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  • View in gallery

    The three computational grids used for all forecasts. Labels indicate the grid intervals. Terrain elevation (km MSL) is shaded.

  • View in gallery

    Physiography within the WSMR 3.3-km grid, with locations of the surface stations. Black stars identify stations referenced in the text.

  • View in gallery

    Example of data used to define statistically significant vector wind shifts. The year-long distribution of 2-h vector changes of 10-m (AGL) winds are shown for stations (a) on a mountaintop, (b) in the valley center, (c) along the eastern mountain flanks, and (d) on the western mountain flanks. Inverted black and white triangles along the abscissas point to the upper quartiles, ΔV75, for the observed and model distributions, respectively, and mark the thresholds beyond which vector changes are considered significant. Station locations are shown in Fig. 2.

  • View in gallery

    Example map of wind events: (a) 10-m (AGL) wind forecast; (b) 2-h wind changes (arrows) and their magnitudes (thick dashed lines), with gray boxes highlighting locations where the changes are significant; (c) 10-m (AGL) wind forecast (arrows) plotted atop the magnitude for each event (shaded); and (d) 10-m (AGL) wind forecast plotted atop the return period for each event (shaded). Also shown are the corresponding plots for wind events defined as significant changes in (e) wind speed and (f) wind direction. Thick black lines show the terrain elevation in increments of 400 m. Vector winds are plotted at approximately every fourth grid point.

  • View in gallery

    Time series of 10-m (AGL) wind events for a day when a cold air mass moved westward through the study area (22–23 Apr 2005). Simulated winds (arrows) are plotted atop the return periods for each event (shaded). The corresponding sample quantiles are shown in the label bar. Thick lines show the terrain elevation in increments of 400 m. Vector winds are plotted at approximately every fourth grid point. All times are UTC. The thick, dashed, blue line marks the major temporally coherent feature described in the text.

  • View in gallery

    As in Fig. 5, but for a day with quiescent synoptic conditions (19–20 Jun 2005).

  • View in gallery

    Distributions of observed 2-h changes in vector winds conditioned upon strong forecast events (≥95th percentile; gray) and nonevents (≤75th percentile; black outline). According to the nonparametric Wilcoxon–Mann–Whitney test, the null hypothesis that the two samples have the same probability distribution can be rejected with a confidence greater than 99.99%.

  • View in gallery

    As in Fig. 7 but for the distributions of maximum observed events occurring within 1 h of the forecast events. The two conditional distributions at each station are distinct with a confidence greater than 99.99%, according to the nonparametric Wilcoxon–Mann–Whitney test.

  • View in gallery

    Comparison of simulated and observed ΔV75 thresholds at each of the 22 stations. Closed circles identify stations referenced in Figs. 2 and 3 and in the text.

  • View in gallery

    Time series of the number of wind events at the four stations during summer (JJA) 2005. Also shown are the average counts for all stations. Counts are accumulated over the 3-h intervals centered on 1200, 1500, 1800 UTC, and so forth.

  • View in gallery

    Distributions of directional changes for wind events during summer (JJA) 2005 for the (top) morning and (bottom) evening. A “petal” extending northward to the middle concentric circle indicates that 20 of the events at that location were from the north. Some reports have been omitted to enhance legibility. Terrain elevation (m MSL) is shaded.

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Temporal Changes in Wind as Objects for Evaluating Mesoscale Numerical Weather Prediction

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Abstract

The study describes a method of evaluating numerical weather prediction models by comparing the characteristics of temporal changes in simulated and observed 10-m (AGL) winds. The method is demonstrated on a 1-yr collection of 1-day simulations by the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) over southern New Mexico. Temporal objects, or wind events, are defined at the observation locations and at each grid point in the model domain as vector wind changes over 2 h. Changes above the uppermost quartile of the distributions in the observations and simulations are empirically classified as significant; their attributes are analyzed and interpreted.

It is demonstrated that the model can discriminate between large and modest wind changes on a pointwise basis, suggesting that many forecast events have an observational counterpart. Spatial clusters of significant wind events are highly continuous in space and time. Such continuity suggests that displaying maps of surface wind changes with high temporal resolution can alert forecasters to the occurrence of important phenomena. Documented systematic errors in the amplitude, direction, and timing of wind events will allow forecasters to mentally adjust for biases in features forecast by the model.

Corresponding author address: Daran L. Rife, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: drife@ucar.edu

Abstract

The study describes a method of evaluating numerical weather prediction models by comparing the characteristics of temporal changes in simulated and observed 10-m (AGL) winds. The method is demonstrated on a 1-yr collection of 1-day simulations by the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) over southern New Mexico. Temporal objects, or wind events, are defined at the observation locations and at each grid point in the model domain as vector wind changes over 2 h. Changes above the uppermost quartile of the distributions in the observations and simulations are empirically classified as significant; their attributes are analyzed and interpreted.

It is demonstrated that the model can discriminate between large and modest wind changes on a pointwise basis, suggesting that many forecast events have an observational counterpart. Spatial clusters of significant wind events are highly continuous in space and time. Such continuity suggests that displaying maps of surface wind changes with high temporal resolution can alert forecasters to the occurrence of important phenomena. Documented systematic errors in the amplitude, direction, and timing of wind events will allow forecasters to mentally adjust for biases in features forecast by the model.

Corresponding author address: Daran L. Rife, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000. Email: drife@ucar.edu

1. Introduction

Verification of numerical weather prediction (NWP) models serves several purposes, some direct, others indirect. One direct purpose is to identify and quantify a model’s deficiencies so they can be understood and remedied. Even deficiencies that are not understood can be at least partially neutralized if they are systematic. For instance, a model’s biased temperature can be automatically adjusted during the postprocessing of a forecast. Adjustments or compensations such as this are an important use of verification, although a less direct one. Indeed, one can imagine many potential textual, tabular, or graphical aids that can be created and supplied to forecasters so they can better interpret the output from an NWP model and can compensate for its known deficiencies. In many cases, creating such aids is technically straightforward because they are often natural by-products, or merely small extensions, of the data and methods already being employed for model verification. However, if verification-derived forecast aids are to be useful, they must be as easy to interpret as standard meteorological graphics, such as a map of the sea level pressure, while blending complex information about a model’s performance with predictions of the atmosphere’s future state.

In this article, we introduce and demonstrate just such a forecast aid, and we describe the method of NWP model verification from which it is derived. The aid is a means of compactly synthesizing and verifying temporal features in gridded fields. To demonstrate it, we apply our approach to wind at 10 m (AGL), as simulated by a mesoscale NWP model.

Variations in 10-m winds over minutes to hours are of great concern to many who rely on weather forecasts. For example, at the test ranges operated by the U.S. Army Test and Evaluation Command (ATEC), who sponsored this work, accurate forecasts of near-surface wind are critical for planning and conducting transport-and-dispersion experiments, precision airdrop exercises, unmanned aerial vehicle operations, and guided and unguided missile tests (Liu et al. 2008).

Our work extends that of Rife and Davis (2005, hereafter RD05), with four distinct differences. First, we use vector winds to identify and characterize temporal features in the near-surface wind field. Second, we use a modified version of RD05’s method to determine what constitutes a significant temporal shift in the vector wind at each location and time. We call these shifts events, for want of a better word. Third, we show how the simulated temporal shifts at each location tend to organize into spatially coherent structures, even though the events at individual locations are identified independently from one another. Last, by-products of the verification of events are used to craft graphical forecast aids.

As we will show, the spatial distribution of wind events enables us to answer the following questions:

  • Will conditions at a given location remain steady or change only slightly, and if so for how long?
  • Is a significant change expected, and if so when and where will the change occur, and how rare a change is it?
  • How well does the model predict these changes?

We will then show examples highlighting the model’s ability to replicate the wind events, by comparing a year-long collection of 24-h time series of simulated 10-m (AGL) winds to the corresponding series of surface station measurements. Though the sparse and unevenly distributed point-based measurements within the study area do not allow us to evaluate the spatial patterns of simulated wind events, we can quantify how well the model replicates several other characteristics of events at the surface stations: (a) magnitudes, (b) directions, (c) number at a given location and time, and (d) return period, which is the average time between the occurrence of events of a given magnitude or greater.

2. Data

a. Numerical forecasts

Although our technique can be applied to any NWP system and to any prognostic quantity, in this study we demonstrate it on high-resolution near-surface wind forecasts produced by a specially adapted version of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). We focus on forecasts generated between 1 January 2005 and 1 January 2006 over the White Sands Missile Range (WSMR) in southern New Mexico. The version of the MM5 used in this study is part of a rapidly deployable, operational, mesogamma-scale weather analysis and forecast system that has been developed by the National Center for Atmospheric Research (NCAR) for various ATEC facilities (Davis et al. 1999; Liu et al. 2006; Liu et al. 2008). The model is nonhydrostatic and uses telescoping, two-way-interacting, computational grids, with the finest grid centered over the test range. It features a full suite of physical-process parameterizations, including the Medium-Range Forecast (MRF) model PBL scheme (Hong and Pan 1996); the Grell (1993) cumulus parameterization on grids using a 10-km or larger grid increment; a modified version of the Oregon State University land surface model (Chen and Dudhia 2001a,b); the explicit cloud microphysical scheme of Reisner et al. (1998), which predicts the mixing ratio of four hydrometeor species (cloud droplets, cloud ice, rain, and snow); and short- and longwave radiation effects represented by the Dudhia (1989) and Mlawer et al. (1997) schemes, respectively. Some nonstandard adaptations to the MM5 are also used. For example, the standard MM5 land cover and soil properties have been modified to include the salt flats in northern Utah and the white gypsum sands and lava flows in southern New Mexico (Rife et al. 2002). Initial and lateral boundary conditions are specified using linear temporal interpolations between 3-hourly Eta Model analyses and forecasts with a 40-km grid increment.

The grid configuration, centered over WSMR, has three nested, two-way-interacting, computational grids. Grid increments are 30, 10, and 3.3 km; and mesh sizes are 98 × 84, 106 × 67, and 61 × 61, respectively. All computational grids use 36 unevenly spaced vertical layers, with approximately 12 levels in the lowest 1 km. The configuration of the computational grids is shown in Fig. 1. Eight 24-h forecasts were performed per day, with the first initialized at 0000 UTC, and a new one initialized every 3 h thereafter. Only forecasts initialized at 1200 UTC from the finest grid (3.3-km grid increment) are used for this study. Output is hourly. We focus on the winds at 10 m (AGL) from the model, in both gridded form and interpolated to the locations of observation stations.

b. Observations

Within the finest domain at WSMR there are about 30 surface observation sites operated by the National Weather Service, the U.S. Air Force, the ATEC, the National Resources Conservation Service, and the Bureau of Land Management (Fig. 2). Observations were obtained in real time, primarily through the Meteorological Assimilation Data Ingest System (MADIS; information online at http://madis.noaa.gov), from 1 January 2005 through 1 January 2006. Because each network is designed to meet the needs of its operating agency, there are differences in site characteristics, sensor types and heights, and reporting intervals. For verification, we used data from the 22 most reliable stations located well away from the boundaries of the model’s computational domains. In most cases the modeled terrain matches the elevations of the observation sites reasonably well, but in several notable cases the match is quite poor (Table 1), especially for S09, which sits atop a mountain whose height is underrepresented in the model. We return to this point later in the paper.

3. Identifying and characterizing surface wind events

a. Concept

Our goal in this paper is to identify, and to quantify the characteristics of, temporal features in observed and simulated 10-m (AGL) winds. One natural definition of a feature in a time series is a temporal change that exceeds a threshold. For this example application, we choose a threshold and a sampling strategy that maximize the coherence between events at neighboring locations and times, and that allow us to connect the present results to those from RD05. Both the threshold and sampling strategy can easily be adjusted to suit the needs of a particular application. For example, to evaluate extreme events, wind shifts might be sampled over years or decades, wherein only shifts whose magnitudes lie within the upper decile of the distribution are considered.

b. Sampling temporal changes in wind

We start by computing the vector difference for 10-m (AGL) winds in each contiguous 2-h interval within a given 24-h series (VtVt−2h), while noting the location, time of occurrence, magnitude, and direction of each vector change. The diagnosed altitude of 10 m matches most of the observations (a few are taken at 2 m AGL) and is the same altitude of the “surface winds” in the Advanced Weather Interactive Processing System (AWIPS) displays that are so familiar to many forecasters. Observed and forecast changes are treated separately and grouped according to station location. A distribution of wind changes comprises a collection of observed or forecast 2-h changes for each station. In addition, every point in the model not nearest to an observing station has its own distribution of 2-h wind changes (about 3580 points for the domain considered). For any location, a distribution contains a maximum of 8030 possible 2-h changes: twenty-two 2-h changes, ending on the hour, for each of the 365 days. At each location the sizes of the observed and forecast distributions are exactly the same because if an observation is missing, we omit the corresponding forecast, and if a forecast is missing, we omit the corresponding observation; only paired data are included in the distributions. There are 22 changes per day, not 24, because successive 2-h periods overlap by 1 h, and the first 2-h period begins at forecast hour 1, the last at forecast hour 22.

c. Defining significant wind shifts

A significant event is empirically defined as any 2-h change whose magnitude falls in the upper quartile of the year-long distribution of 2-h changes. The magnitude of the wind change at the 75th percentile is denoted ΔV75. Observed and simulated values of the rank of the 75th percentile, q0.75, are derived separately to account for the model’s possibly errant estimation of the observed variability, thus ensuring an equal number of significant events in the observed and simulated distributions. All wind events at a given station are found, and their times of occurrence, magnitudes, and directions are retained in the database.

Figure 3 presents the data used to define statistically significant wind events at four stations in different geographical regions: S09 in the mountains, S32 in a valley, and S31 and ALM on the western and eastern slopes of the Tularosa Basin, respectively. Overall, the distributions of the observed and simulated wind changes are similar to each other, but with local differences. For instance, at the mountain station S09, the simulated distribution has a pronounced low bias. A similar, but smaller, bias is evident at ALM.

The ΔV75 thresholds defined from 90- and 180-day samples yielded values similar to those from the 365-day dataset, so our approach would still be useful when archived data cover less than 1 yr.

d. Constructing geographic maps of wind events

Wind events can be plotted on a map in the same manner as ordinary meteorological fields are plotted. When arranged in chronological order, the maps clearly depict how clusters of events move through space and time (described in the next section). Figure 4 illustrates how a map is constructed for a single output time. From the original gridded 10-m wind forecast (Fig. 4a), the magnitude of the 2-h vector change at each location is computed (Fig. 4b). Based on the precalculated values of ΔV75 at each grid point, significant vector changes are highlighted (gray boxes in Fig. 4b). Events can then be color coded according to their characteristics. For example, the colored boxes in Fig. 4c mark where a significant change in wind direction and/or speed is predicted; each box is shaded in proportion to the magnitude of the predicted change. Vectors in Figs. 4a, 4c, and 4d show the wind field at the forecast’s valid time (i.e., the wind field resulting from the changes in the previous 2 h).

Wind events can also be shaded according to their return period (Fig. 4d), which objectively quantifies the “significance” of a given wind shift by casting it in terms of rarity. The return period, R, is defined as
i1520-0434-24-5-1374-e1
wherein To is the temporal separation between points in the original time series (1 h in this case), q the rank of the event within its respective distribution, and N the number of 2-h vector changes within that distribution. Because events are defined as any wind shift whose magnitude is greater than the data-specific ΔV75 threshold, return periods range from 4 h (for q = ¾N) to 1 yr (for q = N − 1, the rarest event). The similarity between Figs. 4c and 4d results from the relative invariance of the model-derived value of ΔV75 across the domain. When ΔV75 varies substantially across a domain, the field of vector wind changes will not be similar to the field of the recurrence frequency.

We define events in terms of vector changes in the wind, but one might also choose a definition based on direction and speed. Such a choice does not greatly alter the visual depiction of the results (Figs. 4e and 4f), nor the overall approach described in this paper. A definition based on vector change has some advantages. For example, wind direction is overly sensitive to measurement error at low wind speeds; vector changes have no such limitation.

Figure 5 depicts the spatial distribution of a sequence of wind events, with the forecast wind field plotted atop the return periods. Within the context of cumulative probability, a return period associated with a quantile, q, is typically interpreted as the average time between occurrences of events of that magnitude or greater. Thus, the value of a variate, x, associated with a return period of 45 days would be called a 45-day event (Wilks 2006, p. 108). For the examples shown in Fig. 5, the average time separating many events is 2 days or less. This results from our choosing a threshold of q0.75 for defining significance, which maintains good coherence between events. This can easily be adjusted to filter out all but the strongest and rarest events.

Magnitudes and return periods of events depend strongly on location. For example, wind shifts of 10 m s−1might be common on a high mountain peak but uncommon in a sheltered valley. The purpose of expressing changes in terms of return period is to account for this local variability in the magnitude of wind changes. When a feature moves through a very heterogeneous environment, plots of the return period produce a cleaner depiction of the feature’s structure than would a plot of the magnitude of a change. Table 2 illustrates the geographic variability of event characteristics at four stations within the study area.

4. Using wind event maps to highlight rapidly changing conditions

Maps of the horizontal clustering of wind events, especially when animated or displayed sequentially, as in Figs. 5 and 6, draw forecasters’ attention to locations where conditions are expected to change rapidly. Often, such occurrences are less obvious from the actual predicted wind field at any one time. Figure 5 is a sequence of images showing wind events for 22–23 April 2005, when a stably stratified air mass moved westward through the study area. Cold air approached from the east at 1800 UTC, and by 2000 UTC it had entered the southern Tularosa Basin, with a vortex developing in the lee of the Sacramento Mountains. At 0000 UTC, cold air and the associated strong winds filled the entire domain. At the center of the basin, the flow was stagnant. Finally, at 0400 UTC winds in the western half of the domain rotated clockwise in response to a broad synoptic pressure ridge to the east and northeast of the domain. Lee vortices were present downstream of the Sacramento Mountains, a cyclonic vortex at the northwestern flank, and an anticyclonic one at the southwestern flank. Flow stagnation and lee vortices are commonly observed along the western flanks of the Sacramento Mountains under these conditions, especially at stations S18, S07, ALM, S27, and S14. The shaded field beneath the wind vectors highlights locations where the winds changed significantly (according to the 75th-percentile definition) during the previous 2 h.

Because events are defined according to changes in speed and/or direction, they are not necessarily synonymous with strong winds. For example, at 2200 UTC on 22 April, wind events are predicted along the cross-valley stretch of the southern Tularosa Basin. Yet no events are predicted south and southwest of this area, even though the winds there are just as strong as in the southern part of the basin. This is because the winds to the south and southwest have undergone little change since 2000 UTC. Similarly, events are predicted at the southeastern flanks of the San Andres Mountains at 0400 UTC, even though winds in that area are weak relative to their surroundings. By comparing the predicted winds at this time and location to those from 2 h earlier (0200 UTC), we see that they have weakened and shifted direction by well more than 90°, while those at neighboring points have changed very little.

Even without animation, the panels in Fig. 5 convey just how coherent such clusters of events can be, even over many hours, as they move across the domain. In many cases this is because such clusters are closely tied to meteorological phenomena, which is partly what makes such maps useful to forecasters. The cluster moving through the center and southern part of the domain from 2200 to 0400 UTC has return periods as high as 25.8 days, or a probability of occurrence as low as 1 − 0.999 = 0.001; this is a rare event that a forecaster might want to closely monitor. In the southwest corner of the domain at 0600 UTC (not shown), there are events whose return periods exceed 50 days, with a probability of occurrence of 1 − 0.9993 = 0.0007.

A second example of wind event maps is shown in Fig. 6, for 19–20 June 2005, when synoptic forcing was weak. These wind events were primarily associated with the transition from downslope to upslope flow during the day, and the opposite transition during the night, as indicated by the slope–valley signatures in the wind field, and the semidiurnal return periods for events. At 1800 UTC, significant wind changes were predicted over the San Andres Mountains, as the low-level flow transitioned from downslope to upslope. The return periods for events over the northern half of the mountains are somewhat longer than for those over the southern half, which indicates that shifts predicted in this area are either somewhat stronger than those over the southern half, or that events of this strength occur less often over the northern half of the San Andres Mountains compared to the southern half. During the afternoon, when the PBL is well mixed, few events are predicted, as might be expected under light synoptic forcing, and in the absence of deep moist convection. In addition, the predicted events have very short return periods of 4–6 h. By 0200 UTC, the nighttime transition has begun, with winds shifting downslope over the San Andres Mountains, and by 0400 UTC downslope flows are well developed over all mountains in the area.

As mentioned above, maps of wind events can be used for tracking meteorological features. Using conventional meteorological fields to track features through complex terrain is difficult because observations typically are sparse and scattered across a range of altitudes, and any feature moving across the terrain experiences complex forcing on many scales, which muddies its signature (Hill 1993). This is especially true for features in near-surface wind and surface pressure, which seemingly disappear as they enter mountainous terrain, then reappear on the lee, often displaced from their original axis of forward movement (e.g., Sanders 1999; Schultz and Doswell 2000). Our process for defining wind events highlights temporally and spatially coherent features, and filters out those that are more transitory, even in complex terrain. For example, in Fig. 5, events in the southern Tularosa Basin and southwestern slopes of the Sacramento Mountains are arranged in a reversed L-shaped feature at 2000 UTC (dashed blue line in the figure). This feature moves coherently northwestward to the center of the basin at 0000 UTC, when flows from the east and south converge, and continues to advance to the northwestern corner of the domain by 0200 UTC. The coherence of features in clustered wind events is a function of how frequently they occur, of course. In the upper extreme of the wind change distribution (say the 99th percentile or higher), there is little spatial continuity to such rare events.

5. Verifying the characteristics of wind events

By defining verification metrics in terms of wind events, one can evaluate the overall kinematical statistics of a model. For demonstration, we focus on quantifying how well the model predicts the magnitude, return period, and number of events at a given station.

a. Timing and discrimination of events

A basis for the object-based verification of quasi-deterministic forecasts is that features in the forecast often have some correspondence to observed features. If this is not true, then a forecaster would have little reason to examine the model solution for evidence of important features, and mental adjustment of the forecasts would not produce beneficial results. Hence, we first consider whether the model can discriminate between small and large wind changes in the observations.

The performance metric we adopt is the distinction in the observed distributions of wind changes for instances when the model predicts a strong event versus when the model does not predict even a significant event. First, we define strong events as 2-h changes above the 95th percentile and identify them in the forecasts at each of the four locations of interest during winter [January–March (JFM)] and summer [June–August (JJA)]. Next, we find the observed 2-h change in vector wind that is exactly coincident with the forecast event. Then, we calculate the corresponding distributions for times when no significant event is predicted (2-h changes less than the 75th percentile). The two conditional distributions are distinct (Fig. 7) with a confidence greater than 99.99%, according to the nonparametric Wilcoxon–Mann–Whitney test. Results for other stations are similar.

The requirement that the forecasts and observations match exactly in time is quite strict. In some instances this strictness is appropriate. In other instances, a forecast might be considered sufficiently accurate if a change in wind occurs within an hour of the time it is predicted to occur. When our performance metric is relaxed to permit this window of ±1 h, the visual distinction between the forecast and observed events is even greater (Fig. 8). The nonparametric Wilcoxon–Mann–Whitney test again produces a confidence of greater than 99.99%. When the window is increased to ±3 and ±6 h (not shown), the results look quite similar to those in Fig. 8; such liberally wide windows are not necessary to make the model appear to perform better.

The MM5 is capable, then, of distinguishing between strong (rare) wind shifts and weak (common) wind shifts, even when a fairly stringent one-to-one correspondence is required between the predicted and observed shifts. We note that this simple calculation does not account for differences in forecast lead time, nor does it account for misses (a feature observed but not predicted). In principle, knowledge of missed features is important; however, owing to the incompleteness of observations, it is difficult to depict the spatial coherence of the observed features.

b. Magnitudes of events

Because of the manner in which events are defined, any systematic error in the magnitude of the 10-m winds is revealed as a difference in the quantile value of the vector wind changes between the prediction and observations. A comparison of the forecast and observed ΔV75 values, for example, is sufficient to indicate any bias in event strength or, alternatively, any bias in event frequency for a given threshold of the wind change magnitude. (Recall that choosing a particular quantile as a threshold results in the same number of simulated and observed events.) Thus, in Fig. 3 for example, if a model’s amplitudes are biased low, it will predict fewer events above the threshold defined by the observations. This quality is most obvious at S09 and ALM. To the extent that the forecasts and observations adhere to the same type of distribution (a modified gamma distribution in this case), we can also infer that the model will overestimate the return period of extreme events as well.

The amplitude bias at all stations can be summarized with a scatterplot (Fig. 9) in which the abscissa is the observed vector wind change for some quantile (ΔV75 in this case) and the ordinate is the forecast vector change for that quantile. From this graph, it is apparent that the MM5 underpredicts events’ strengths and/or frequencies at all but four stations. The underprediction is particularly large at S09, perhaps partly because of the difference in the station’s simulated and actual altitudes (Table 1). Averaged over all stations, ΔV75 in the MM5 is about 70% of what is observed. Even more striking is the model’s muted range in ΔV75 compared to the range in the observations. Observed ΔV75 is about 1.7–4.3 m s−1, whereas forecast ΔV75 is only about 2.4–2.9 m s−1. This discrepancy of about a factor of 5 suggests that while the overall variance predicted by the MM5 has a modest shortfall, the model does not capture the heterogeneity of the variance even approximately well. Plots of vector changes in higher quantiles, such as ΔV95 (not shown), display similar patterns. The reasons for this behavior are not entirely clear, but may have to do with the siting of individual stations in locations that do not represent the surroundings on a scale that the model can resolve. Stations that are sheltered by man-made or natural obstacles (sand dunes, trees, etc.) might produce a relatively small variability that cannot be replicated.

c. Number of events at a given location and time

Another measure of the performance of the forecast model considers the diurnal variation in the number of events. Both the simulated and observed winds change most frequently in the evening (Fig. 10). The model’s peak frequency is later in the evening, at 0300 UTC (2100 LT) during June, July, and August, about 1 h after sunset. The observed timing of events is less peaked than is the simulated timing. The highest observed frequency at the mountain station S09 is also 6 h later than at the other three stations.

There is probably more than one reason for the model’s biased timing. The relatively sharp peak in the simulated event frequency at 0300 UTC is consistent with the behavior in the diurnally dominated case shown in Fig. 6, wherein significant events suddenly appear between 0200 and 0400 UTC. It is quite likely that the sharp peak in the forecasts represents the transition to the nocturnal boundary layer, partly originating from cooling on the terrain slopes. The real atmosphere’s transition is less synchronized among stations. One possible reason for the difference is that these simulations do not include shadowing effects (i.e., in the model, the terrain casts no shadows, and the shortwave radiation’s angle of incidence is not affected by slope) that might broaden the distribution of the timing. It is also likely that in a regime-dependent boundary layer scheme, the switch to a stable regime decoupled from the free atmosphere is too abrupt, and there is no intermittent turbulence to lengthen the transition and to reduce the magnitude of the wind changes. Although this conclusion is speculative, its suggestion in the data is an example of how examining events rather than full wind fields can direct model developers and model users in perhaps more imaginative directions in their attempts to better understand the sources of model error.

d. Events defined by changes in direction

Perhaps a more physically interpretable measure of error is in terms of the direction of the vector wind changes. The simulated and observed directions are compared using wind roses (Fig. 11). A bar’s orientation in Fig. 11 represents the direction from which a change vector points, and a bar’s length represents the frequency of a change in that direction. Because the bars represent actual counts, not relative frequencies, there are differences in the number of events at each station.

During the mid- to late morning (0700–1100 LT; see Fig. 11a), southerly wind changes prevail in the northern Tularosa Basin. These changes probably represent the transition from down-valley to up-valley flow forced by heating of the gently sloping valley floor; the gain in elevation from S01 at the southern end of the valley to S14 in the north is 153 m (Table 1). Although this tendency toward a southerly change appears over the northernmost part of the valley in the simulations (Fig. 11b), it is missed elsewhere. The simulations are more characterized by easterly accelerations over the western valley, and westerly accelerations over the central and eastern valley. This is the expected response from upslope flow near north–south-oriented ridges (e.g., Whiteman 2000). For some reason, in the simulations the signature of the change to upslope flow is stronger than that of the change to up-valley flow. Over the southern part of the basin, the observed and simulated changes tend to be westerly or northwesterly during the morning.

During the evening (Figs. 11c and 11d), to first order, the wind change patterns at many stations are reversed from what they were in the morning. The model performance over the southern part of the basin again appears better than over the northern part. Although the signal is less coherent overall, the simulations display more changes in the zonal wind (across the valley) than in the meridional wind (along the valley) over the northern half of the valley. This is not observed.

One might expect the realism of the wind roses in Fig. 11 to depend strongly on the match between sites’ simulated and actual altitudes (Table 1), but that is not always the case. Although some sites with large discrepancies in altitude do suffer from inaccurate forecasts of wind direction (e.g., S09 and SRR), there are also locations with comparatively good forecasts despite poor matches in altitude (e.g., S17 and S19), and locations with comparatively poor forecasts despite good matches in altitude (e.g., S27).

6. Summary and commentary

This study describes the potential utility of constructing distributions of temporal changes of the wind and evaluating numerical forecasts by comparing simulated and observed attributes of those distributions. The basic approach has the advantage of being relatively simple, yet fundamental, when one considers that the local change in the horizontal wind represents the sum of all acting forces. Therefore, the approach aims directly at the ability of models to simulate the frequently small residual among the various forces that drive local weather.

We demonstrated our approach with a year of 1-day simulations by the MM5, with an innermost grid increment of 3.3 km, over southern New Mexico, centered on the White Sands Missile Range (WSMR). Temporal objects, or events, defined as local vector wind changes over 2 h, were calculated at observed surface stations and for each grid point over the entire fine domain of the model. From the distributions of wind changes aggregated over 1 yr, we empirically chose the changes above the uppermost quartile of each respective distribution to be significant.

We demonstrated that the magnitude of the observed wind changes at the station locations was significantly greater when the model forecast a strong wind event as opposed to forecasting no significant event. According to the nonparametric Wilcoxon–Mann–Whitney test, the two conditional distributions are distinct with a confidence greater than 99.99%. This discrimination is necessary in object-based verification if we are to have any confidence that a predicted event has an observed counterpart.

When viewed spatially, clusters of these locally defined significant events exhibited considerable spatial and temporal continuity. Most events were not associated with a synoptic-scale front. Rather, they were products of the diurnal and topographic forcing around WSMR, modified by the synoptic conditions. The continuity of events over many hours suggests that displaying them on two-dimensional maps with high spatial and temporal resolutions could be useful to forecasters.

We found that the MM5, with a horizontal grid increment of 3.3 km, presented a modest low bias in the magnitude of events, consistent with results from Rife et al. (2004). However, the MM5 could not replicate the spatial heterogeneity of the threshold that we used to define events (ΔV75). We infer that models with grid increments of roughly 1 km can reasonably reproduce the overall temporal variance as measured by surface station winds averaged over several minutes, but even on these scales the factors that govern the spatial variation of temporal variability apparently are not resolved.

Given the sparseness of the observations, even with the WSMR mesoscale network of ∼20 reliable stations, it was not possible to verify clustered events’ spatial structures directly. However, these structures in the simulations, combined with statistical verification of events’ characteristics, should allow forecasters to monitor real-time observations for indications of such features and mentally to adjust the forecasts based on systematic errors in the amplitude, direction, and timing of wind events.

Imagine, for example, that safe operation of some heavy machinery is only possible when wind speeds do not exceed 20 m s−1, and a model predicts an apparently safe maximum gust of 15 m s−1. A forecaster who knows that the model typically underpredicts wind gusts at that machinery’s location will be justifiably cautious in accepting the prediction of 15 m s−1 at face value and might choose to issue an alert for gusts exceeding the 20 m s−1 threshold. Second guessing a model—adjusting a forecast for the model’s known weaknesses—is precisely what gives an experienced forecaster an advantage over an inexperienced one, whether it involves an example like the one above, or any number of other examples, such as the position of a cold front, the onset of freezing rain, or the low temperature in an orchard on a clear, calm night.

Although we have focused on the temporal changes of a single variable over a particular region, the methods herein are easily generalized to other variables and regions. Regions devoid of physiographic variations still exhibit substantial wind shifts associated with fronts, convectively generated outflows, drylines, or boundary layer growth and decoupling, for example. Changes in pressure, temperature, or humidity can also be evaluated using the same approach and would be applicable to morning or evening boundary layer transitions, mountain waves (detectable from surface pressure changes), or the removal of shallow cold-air masses. Focusing on quantiles of distributions effectively normalizes events so that model performance across disparate geographical regions can be compared more easily.

Future work will include applying these techniques to forecasts from the WRF model (Skamarock et al. 2005) and exploring the variations of forecast quality with grid spacing. There is no doubt that NWP models’ ability to accurately simulate lower-tropospheric wind features, especially when strongly affected by terrain, depends on spatial resolution. However, predictability limitations can prevent accurate forecasts even at short lead times and fine resolution (e.g., Davis et al. 1999; Mass et al. 2002; Hart et al. 2004; Rife et al. 2004). Object-based verification such as outlined herein can provide insight into phenomenologically based model errors even when there are significant spatial and temporal errors in features. We intend to exploit diagnostic information obtained from this verification approach regarding the sources of error, whether from model physics or initialization errors. Finally, in a separate line of inquiry, we will evaluate how well wind events are represented in a 21-yr set of dynamically downscaled reanalyses, currently being generated by NCAR for application to research on transport and dispersion and renewable energy.

Acknowledgments

This research was funded by the U.S. Army Test and Evaluation Command through an interagency agreement with the National Science Foundation. We thank Tom Warner (NCAR) for reviewing an early version of the manuscript, and the two anonymous reviewers for helping us to improve the final manuscript.

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Fig. 1.
Fig. 1.

The three computational grids used for all forecasts. Labels indicate the grid intervals. Terrain elevation (km MSL) is shaded.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 2.
Fig. 2.

Physiography within the WSMR 3.3-km grid, with locations of the surface stations. Black stars identify stations referenced in the text.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 3.
Fig. 3.

Example of data used to define statistically significant vector wind shifts. The year-long distribution of 2-h vector changes of 10-m (AGL) winds are shown for stations (a) on a mountaintop, (b) in the valley center, (c) along the eastern mountain flanks, and (d) on the western mountain flanks. Inverted black and white triangles along the abscissas point to the upper quartiles, ΔV75, for the observed and model distributions, respectively, and mark the thresholds beyond which vector changes are considered significant. Station locations are shown in Fig. 2.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 4.
Fig. 4.

Example map of wind events: (a) 10-m (AGL) wind forecast; (b) 2-h wind changes (arrows) and their magnitudes (thick dashed lines), with gray boxes highlighting locations where the changes are significant; (c) 10-m (AGL) wind forecast (arrows) plotted atop the magnitude for each event (shaded); and (d) 10-m (AGL) wind forecast plotted atop the return period for each event (shaded). Also shown are the corresponding plots for wind events defined as significant changes in (e) wind speed and (f) wind direction. Thick black lines show the terrain elevation in increments of 400 m. Vector winds are plotted at approximately every fourth grid point.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 5.
Fig. 5.

Time series of 10-m (AGL) wind events for a day when a cold air mass moved westward through the study area (22–23 Apr 2005). Simulated winds (arrows) are plotted atop the return periods for each event (shaded). The corresponding sample quantiles are shown in the label bar. Thick lines show the terrain elevation in increments of 400 m. Vector winds are plotted at approximately every fourth grid point. All times are UTC. The thick, dashed, blue line marks the major temporally coherent feature described in the text.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 6.
Fig. 6.

As in Fig. 5, but for a day with quiescent synoptic conditions (19–20 Jun 2005).

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 7.
Fig. 7.

Distributions of observed 2-h changes in vector winds conditioned upon strong forecast events (≥95th percentile; gray) and nonevents (≤75th percentile; black outline). According to the nonparametric Wilcoxon–Mann–Whitney test, the null hypothesis that the two samples have the same probability distribution can be rejected with a confidence greater than 99.99%.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 8.
Fig. 8.

As in Fig. 7 but for the distributions of maximum observed events occurring within 1 h of the forecast events. The two conditional distributions at each station are distinct with a confidence greater than 99.99%, according to the nonparametric Wilcoxon–Mann–Whitney test.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 9.
Fig. 9.

Comparison of simulated and observed ΔV75 thresholds at each of the 22 stations. Closed circles identify stations referenced in Figs. 2 and 3 and in the text.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 10.
Fig. 10.

Time series of the number of wind events at the four stations during summer (JJA) 2005. Also shown are the average counts for all stations. Counts are accumulated over the 3-h intervals centered on 1200, 1500, 1800 UTC, and so forth.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Fig. 11.
Fig. 11.

Distributions of directional changes for wind events during summer (JJA) 2005 for the (top) morning and (bottom) evening. A “petal” extending northward to the middle concentric circle indicates that 20 of the events at that location were from the north. Some reports have been omitted to enhance legibility. Terrain elevation (m MSL) is shaded.

Citation: Weather and Forecasting 24, 5; 10.1175/2009WAF2222223.1

Table 1.

Simulated and actual terrain elevation (m MSL) at the observation sites, and the difference between the two (m).

Table 1.
Table 2.

Geographic variability of the observed magnitudes and return periods for events occurring at each of three sample quantiles. The return period, R, for each quantile’s threshold is also shown.

Table 2.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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