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  • View in gallery

    Base map showing the locations of S-band radars used in the freezing-level forecast performance analysis (stars), 915-MHz wind profilers used for supporting analysis (circles), and river gauge sites used by White et al. (2002) to study the sensitivity of basin runoff to the freezing level (diamond, plus, square, triangle). The forecast evaluation point for the Sierra Nevada is Georgetown (x), whereas the coastal mountain forecast evaluation site is Cazadero (star).

  • View in gallery

    (left) Example of vertical profiles of range-corrected radar SNR (dots), radar Doppler vertical velocity (triangles), and (right) rawinsonde temperature during a precipitation event when a bright band was present. Radar data were collected by the 915-MHz wind profiler at SHS and the rawinsonde was launched from the same site. Both datasets were collected near 1100 UTC 14 Jan 2006.

  • View in gallery

    Histogram of temperatures measured at the radar-derived snow levels above (a) BBY during PACJET-01 and above (b) SHS during HMT-06. The snow levels were detected using the snow-level algorithm applied to 915-MHz wind profiler data. The temperatures were measured with serial rawinsondes launched from the wind profiler location.

  • View in gallery

    Frequency of occurrence of (top) observed snow level and the (bottom) layer depth between the observed freezing level and snow level. Observed snow levels at or below 1.2 km are absent from Alta because the first data point is just shy of 1.2 km MSL owing to the Alta’s site elevation (1.08 km MSL) and the minimum detectable range of the radar (0.11 km).

  • View in gallery

    Frequency of occurrence of height differences between radar-derived freezing level and snow level as a function of radar-derived snow level for (top) Alta and (bottom) Cazadero.

  • View in gallery

    (top) Frequency of occurrence of freezing-level forecast bias for all heights and forecast verification times. The bias distribution, as a function of observed (i.e., radar derived) freezing level and forecast verification time are shown for (middle) Alta and (bottom) Cazadero.

  • View in gallery

    (top) Mean difference between CNRFC forecast and observed radar-derived freezing levels for different forecast lead times. (bottom) The standard deviation of the differences is shown. Sample populations are denoted at the top end of each standard deviation bar.

  • View in gallery

    Directional shear calculated from wind profiler observations collected at BBY (near Cazadero), and SHS (near Alta), for observed (i.e., radar derived) freezing levels (left) below and (right) above 2.3 km MSL at (top) day 1, (middle) day 2, and (bottom) day 3 forecast periods. Negative (positive) values of directional shear correspond to cold (warm) advection.

  • View in gallery

    Two-hour accumulated rainfall plotted as a function of observed (i.e., radar derived) freezing level.

  • View in gallery

    Peak flow and percentage error resulting from freezing-level forecast bias for the Klamath River near Tuwar Creek (see Fig. 1), assuming an observed freezing level of 914 m and based on the results of White et al. (2002). The dashed curves were drawn manually to represent the asymptotes that correspond to a freezing level (upper right) higher and (lower left) lower than the complete basin.

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Developing a Performance Measure for Snow-Level Forecasts

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  • 1 NOAA/Earth System Research Laboratory, Boulder, Colorado
  • | 2 NOAA/NWS, California–Nevada River Forecast Center, Sacramento, California
  • | 3 NOAA/Earth System Research Laboratory, Boulder, Colorado
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Abstract

The snow level, or altitude in the atmosphere where snow melts to rain, is an important variable for hydrometeorological prediction in mountainous watersheds; yet, there is no operational performance measure associated with snow-level forecasts in the United States. To establish a performance measure, it is first necessary to establish the baseline performance associated with snow-level forecasts. Using data collected by vertically pointing Doppler radars, an automated algorithm has been developed to detect the altitude of maximum radar reflectivity in the radar bright band that results from the precipitation melting process. This altitude can be used as a proxy for the snow level, partly because it always exists below the freezing level, which is defined as the altitude of the 0°C isotherm. The skill of freezing-level forecasts produced by the California–Nevada River Forecast Center (CNRFC) is evaluated by comparing spatially interpolated and forecaster-adjusted numerical model freezing-level forecasts with observed freezing levels estimated by radars operating at 2875 MHz (S band). The freezing level was chosen instead of the snow level as the comparison parameter because the radar algorithm and the CNRFC have different interpretations of the snow level. The evaluation occurred at two sites: one in the coastal mountains north of San Francisco and the other in the Sierra Nevada. The evaluation was conducted for forecasts made during the winter wet season of 2005/06. Although the overall mean freezing-level forecast bias is small enough not to be hydrologically significant, about 15% of the forecasts had biases greater than 300 m (forecast too low). The largest forecast biases were associated with freezing levels above 2.3 km that were underforecasted by as much as 900 m. These high freezing-level events were accompanied by the heaviest precipitation intensities, exacerbating the flood threat and making the forecast even more challenging.

Corresponding author address: Dr. Allen B. White, NOAA/ESRL, R/PSD2, 325 Broadway, Boulder, CO 80305. Email: allen.b.white@noaa.gov

Abstract

The snow level, or altitude in the atmosphere where snow melts to rain, is an important variable for hydrometeorological prediction in mountainous watersheds; yet, there is no operational performance measure associated with snow-level forecasts in the United States. To establish a performance measure, it is first necessary to establish the baseline performance associated with snow-level forecasts. Using data collected by vertically pointing Doppler radars, an automated algorithm has been developed to detect the altitude of maximum radar reflectivity in the radar bright band that results from the precipitation melting process. This altitude can be used as a proxy for the snow level, partly because it always exists below the freezing level, which is defined as the altitude of the 0°C isotherm. The skill of freezing-level forecasts produced by the California–Nevada River Forecast Center (CNRFC) is evaluated by comparing spatially interpolated and forecaster-adjusted numerical model freezing-level forecasts with observed freezing levels estimated by radars operating at 2875 MHz (S band). The freezing level was chosen instead of the snow level as the comparison parameter because the radar algorithm and the CNRFC have different interpretations of the snow level. The evaluation occurred at two sites: one in the coastal mountains north of San Francisco and the other in the Sierra Nevada. The evaluation was conducted for forecasts made during the winter wet season of 2005/06. Although the overall mean freezing-level forecast bias is small enough not to be hydrologically significant, about 15% of the forecasts had biases greater than 300 m (forecast too low). The largest forecast biases were associated with freezing levels above 2.3 km that were underforecasted by as much as 900 m. These high freezing-level events were accompanied by the heaviest precipitation intensities, exacerbating the flood threat and making the forecast even more challenging.

Corresponding author address: Dr. Allen B. White, NOAA/ESRL, R/PSD2, 325 Broadway, Boulder, CO 80305. Email: allen.b.white@noaa.gov

1. Introduction

The “snow level” is a term used by National Oceanic and Atmospheric Administration’s (NOAA) forecasters at the National Weather Service (NWS) to ascribe the altitude in the atmosphere where falling snow melts to rain. The snow level should be distinguished from another term used by forecasters, the “free atmosphere freezing level,” which is the altitude corresponding to the 0°C isotherm. However, in cloud physics and in other fields, the term “melting level” is often used in place of the freezing level, owing to the fact that supercooled liquid water can exist at temperatures well below 0°C. The freezing level is chosen here and used throughout this paper to be consistent with the terminology used by the NWS. The efficiency of commerce and transportation, as well as the general safety of the traveling public, are contingent on the phase of precipitation when it reaches the ground. The snow level is also critical to hydrometeorological forecasts because it determines the areal extent of a basin that is exposed to rain versus snow, which can dictate whether a flood will ensue. For example, White et al. (2002) used the operational River Forecasting System (Smith and Page 1993) of the NWS’s California–Nevada River Forecast Center (CNRFC) to examine the sensitivity of runoff to the snow level for four different watersheds in California. They found that for three out of the four watersheds they examined, a 600-m rise in the freezing level tripled the peak outflow of the basin.

Given its importance to river flow forecasts in mountainous regions and to cool-season flooding, in general, it is important to establish an operational performance measure tied to snow-level forecasts. A key development was required to enable this work, that is, an efficient and accurate measurement of the snow level in precipitation with hourly or better resolution (White et al. 2002). This paper works toward developing such a performance measure by establishing the baseline performance of National Weather Service freezing-level forecasts for the coastal and inland mountains of California. The reason that the freezing level is chosen as the evaluation parameter instead of the snow level is explained in sections 2 and 3.

During a planning meeting for NOAA’s Pacific Landfalling Jets Experiment (PACJET; e.g., Ralph et al. 2005a), forecasters from California indicated that they would like more information about the snow level, partly to evaluate the efficacy of their forecasts with respect to this important variable. Research scientists in NOAA’s Earth System Research Laboratory (ESRL) responded by developing a snow-level algorithm to use in conjunction with vertically pointing Doppler radars (White et al. 2002, 2003). Later, Lundquist et al. (2008) documented the connection between the radar-derived snow level and surface snow accumulation. The PACJET field program was a forerunner of NOAA’s Hydrometeorological Testbed (HMT) program (e.g., Ralph et al. 2005b), upon which the current study is based. For the 2006 HMT field program (HMT-06), the available Doppler radars consisted of four 915-MHz Doppler wind profiling radars (Carter et al. 1995) deployed at various low-elevation sites in California (two of which are used in this study; see Fig. 1 and Table 1), in addition to two 2875-MHz (S band) precipitation profilers (S-PROF; White et al. 2000) deployed at a coastal mountain and a Sierra Nevada site (see Fig. 1 and Table 1) where precipitation often is enhanced by orography (e.g., Neiman et al. 2002; Dettinger et al. 2004).

Both the 915-MHz and the S-PROF radars are capable of detecting precipitation and the bright band. The radar reflectivity or scattering cross section per unit volume, η (m−1), is a measure of the scattering intensity. Neglecting the clear-air contribution to radar backscatter, the standard Rayleigh scattering approximation for spherical particles is given by (Battan 1973)
i1525-7541-11-3-739-e1
where λ is the radar operating wavelength, |K|2 = 0.93 is the refractive-index factor for liquid water, and Z is the radar reflectivity factor given by
i1525-7541-11-3-739-e2
where D is the droplet diameter and N(D) is the droplet-size spectral density. In the radar community, it is common to represent the reflectivity factor as dBZ, defined as
i1525-7541-11-3-739-e3
where the factor of 180 results because Z is expressed in units of cubic meters (m3) in Eq. (3), whereas the dBZ notation assumes conventional units (mm6 m−3).

When considering radar wavelength alone, Eq. (1) indicates that the shorter wavelength of the S-PROF (10 cm) makes it more sensitive for detecting precipitation and the bright band than the 915-MHz profiler (33 cm). In addition, the S-PROF points vertically and samples the atmosphere more often than the 915-MHz profiler, which is operated primarily to measure horizontal winds through the Doppler beam–swinging technique (Carter et al. 1995). To increase the signal-to-noise ratio (SNR) of the clear-air returns (i.e., not during precipitation) allowing for an all-weather wind profiling capability, longer sampling periods are used with the 915-MHz profiler.

The HMT-06 dataset was chosen for analysis primarily because the 2006 water year produced a prodigious amount of precipitation in California. Precipitation totals from each of the evaluation sites exceeded a 200-cm liquid equivalent. However, the S-PROF at the Sierra Nevada site (Alta, California) was not installed until mid-December 2005 (Table 1), so it missed some of the early storms that were captured by the S-PROF at the coastal mountain site (Cazadero, California). In addition, approximately one-fourth of the precipitation that fell at Alta was in the form of snow or mixed precipitation, that is, cases when the bright band was either nonexistent or too low to be detected by the radar. The remaining precipitation cases provided a sufficient number of brightband events to establish the baseline performance of CNRFC freezing-level forecasts.

2. The ESRL snow-level algorithm

ESRL’s snow-level algorithm (White et al. 2002, 2003) is based on the detection of the radar bright band that results from the precipitation melting process (e.g., Battan 1973). The top and bottom of the bright band define approximately the melting layer over which the precipitation phase change occurs. As precipitation passes through this layer, it produces enhanced radar reflectivity because of the difference in the dielectric factor for water and ice and the aggregation of hydrometeors. As melting continues below the freezing level, the radar reflectivity begins to decrease because hydrodynamically unstable large drops split into smaller, less reflective drops [see Eq. (2)], and the continual increase in downward vertical velocity of hydrometeors through the melting layer causes a mass flux divergence at the bottom of the layer. The altitude of maximum radar reflectivity in the bright band serves as the radar estimate of the snow level. However, in this study, we are more interested in the altitude at the top of the bright band that serves as the radar estimate of the freezing level because it can be compared directly to the model-generated and forecaster-adjusted freezing level at selected forecast evaluation points (see section 3a for more details on the methodology used in this paper).

These brightband features are displayed in Fig. 2, which shows vertical profiles of pseudoradar reflectivity, in the form of range-corrected signal-to-noise ratio of the backscattered radar signals and Doppler vertical velocity (DVV) that is dominated by the fall speeds of the hydrometeors. Shown alongside the radar profiles is a temperature sounding retrieved from a rawinsonde launched from the radar site. The radar profiles were measured with the 915-MHz wind profiling radar deployed at Sloughhouse, California (SHS), during the HMT-06 field study (see Fig. 1 and Table 1).

The question may arise as to how accurately the altitude of the peak radar reflectivity in the bright band approximates the snow level. The radar-based estimate of the snow level should always be below the freezing level because of the time (and fall distance) required for particles to achieve wet surfaces once melting has begun. The U.S. Army Corps of Engineers (1956) related surface temperatures to precipitation types and found that at temperatures below 0°C, >90% of precipitation events occur as snow; at temperatures above 3°C, >90% of precipitation events occur as rain; and at a temperature of 1°C, 50% of the precipitation events occur as snow (Lundquist et al. 2008). Yuter et al. (2006) used an optical disdrometer in the Oregon Cascades to distinguish rain particles from snow particles and found that rain particles accounted for 93% of the measured precipitation when the surface temperature was in the range of 0.5°C–1.5°C. Using a similar analysis approach with the same type of disdrometer, D. Kingsmill (2008, personal communication) found a comparable result for the Sierra Nevada.

White et al. (2002) found that the radar-derived snow level existed, on average, 212 m below the freezing level, based on 27 rawinsondes launched from the wind profiler at Bodega Bay, California (BBY), during PACJET-01. This same dataset was used to produce Fig. 3a, which examines the range of temperatures that were observed at the radar-derived snow levels. The same analysis technique was applied to the radar-derived snow levels and serial rawinsonde ascents collected at Sloughhouse during HMT-06 (Fig. 3b). These are not perfectly collocated comparisons because the sondes may have drifted into a different air mass by the time they had ascended to the freezing level. This may help to explain why one of the temperatures measured at the snow level above Bodega Bay was below 0°C. Despite the fact that during more than half of the rawinsonde profiles collected at Sloughhouse, either it was not precipitating or the wind profiler was inoperable, there were 28 coincident temperature–snow-level measurements available from Sloughhouse, which is nearly equivalent to the 27 available from Bodega Bay. The averages of the distributions in Fig. 4 are 1.1°C for Bodega Bay and 1.0°C for Sloughhouse, which are remarkably similar to the independent results of the U.S. Army Corps of Engineers (1956), Yuter et al. (2006), and D. Kingsmill (2008, personal communication), indicating that the altitude of maximum radar reflectivity in the bright band serves as an adequate and appropriate proxy for the snow level. The warmest snow level in Fig. 3b corresponds to the radar profiles shown in Fig. 2.

3. Freezing-level forecast performance

a. Methodology

Two S-PROF observation sites were used for verification (see Fig. 1 and Table 1): one located in the near-coastal hills of the Coast Range at an altitude of 475 m (Cazadero) and the other in the inland foothills of the Sierra Nevada at an altitude of 1085 m (Alta). These two sites were chosen to provide contrast in geophysical factors that may have affected the snow levels at each of the sites: topography, proximity to the ocean, dynamical forcing (e.g., effect of the barrier jet on snow levels measured in the Sierra Nevada, synoptic regime), and thermodynamic structure (e.g., inland valley cold pooling, moist static stability profile).

The CNRFC freezing-level forecasts were produced from a systematic process that has been in place there for several years. Numerical model freezing-level forecasts were generated by NOAA’s operational Global Forecast System (GFS). On the basis of this numerical guidance, CNRFC Hydrometeorologic Analysis and Support (HAS) forecasters produced 6-hourly instantaneous freezing-level forecasts out to 72 h for 68 selected forecast points that are coincident with locations where HAS forecasters also produced point quantitative precipitation forecasts (QPFs). Because of operational time constraints and the prioritization of the QPFs, adjustment of the GFS freezing-level forecast by the HAS forecaster was infrequent and was done mainly only with large storm systems to change forecast timing (e.g., associated with frontal passage) over a portion of the forecast domain and to maintain consistency with the QPFs. Then the point forecasts were interpolated to the Hydrologic Rainfall Analysis Project (HRAP) grid with approximately 4.7-km spacing, which was followed by aggregation into basin and subbasin forecasts that are the basis for forcing the lumped river forecast models. To produce CNRFC freezing-level forecasts for the S-PROF site at Cazadero, a nearest-neighbor interpolation was performed using the surrounding HRAP grid points to help reduce meteorological noise caused by relatively large fluctuations in terrain elevation (300–600 m) over relatively small distances (<15 km). For the S-PROF site at Alta, the closest of the 68 forecast points was selected because it was within ∼30 km of the radar site and the altitude difference was only 94 m (less than 10% of the total elevation).

At the CNRFC, the translation of freezing level to snow level was calibrated on a basin-by-basin basis using historical surface temperature observations and the setting of a calibration parameter that specifies the temperature offset from 0°C. In general, this offset is mostly in the range of 1°–2°C, but a larger–smaller offset could be chosen to compensate for local factors, such as the basin geometry (e.g., trapping–pooling of cold air) and the distribution of temperature sensors in the observing network. If the temperature offset is 1.7°C, and the moist adiabatic lapse rate is assumed, then the vertical offset is 305 m, which is generally presented as CNRFC’s “standard” offset for converting the freezing level to the snow level in the forecast domain.

The profiles of radar reflectivity and DVV (as in Fig. 3) collected by each S-PROF were analyzed to determine if a snow level was present, and all snow-level measurements collected within each half hour were averaged using the consensus technique described in White et al. (2002). A 2-h window, centered on each forecast time, was used to match the observation data with the CNRFC forecast. This was done in an attempt to maximize the comparison sample population while still maintaining an accurate verification time. However, because the CNRFC forecasts are generated every 6 h, this selection process ignores two-thirds of the data collected between successive forecasts. When more than one radar snow level existed within the 2-h window, averaging was performed to help reduce the meteorological noise associated with temporally varying snow levels. This selection process yielded 64 forecast-and-observation comparison pairs for Alta and 74 pairs for Cazadero. However, because three independent forecasts (day 1, day 2, and day 3) are used to compare with the observed snow levels, there are 192 comparison pairs for Alta and 222 for Cazadero.

To compare radar-derived and CNRFC-forecasted snow levels, the definition of snow level for each technique must be considered. For the S-PROF, the snow level corresponds to the height of maximum radar reflectivity within the bright band (the bright band, or melting layer, can be a few hundred meters thick). At the CNRFC, hydrologists are most interested in the elevation at which snow begins to accumulate on the ground to help determine the proportionate amount of a basin that will contribute to runoff (e.g., Lundquist et al. 2008). The altitude in the atmosphere corresponding to this ground elevation is currently assumed to be 305 m below the forecasted freezing level, but there is also an understanding that this altitude can vary between 152 and 457 m (as stated in the publicly issued forecasts of freezing level). In reality, the relationship between the radar-derived snow level and the elevation where snow accumulates on the ground is quite complex and variable, and it is dependent on several physical parameters/processes, such as snowfall rate, sublimation, atmospheric lapse rate, and ground heat flux. For example, owing to the time required by the melting process both in the atmosphere and on the surface, the effect of snowfall rate alone allows snow to accumulate on the surface at a lower (higher) level in the melting layer for faster (slower) snowfall rates.

Because of the altitude uncertainty associated with the differing snow-level definitions of the radar and the CNRFC, it is difficult to isolate and assess forecast performance when snow level is used as the comparison parameter. To help resolve this comparison discrepancy, the freezing level in the radar data was identified, so that it could be compared directly to the freezing-level forecasts provided by the CNRFC. The features associated with the freezing level in the radar reflectivity and velocity profiles are more subtle and, therefore, more difficult to detect than the peak reflectivity in the bright band. A small collocated rawinsonde and radar dataset, collected from Sloughhouse during the HMT-06 field study, was used to identify and validate these features. As depicted in Fig. 2, the magnitude of the radar reflectivity slope increases with decreasing height just below the freezing level (because of water coating on the frozen hydrometeor’s surface and the larger effective diameter of the hydrometeor aggregates). At a slightly lower altitude below the freezing level (∼60 m), the magnitude of the DVV also increases with decreasing height (because of increasing fall velocity associated with increasing hydrometeor size and density). Using these associations, the individual profiles of radar reflectivity and DVV collected during each forecast verification window were manually examined to determine the freezing level.

The identification of the freezing level in the radar data is subject to some uncertainty. First, because the radar measurement is a pulse volume-averaged quantity, it is not possible to determine the exact height of the freezing level along the vertical dimension of the radar pulse. With the radars used in this study, this error is potentially as large as ±60 m. Second, some uncertainly lies in the interpretation of slope changes in SNR and DVV in the vicinity of the freezing level. For example, owing to the coarse radar-pulse resolution and the presence of variable microphysical conditions near the freezing level, the change in SNR and DVV slope curvatures is somewhat ambiguous to detect on occasion. During these limited times, this ambiguity resulted in an additional potential error for the radar interpretation of freezing level of about 60 m.

b. Snow-level displacement height

Even though the radar-derived freezing levels were chosen for the forecast evaluations, it is instructive to view the distribution of radar-derived snow levels, since this variable is more commonly reported to the public in NWS operational forecasts and is routinely provided to the NWS and other end users on the ESRL Physical Sciences Division real-time data Web page (available online at http://www.esrl.noaa.gov/psd/data/obs/). The height distribution of radar-derived snow levels, for all cases used in this study, is shown in the top panel of Fig. 4. The distribution shows that a wide range of snow levels occurred throughout the evaluation period ranging from 0.7 to 3.3 km. In addition, there are two peaks in the distribution from Cazadero, with a relatively greater frequency of snow-level occurrence at altitude ranges of 0.9–1.3 and 2.5–2.7 km. The latter range is close to the most commonly occurring altitude range for snow levels measured at Alta: 2.3–2.5 km. The higher peak in the distribution of freezing levels observed at Cazadero and at Alta is associated with warmer precold-frontal conditions, whereas the lower peak observed at Cazadero is tied to the colder postfrontal environment. Given the higher altitude of Alta, postfrontal conditions often yielded snow, thereby precluding a lower peak similar in altitude range to the lower peak observed at Cazadero from appearing in the Alta snow-level distribution.

In addition to providing a more accurate assessment of forecast performance, the process of determining the freezing level in the radar data also presents an opportunity to evaluate the variability in the height difference between the freezing level and the snow level, which is referred to throughout as the snow-level displacement height (SLDH). The bottom panel of Fig. 4 is a histogram of the SLDH. For both evaluation sites, all of the variability lies between 122 and 427 m, and the most frequently occurring SLDH occurs between 180 and 300 m. The range of the observed SLDH is very similar to the SLDH guidelines provided by the CNFRC (152–457 m) and is consistent with the results of past brightband studies (e.g., Fabry and Zawadzki 1995; Stewart et al. 1984). The average SLDH derived by the radars used in this study is 237 for Alta and 230 m for Cazadero. These results indicate that the constant SLDH currently employed with the CNFRC forecasts is slightly greater [by ∼(68–75 m)] than the mean radar-derived SLDH. Figure 5 shows the frequency of radar-derived SLDH as a function of radar-derived snow level for each evaluation site. Here it is evident that no noticeable relationship exists between the SLDH and the snow level; that is, there is no preference for a particular SLDH to occur at a particular snow level.

c. Forecast performance results

The distributions of the freezing-level forecast biases are shown in Fig. 6. Without regard to forecast lead time (top panel), the distributions from Cazadero and Alta are quite similar. For example, both sites exhibit distributions that are skewed more heavily to negative or “cold” forecast biases (i.e., forecasts lower than observations) than to positive or “warm” forecast biases (i.e., forecasts higher than observations). Cold and warm forecast biases as large as ∼750 m occur at both sites, and cold forecast biases nearly as large as 1 km occur at Cazadero. Three other features of interest are also worth noting regarding the largest forecast biases (LFBs). First, the LFBs are more frequently cold biases. Out of the combined number of forecast and observation pairs from both sites (414), approximately 15% have cold forecast biases greater than 300 m. All else being equal, these are the events that would cause the River Forecasting System to underpredict basin outflow. Second, as might be expected, the cold LFBs are most frequently associated with the longer forecast lead times (days 2 and 3) at Cazadero, although cold biases as large as 300 m also commonly occur at both sites during the day 1 forecast (see bottom two panels of Fig. 6). Oddly, two of the three largest cold forecast biases at Alta occur with the day 1 forecasts. Lastly, the cold LFBs tend to occur with higher freezing levels.

The comparisons between the radar-derived and forecasted freezing levels were also stratified by forecast lead time, as shown in Fig. 7. Here, the mean differences and standard deviation of the differences are plotted for each 6-h forecast period. A consistent trend exists in the mean forecast bias at both sites because the longest forecast lead time (66 h) exhibits a cold bias as large as 175 m that translates into a warm bias as large as 100 m for shorter (0–12 h) forecast lead times. For forecast lead times longer than 18 for Alta and 36 h for Cazadero, a cold bias exists ranging between 50 and 120 m. On average, a cold bias exists for each site, and the magnitude of the bias is nearly the same (54 at Cazadero and 53 m at Alta).

The source of the 0–12-h forecast lead time warm bias in the freezing level is difficult to discern. Because of the subtleties associated with identifying the freezing level in the radar data, the introduction of a systematic error associated with this retrieval method cannot be ruled out. For example, a systematic offset of one radar range gate would produce a bias of about 60 m. The forecast initialization data (0-h forecast) could be used as ground truth to verify whether the radar retrieval method is a source of bias. However, the large degree of variability associated with these comparison pairs—that is, standard deviations of ∼105 and ∼250 m for Cazadero and Alta, respectively (see bottom panel of Fig. 7)—greatly lowers confidence in the fact that the forecast initialization fields are reliably correct. Even if the radar freezing-level retrieval method is contributing partly or completely to the shorter forecast lead time warm bias and this bias was subtracted from the entire distribution, then the cold bias at the longer forecast periods would increase. The large degree of variability in the forecast bias, as noted by the large standard deviations shown in Fig. 7, indicates that there are frequently occurring cases, with associated large biases (standard deviations between 150 and 300 m), that could greatly affect a hydrologic forecast.

d. Wind profiler diagnostics

A 915-MHz radar wind profiler located near each S-band radar (see Fig. 1 and Table 1) was used to characterize the flow regime for each forecast–observation pair. This analysis was conducted in an attempt to identify flow patterns and their associated physical processes that might be handled inaccurately by the forecast model. An examination of forecast bias as a function of wind direction at the height of the bright band (not shown) determined that the magnitude of the bias was not correlated with preferred wind directions. For all comparison pairs, the wind direction ranged from 160° to 300°, with most of the variability existing between 180° and 260°. This range of wind directions indicates that the majority of the precipitation data used in this study probably occurred during precold-frontal conditions.

The wind profiler data were also used to compare the forecast bias with vertical directional shear, which is used as a surrogate for temperature advection under the assumption that geostrophic flow conditions dominate (e.g., Neiman and Shapiro 1989). This was performed by calculating the difference in the vector-averaged wind direction in the 610-m layer above and below the freezing level. The results are shown in Fig. 8 as a function of forecast time (lengthwise on the page) and observed (i.e., radar derived) freezing level (widthwise on the page). The freezing levels were separated into two groups: one below and one above 2.3 km above mean sea level (MSL). As discussed earlier, this height approximates the threshold above which most of the cold LFBs occurred. Here, it is apparent that many of the LFBs, at all elevations and forecast times, are associated with near-neutral or warm advection patterns. In particular, for freezing levels above 2.3 km MSL, most of the cold LFBs occur during near-neutral or warm advection regimes. It is unclear why the cold LFBs occur most often in these conditions. The GFS model systematically may be too progressive in bringing the cold front through the Coast Range and the Sierra Nevada. Another option is that the warm advection often present in the warm sector of landfalling storms may be underrepresented in the model. Finally, the wind profiler may be capturing the ageostrophic clockwise turning of winds with height through the top of the barrier jet flow. Hence, cold LFBs may occur most often when a barrier jet is present.

4. Hydrologic implications

The implications of large cold biases (>300 m) observed in about 15% of the forecasts (irrespective of forecast lead time; Fig. 6) are potentially very significant from a hydrologic perspective. Freezing levels that exist at the higher elevations of the Sierra Nevada (e.g., 2.4–3.4 km) increase watershed runoff because of the increased areal coverage of rain over the higher terrain, with a smaller contribution to increased runoff resulting from melting of the existing snowpack (also known as rain-on-snow events). Also, to compound the issue, many of these higher freezing-level events are associated with heavier rain rates, as indicated by Fig. 9. This result might be expected, since higher freezing levels result from warmer lower atmospheric temperatures, which, in turn, can produce higher water vapor contents. In fact, based on four winter wet seasons, Neiman et al. (2009) demonstrated a close relationship (correlation coefficient = 0.9) between radar-derived snow levels and vertically integrated water vapor measured with a global positioning system (GPS) receiver collocated with the radar.

Another exacerbating factor is that the higher freezing-level events are often associated with winter storms that have atmospheric rivers (ARs) imbedded within them. ARs (Ralph et al. 2004) are narrow regions of enhanced water vapor transport that exist in the warm sectors of some extratropical cyclones. When these ARs encounter the coastal terrain along the U.S. West Coast, they enhance rainfall locally through orographic forcing that can lead to flooding. For example, Ralph et al. (2006) showed that all seven floods that occurred between September 1997 and January 2006 on the Russian River north of San Francisco were tied to winter storms containing ARs. A companion analysis of satellite- and ground-based GPS measurements of integrated water vapor collected during the snow-level forecast evaluation period (not shown) was used to identify when an AR was affecting the coastal evaluation site at Cazadero. This analysis indicated that during AR events, the snow levels were on average 440 m higher than during non-AR events.

As demonstrated by these results, the challenges facing weather and hydrologic forecasters with respect to landfalling AR events are paramount. First, forecasters must quantitatively predict how much precipitation will fall, which, based on a recent study by Ralph et al. (2010), is a formidable challenge in and of itself, especially for extreme events. Second, forecasters must take into account soil moisture conditions in the basin(s) of interest as well as whether an existing snowpack exists in the basin(s). Lastly, forecasters must guard against a grossly underforecasted freezing level during a prolonged warm precipitation event, as this would cause an underprediction of basin outflow and underestimate the threat of flooding. To illustrate the effects of snow-level forecast bias considered alone, river flow simulation for the Klamath River from White et al. (2002) are replotted in Fig. 10 in terms of the runoff error assuming an observed snow level of 914 m; the same 24-h, 10-cm rainfall accumulation used by White et al. (2003); and the corresponding runoff of 1246 m3 s−1. On the basis of these assumptions, a 0.3-km error in the snow-level forecast (forecast too low) would result in a substantial (45%) error in the streamflow forecast.

5. Summary

The snow level is an important parameter for hydrometeorological forecasting in mountainous regions and in cool-season flooding, in general. Currently, there is no operational performance measure tied to snow-level forecasts. To help establish the baseline performance of snow-level forecasts in the western United States, this study examined the performance of freezing-level forecasts produced by the California–Nevada River Forecast Center (CNRFC) for the period November 2005 through March 2006. This was an exceptionally wet winter, which provided a sufficient number of storms to establish forecast performance. Two verification sites were chosen, one in the coastal mountains north of San Francisco and the other farther east in the foothills of the Sierra Nevada. The forecasts were evaluated against freezing levels derived from vertically pointing 2875-MHz (S band) precipitation profiling radars. The freezing level was chosen for comparison instead of the snow level because of differing definitions associated with the radar-derived snow level and the CNRFC snow level. The following is a summary of several key findings of this research:

  • On average, the CNFRC snow-level displacement height (or offset from 0°C; assumed to be 305 m for most cases) is 68–75 m lower than the ESRL radar–derived snow level. The implementation of a variable displacement height would require investigating how physical processes—such as lapse rate, snowfall rate, and sublimation—affect the displacement height.
  • The height difference between the freezing level and the radar-derived snow level varies between 122 and 427 m and is not dependent on the height of the snow level. This variability is consistent with the 152–457-m range that the CNFRC publicly reports as being the range of snow-level offsets typically used.
  • On the basis of these first two results, and the result that the radar-derived snow level exists, on average, at the reported temperature when precipitation reaches the ground as snow 50% of the time, future forecast performance can rely on the snow-level forecasts made by the NWS verified by the radar-derived snow level.
  • A small but consistent forecast bias in freezing level exists in the day 2 and day 3 forecasts, where the forecast was lower than observations by 50–120 m. The standard deviations throughout all forecast periods were 105–340 m. At shorter forecast lead times (<12 h) a warm bias (forecast too high) of 15–90 m was evident.
  • Other than a larger range of forecast error in the lowest elevations at the inland site (Alta), the forecast bias magnitude and distribution are similar at both the coastal and inland sites.
  • Approximately 15% of all forecasts had cold biases (forecast too low) with magnitudes that were greater than 300 m. On the basis of geostrophic thermal advection arguments, vertical wind shear measured by the wind profilers at Bodega Bay and Sloughhouse indicated that most of these large cold biases were associated with near-neutral or warm advection conditions. A set of plausible explanations for this relationship was given. First, the numerical model guidance may be too fast in translating cold fronts across the Coast Range and Sierra Nevada. Second, the warm advection may be underrepresented in the model. Lastly, the vertical wind shear measured by the wind profilers may be due to ageostrophic turning of the winds at the top of the barrier jet flow. The latter suggests a connection between large cold forecast bias and the existence of a barrier jet.
  • Most of the largest cold forecast biases were associated with freezing levels above 2.3 km, which were forecasted lower than what was observed by 300–900 m. Many of these cases were associated with the wettest storms. These forecast biases can have a major effect on water resource, flood, and emergency management operations.

A more detailed analysis of the atmospheric structure associated with the larger freezing-level forecast biases should be conducted to determine the physical processes that are associated with these biases. For example, terrain-induced blocked flow patterns, which can occur along the Coast Range as well as along the Sierra Nevada, may slow the upslope and eastward progress of baroclinic zones, thereby producing large negative forecast biases if the blocked conditions are not captured correctly by the numerical weather prediction models used to generate the initial freezing-level forecasts.

This paper documented the performance of freezing-level forecasts produced by one NWS River Forecast Center for one wet water year. If the newly updated wind profilers in NOAA’s Profiler Network or other suitable profiling radars were deployed to locations where the snow-level forecasts are important to hydrologic prediction, then a performance measure for snow-level forecasts could be implemented nationally. At the time of this publication, ESRL was finishing the development of a portable, low-powered, frequency-modulated, continuous-wave (FM-CW) S-band radar designed to detect and monitor the snow level in precipitation. ESRL plans to deploy several of these radars in key California watersheds at the request of the California Department of Water Resources.

Recommending the specific format for a national snow-level performance measure is beyond the scope of this paper. Clearly, the tails in the distribution of forecast bias are most important. One way to capture this information would be to base the performance measure, for example, on the percentage of day 2 forecasts that have a forecast bias magnitude greater than 300 m for a particular forecast verification point. For this particular study, 9% (11%) of the day 2 forecasts satisfies this criterion at Cazadero (Alta).

The effect of snow-level forecast biases on streamflow was quantified using the previous results of White et al. (2003). While these results are informative alone, it would be useful to quantify the combined effect of snow-level forecast biases and QPF biases. For example, Fig. 10 showed that the highest snow levels occurred with the heaviest rainfall rates. Given the importance of the snow level to flooding, annual snowpack, timing of spring snowmelt, and water supply, a long-term record of snow levels in storms affecting the Sierra Nevada should be undertaken to verify if the projected increases in snow level that result from warming surface temperatures are realized.

Acknowledgments

This study would not have been possible without the dedicated support of the talented engineering and technical team located in the Physical Sciences Division of NOAA’s Earth System Research Laboratory, which built, deployed, and maintained the radars used in this study. In particular, we acknowledge Mr. James R. Jordan and Dr. Clark W. King for managing the staff and field deployments. We thank Mr. Robert Mann for his ongoing generosity in providing a site for the S-PROF radar near Cazadero, California, and the California Department of Forestry and Fire Protection for their cooperation in providing a site for the S-PROF at Alta, California. This research was supported by NOAA’s Hydrometeorological Testbed program and NOAA’s Weather–Climate Connection project.

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Fig. 1.
Fig. 1.

Base map showing the locations of S-band radars used in the freezing-level forecast performance analysis (stars), 915-MHz wind profilers used for supporting analysis (circles), and river gauge sites used by White et al. (2002) to study the sensitivity of basin runoff to the freezing level (diamond, plus, square, triangle). The forecast evaluation point for the Sierra Nevada is Georgetown (x), whereas the coastal mountain forecast evaluation site is Cazadero (star).

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 2.
Fig. 2.

(left) Example of vertical profiles of range-corrected radar SNR (dots), radar Doppler vertical velocity (triangles), and (right) rawinsonde temperature during a precipitation event when a bright band was present. Radar data were collected by the 915-MHz wind profiler at SHS and the rawinsonde was launched from the same site. Both datasets were collected near 1100 UTC 14 Jan 2006.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 3.
Fig. 3.

Histogram of temperatures measured at the radar-derived snow levels above (a) BBY during PACJET-01 and above (b) SHS during HMT-06. The snow levels were detected using the snow-level algorithm applied to 915-MHz wind profiler data. The temperatures were measured with serial rawinsondes launched from the wind profiler location.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 4.
Fig. 4.

Frequency of occurrence of (top) observed snow level and the (bottom) layer depth between the observed freezing level and snow level. Observed snow levels at or below 1.2 km are absent from Alta because the first data point is just shy of 1.2 km MSL owing to the Alta’s site elevation (1.08 km MSL) and the minimum detectable range of the radar (0.11 km).

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 5.
Fig. 5.

Frequency of occurrence of height differences between radar-derived freezing level and snow level as a function of radar-derived snow level for (top) Alta and (bottom) Cazadero.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 6.
Fig. 6.

(top) Frequency of occurrence of freezing-level forecast bias for all heights and forecast verification times. The bias distribution, as a function of observed (i.e., radar derived) freezing level and forecast verification time are shown for (middle) Alta and (bottom) Cazadero.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 7.
Fig. 7.

(top) Mean difference between CNRFC forecast and observed radar-derived freezing levels for different forecast lead times. (bottom) The standard deviation of the differences is shown. Sample populations are denoted at the top end of each standard deviation bar.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 8.
Fig. 8.

Directional shear calculated from wind profiler observations collected at BBY (near Cazadero), and SHS (near Alta), for observed (i.e., radar derived) freezing levels (left) below and (right) above 2.3 km MSL at (top) day 1, (middle) day 2, and (bottom) day 3 forecast periods. Negative (positive) values of directional shear correspond to cold (warm) advection.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 9.
Fig. 9.

Two-hour accumulated rainfall plotted as a function of observed (i.e., radar derived) freezing level.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Fig. 10.
Fig. 10.

Peak flow and percentage error resulting from freezing-level forecast bias for the Klamath River near Tuwar Creek (see Fig. 1), assuming an observed freezing level of 914 m and based on the results of White et al. (2002). The dashed curves were drawn manually to represent the asymptotes that correspond to a freezing level (upper right) higher and (lower left) lower than the complete basin.

Citation: Journal of Hydrometeorology 11, 3; 10.1175/2009JHM1181.1

Table 1.

Names, locations, and operating periods of the ESRL radar observation sites and CNRFC forecast points used in this study. Operating periods are for the wind profilers, S-PROF radars, and CNRFC snow-level forecasts. There were 94 rawinsondes launched from SHS between 30 Dec 2005 and 6 Mar 2006.

Table 1.
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