improve the wind analysis, but locally, the adjustments may actually degrade the analysis. Finally, there is a degree of uncertainty/representativeness associated with the observations that can also play a role in the determination of forecast accuracy. The overall forecast improvement is a combination of all but not limited to these factors.

This paper is the second in a two-part study that examines the variability in model initial sensitivity and corresponding forecast impact that is associated with gradients in the atmospheric fields. Part I illustrated that sensitivity of the model to initial condition adjustments is related to the dynamics of the airflow over the terrain obstacle and that the magnitude of the impact was related the height of the barrier. While Part I of study demonstrated that the model is more sensitive to initial perturbations where gradients in the flow velocity are present as a result of the terrain using analytic and idealized numerical experiments, it is often difficult to translate this type of result into a tangible positive result (e.g., more accurate forecast) in a more operationally realistic setting. The part of this study extends the prior work to a situation with actual terrain, Doppler radar wind observations over the terrain, and observations from a surface mesonet for model verification.

In this part of this study we used a similar initial condition sensitivity methodology as was used in Part I. However, instead of forecast impact, we examined the accuracy for a surface wind forecast in a small downwind mountain valley in a study that utilized real terrain, targeted observations from an upstream Doppler weather radar, and surface mesonet observations as ground truth are used to evaluate the relationship between the gradients associated with the terrain and forecast improvements. An adjoint sensitivity analysis was used to identify the locations of surface wind initial condition sensitivity, as a function of forecast length. Because the initial analysis was adjusted, based on radar observations, where initial condition sensitivity existed, this technique emulates the effect of targeting observations in all locations of initial condition sensitivity. Consequently, it was possible to diagnose the impact of the observations on the forecast for different underlying terrain heights. Next, four, 3.5-h forward simulations were performed, where the wind forecasts were evaluated every 5 min. The first simulation was the control and contained no additional observations. The second was the experimental simulation using an initial wind analysis that had been adjusted with wind observations from the KENX WSR-88D. This initial analysis provided wind adjustments over regions of adjacent sloping and flat terrain, upstream from the target forecast area. The third and fourth simulations examined the forecast sensitivities to adjusting the winds inside and outside the sensitive zone identified by the adjoint model. The atmospheric conditions for this study were a cross-barrier flow scenario comparable to the 650-m elevation idealized terrain from Part I. Forecast error was measured by comparing the model forecast with an objective wind analysis that is based on surface observations in the Greylock Valley. Forecast improvements were then determined by comparing the error from experimental simulation containing additional observations to the error from the control forecast that used no additional measurements.

The results of this part of this study demonstrate that the magnitude of the forecast improvement is enhanced more by the observations where the terrain varied than over the more uniform terrain at lower elevations in the Hudson River valley. Furthermore the magnitude of the forecast improvements for similar forecast lengths is also consistent with the forecast impacts seen in Part I. These results are consistent with the overall findings of Part I that initial condition perturbations made in areas with gradients induced by the varying terrain elevations will have a larger impact on the forecast. In this case, the perturbations involve the inclusion of upstream observations, which improve the initial conditions, and the improvements to the initial conditions made over the locations of terrain gradients resulted in larger forecast improvements than those made over the lower elevation flat terrain.

This has potential implications with regards to the deployment of weather sensors. Clearly, in any weather scenario there are always locations that will exhibit more sensitivity to initial conditions than others. Often these areas change as the environmental conditions change. This study, however, indicates that these sensitive areas can also be linked to stationary features such as terrain, which result in gradients in the atmospheric fields. Targeting additional observational resources or redesigning the existing networks to capitalize on these stationary regions of enhanced initial condition sensitivity may provide a means to economically reduce model forecast errors.

Acknowledgments

The authors would like to acknowledge the MIT Lincoln Laboratory, the Lincoln Scholars program, the National Center for Atmospheric Research, Research Application's Laboratory for supporting this work, and the late Dr. Tom Warner for his comments and suggestions, which have greatly improved this work. The authors also wish to express their appreciation to the insightful and constructive comments of the anonymous reviewers.

REFERENCES

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
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  • Vosper, S. B., 2004: Inversion effects on mountain lee waves. Quart. J. Roy. Meteor. Soc., 130, 17231748.

  • Vukićević, T., and R. M. Errico, 1990: The influence of artificial and physical factors upon predictability estimates using a complex limited-area model. Mon. Wea. Rev., 118, 14601482.

    • Search Google Scholar
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  • WATADS, 2000: Reference guide for version 10.2. Storm Scale Applications Division, 200 pp. [Available from Storm Scale Applications Division, National Severe Storms Laboratory, 1313 Halley Circle, Norman, OK 73069.]

  • Williamson, S. P., and Coauthors, 1991: Federal meteorological handbook 11: Doppler radar meteorological observations. Part A: System concepts, responsibilities and procedures. FCC-H11A-1991, Office of the Federal Coordinator for Meteorological Services and Supporting Research (OFCM), 56 pp.

    • Search Google Scholar
    • Export Citation
  • Zou, X., F. Vandenberghe, M. Pondeca, and Y.-H. Kuo, 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-435-STR, 107 pp.

  • Zou, X., W. Huang, and Q. Xiao, 1998: A user's guide to the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-437-IA, 96 pp.

Save
  • Aberson, S. D., and J. L. Franklin, 1999: The impact on hurricane track and intensity forecasts of GPS dropwindsonde observations from the first-season flights of the NOAA Gulfstream-IV jet aircraft. Bull. Amer. Meteor. Soc., 80, 421428.

    • Search Google Scholar
    • Export Citation
  • Bieringer, P. E., P. S. Ray, and A. J. Annunzio, 2013: The effect of topographic variability on initial condition sensitivity of low-level wind forecasts. Part I: Experiments using idealized terrain. Mon. Wea. Rev., 141, 21372155.

    • Search Google Scholar
    • Export Citation
  • Blackadar, A. K., 1976: Modeling the nocturnal boundary layer. Preprints, Third Symp. on Atmospheric Turbulence and Air Quality, Raleigh, NC, Amer. Meteor. Soc., 46–49.

  • Blackadar, A. K., 1979: High resolution models of the planetary boundary layer. Advances in Environmental Science and Engineering, J. R. Pfafflin and E. N. Ziegler, Eds., Vol. I, Gordon and Breach Publishing Group, 50–85.

  • Bluestein, H. B., 1993: Synoptic-Dynamic Meteorology in Midlatitudes. Vol. II, Observations and Theory of Weather Systems, Oxford University Press, 608 pp.

  • Doyle, J. D., C. Amerault, and C. A. Reynolds, 2007: Sensitivity analysis of mountain waves using an adjoint model. Meteor. Z., 16, 607620.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., D. Gill, Y.-R. Guo, K. Manning, and W. Wang, 2000: PSU/NCAR mesoscale modeling system tutorial class notes and user's guide: (MM5 modeling system version 3). National Center for Atmospheric Research, 336 pp.

  • Durran, D. R., 1990: Mountain waves and downslope winds. Atmospheric Process over Complex Terrain, Meteor. Monogr., No. 45, Amer. Meteor. Soc., 59–81.

  • Emanuel, K. A., and R. Langland, 1998: FASTEX adaptive observations workshop. Bull. Amer. Meteor. Soc., 79, 19151919.

  • Emanuel, K. A., and Coauthors, 1995: Report of the first prospectus development team of the U.S. Weather Research Program to NOAA and the NSF. Bull. Amer. Meteor. Soc., 76, 11941208.

    • Search Google Scholar
    • Export Citation
  • Errico, R. M., 1997: What is an adjoint model? Bull. Amer. Meteor. Soc., 78, 25772591.

  • Giering, R., and T. Kaminski, 1998: Recipes for adjoint code construction. ACM Trans. Math. Software, 24, 437474.

  • Grell, G. A., J. Dudhia, and D. R. Stauffer, 1994: A description of the fifth-generation Penn State/NCAR Mesoscale Model (MM5). NCAR Tech. Note NCAR/TN-398+STR, 117 pp.

  • Joly, A., and Coauthors, 1997: The Fronts and Atlantic Storm-Track Experiment (FASTEX): Scientific objectives and experimental design. Bull. Amer. Meteor. Soc., 78, 19171940.

    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and D. K. Lilly, 1975: The dynamics of wave-induced downslope winds. J. Atmos. Sci., 32, 320339.

  • Langland, R. H., and Coauthors, 1999: The North Pacific Experiment (NORPEX-98): Targeted observations for improved North American weather forecasts. Bull. Amer. Meteor. Soc., 80, 13631384.

    • Search Google Scholar
    • Export Citation
  • Pierrehumbert, R. T., and B. Wyman, 1985: Upstream effects of mesoscale mountains. J. Atmos. Sci., 42, 9771003.

  • Reinecke, P. A., and D. Durran, 2009: Initial-condition sensitivities and the predictability of downslope winds. J. Atmos. Sci., 66, 34013418.

    • Search Google Scholar
    • Export Citation
  • Szunyogh, I. Z., Z. Toth, S. J. Majumdar, R. Morss, C. Bishop, and S. Lord, 1999: Ensemble-based targeted observations during NORPEX. Preprints, Third Symp. on Integrated Observing Systems, Dallas, TX, Amer. Meteor. Soc., 74–77.

  • Szunyogh, I. Z., Z. Toth, A. V. Zimin, S. J. Majumdar, and A. Persson, 2002: Propagation of the effect of targeted observations: The 2000 Winter Storm Reconnaissance Program. Mon. Wea. Rev., 130, 11441165.

    • Search Google Scholar
    • Export Citation
  • Vosper, S. B., 2004: Inversion effects on mountain lee waves. Quart. J. Roy. Meteor. Soc., 130, 17231748.

  • Vukićević, T., and R. M. Errico, 1990: The influence of artificial and physical factors upon predictability estimates using a complex limited-area model. Mon. Wea. Rev., 118, 14601482.

    • Search Google Scholar
    • Export Citation
  • WATADS, 2000: Reference guide for version 10.2. Storm Scale Applications Division, 200 pp. [Available from Storm Scale Applications Division, National Severe Storms Laboratory, 1313 Halley Circle, Norman, OK 73069.]

  • Williamson, S. P., and Coauthors, 1991: Federal meteorological handbook 11: Doppler radar meteorological observations. Part A: System concepts, responsibilities and procedures. FCC-H11A-1991, Office of the Federal Coordinator for Meteorological Services and Supporting Research (OFCM), 56 pp.

    • Search Google Scholar
    • Export Citation
  • Zou, X., F. Vandenberghe, M. Pondeca, and Y.-H. Kuo, 1997: Introduction to adjoint techniques and the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-435-STR, 107 pp.

  • Zou, X., W. Huang, and Q. Xiao, 1998: A user's guide to the MM5 adjoint modeling system. NCAR Tech. Note NCAR/TN-437-IA, 96 pp.

  • Fig. 1.

    A depiction of the terrain heights in western Massachusetts, southern Vermont, and eastern New York State. Terrain is given in meters above sea level. The ⊗ denotes the location of the KENX WSR-88D. The dots represent the locations of National Weather Service (NWS) or Federal Aviation Administration (FAA) surface observation sites and the triangle denotes the location of the NWS upper-air site. The small white rectangle indicates the target forecast region.

  • Fig. 2.

    A magnified map depicting the terrain heights near Williamstown in western Massachusetts, southern Vermont, and eastern New York State. Terrain is in meters above sea level. The circles denote the locations of the surface mesonet observation sites used in the verification. The mesonet sites include the following: Williamstown farm (FRM), Mt. Greylock summit (GLK), Harriman-West Airport (HWA), Mt. Ramier summit (MTR), Notch Road (NCH), Greylock School (SCH), Taconic Ridge (TCN), Williamstown landfill (WLL), and Williamstown water tower (WTR).

  • Fig. 3.

    Radial-velocity data from the KENX, Albany, NY, WSR-88D. The data were collected on 1601 UTC 4 Oct 2001 while the radar was operating in clear-air mode. The antenna was pointed at 0.5° elevation angle. The warm colors (reds) represent winds moving away from the radar while the cool colors (greens) represent wind motion toward the radar.

  • Fig. 4.

    The MM5 domain and terrain used in the real-data component of the study. The forecast verification region is located in the Greylock Valley and is designated by the white rectangle in the northeastern corner of the domain.

  • Fig. 5.

    Results from the discrete autocorrelation of the u winds in the control initial model analysis. The autocorrelation was computed at the radar's latitude, 42.6°N across a 175-point grid. The results suggest that the u-wind component of the winds in most of the lowest 10 sigma levels is positively correlated out to ranges of 35–40 km.

  • Fig. 6.

    A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The blue arrows represent the wind analysis after the addition of the radar-derived horizontal wind observations. The blue contours represent the difference between the two u-wind analyses in m s−1, and illustrate the influence radius of the Cressman objective analysis. The ⊗ denotes the location where the vertical profile of the horizontal wind shown in Fig. 7 was taken.

  • Fig. 7.

    Vertical profile of the horizontal winds from the 1600 UTC initial wind analyses used in both the control and experimental simulations. The wind profiles are taken at the radar location and over the sloping terrain southwest of the Greylock Valley at 42.64°N, 73.46°W. The solid line represents the winds without the addition of any radar observations. The dashed line represents the wind profile after it was adjusted using the radar observations. The dotted–dashed line represents the observed wind profile from the radar VAD algorithm.

  • Fig. 8.

    The gridded surface wind analysis and surface wind observations from the Berkshire mesonet valid at 1630 UTC 4 Oct 2001. This gridded wind analysis is used as the ground truth against which the accuracy of the MM5 surface wind forecasts is measured. This image is characteristic of the surface wind analyses used. The dashed rectangle illustrates the forecast verification region used in the study.

  • Fig. 9.

    A map of adjoint sensitivity for a 60-min simulation. Terrain is given in meters above sea level. The solid and dashed contours represent adjoint sensitivity of the u-wind component. The ⊗ denotes the location of the center of the adjoint sensitivity for the 60-min simulation and the dots denote the center locations of adjoint sensitivity for simulations ranging from 10 to 50 min in 10-min intervals.

  • Fig. 10.

    Center points of the adjoint initial condition sensitivity regions. The dots designate the center locations for the regions of adjoint sensitivity for the simulations ranging from 10 to 210 min in 10-min intervals. As the length of the adjoint simulation increases, the initial condition sensitivity tends to be located farther west of the Greylock Valley.

  • Fig. 11.

    RMS forecast error in the u and υ winds in the verification region as a function of simulation length. Terrain elevations are based on values that correspond to the centers of adjoint initial condition sensitivity illustrated in Fig. 10. The experimental forecast, based on an adjustment of the wind field at a single time, typically indicates improved u-wind forecast accuracy, while little or no improvement is evident in the υ-wind forecast.

  • Fig. 12.

    RMS u-wind forecast improvement and the underlying terrain at the location of the adjoint sensitivity vs simulation length. RMS forecast improvement, defined as control RMS error minus experimental RMS error, illustrates the differences between the u-wind RMS error lines in Fig. 11. Terrain elevations are based on values corresponding to the locations identified as the centers of the regions of adjoint initial condition sensitivity illustrated in Fig. 10. The forecast improvement maxima and minima, based on the adjustment of the winds at a single time, suggest that terrain variability influences the impact of the additional wind observations included in the experimental simulations.

  • Fig. 13.

    A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The blue arrows represent the wind analysis in the sensitive zone after the addition of the radar-derived horizontal wind observations. The blue contours represent the difference between the two u-wind analyses in m s−1.

  • Fig. 14.

    A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The white arrows represent the background wind analysis used in the control simulations. The red arrows represent the adjusted wind analysis outside the sensitive zone after the addition of the radar derived horizontal wind observations. The red contours represent the difference between the two u-wind analyses in m s−1.

  • Fig. 15.

    A map at 875 mb of the horizontal wind analyses used to initialize the control and experimental simulations. The black arrows represent the background wind analysis used in the control simulations. The white arrows represent the adjusted wind analysis outside the sensitive zone after the addition of the radar derived horizontal wind observations. The white contours represent the difference between the two u-wind analyses in m s−1.

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