1. Introduction
Observations made using a weather radar are usually physically located above the ground level, as the earth curvature causes radar beams to ascend with distance. When radar is used for ground level precipitation estimation, observations need to be corrected for the effects of beam height. Even though radar precipitation estimates are operationally corrected using schemes such as the vertical profile of reflectivity (VPR), advection of precipitation between the radar contributing volume and ground has received somewhat less attention. In operational radar systems the precipitation measured aloft is usually interpreted to fall vertically to the ground and thus, the radar measurement represents the geographical location immediately below. While this is a reasonable assumption when measuring precipitation close to the radar, when the beam is closest to the ground, longer measuring distances and low melting level height (and consequently greater contribution of snow phase) cause increasing decorrelation between radar-measured and ground level precipitation. Consider the fact that radar beam at 200-km distance (with 0.2° elevation angle and normal atmospheric refraction) is approximately 3 km above ground level. With a horizontal mean wind of 10 m s−1 and snowfall speed of 1 m s−1, the measured hydrometeors will be advected 30 km downwind from the location of the measurement before reaching the ground.
The displacement of precipitation between the radar-contributing volume and ground due to wind is referred to as “wind drift” or “snow drift” by previous authors (Collier 1999; Mittermaier et al. 2004; Lack and Fox 2007; Rasmussen et al. 2003). We call this effect “advection” to avoid confusion when discussing wind drift in snowfall. As snow drift is a term sometimes associated with the horizontal transport of snow on the ground, there is a possibility of confusion between the terms.
Previous studies such as Collier (1999) have shown that errors caused by precipitation advection are largest when high-resolution measurements from areas of steep rainfall gradient are required. Such circumstances are typical in urban hydrology. His work also demonstrates the fact that the magnitude of the advection error depends not only on the characteristics of the measured precipitation, but also on the spatial and temporal resolution of the end product. Consequently, instantaneous high-resolution measurements are most prone to errors caused by advection.
Mittermaier et al. (2004) demonstrated the use of vertical wind profiles from the Met Office numerical weather prediction (NWP) model to estimate advection distances above the melting level. The advection could be corrected to within 20% of the observed displacements. They concluded that model winds are sufficient when estimating precipitation advection. Furthermore, they observed snow advection distances of 10–20 km between the originating level height and the melting level. Lack and Fox (2007) used Doppler radar wind fields with an assumed constant shear vertical wind profile to estimate the effect of precipitation advection on high-resolution rainfall fields. They found out that the impact of advection is most prevalent in strong convective cases, although in these cases the accurate determination of hydrometeor trajectories is difficult. Rasmussen et al. (2003) used a pattern-matching technique to estimate precipitation motion vectors and, combined with surface wind measurements, they estimated hydrometeor trajectories. Trajectories were then used to forecast liquid equivalent amount of snow with emphasis on adjusting the radar Ze–S algorithm. They also point out that the most obvious advantage of an advection adjustment is the correct identification of the edges of precipitation patterns at ground level.
Precipitation advection in Finnish conditions can be significant throughout the year. As melting level heights rarely exceed 2 km, most of the precipitation originates as snow and because of the lower fall speeds is more susceptible to advection. To estimate advection distances, a fall speed scheme for falling hydrometeors is needed. The scheme used in the scope of this study is defined in Fig. 1.
Fall speed scheme used in trajectory calculation in this study. Snow and rain have constant fall speeds of 1 and 5 m s−1, respectively. In between, a melting layer with depth dml of 700 m is assumed. Within the layer the fall speed is linearly interpolated between the two values; hml denotes the melting level height, which is defined as the height of the 0° isotherm.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
Cumulative probability distributions of (a) advection distance on a logarithmic scale and (b) reduction in effective radar-measuring area. Statistics are calculated from approximately 1400 Finnish soundings classified as potential rainfall on the surface. Measuring area reduction is calculated assuming unidirectional wind. Elevation angle is fixed at 0.3°.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
Example of the effect of advection masking on single radar-measuring area in a snowfall case from 23 Nov 2008. Advection near the edge of the measuring area results in a reduced effective radar-measuring area Aeff as opposed to the original area A0. The trajectory-corrected radar image is calculated using the scheme described in section 2. Maximum radar range is 250 km and the elevation angle of the measurements is 0.3°.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
In this paper, a new method for advection adjustment of radar measurements using NWP model forecasts is presented. The method is developed from an operational perspective and is demonstrated by applying it to the operational radar composite of the Finnish Meteorological Institute (FMI). We will describe the observed effects of the adjustment method and further discuss the implications and challenges associated with an operational advection adjustment.
2. The four-dimensional trajectory adjustment method
If we follow the nomenclature of Mittermaier et al. (2004), there are two principal ways to apply advection adjustment to a radar measurement, “prognostic” and “diagnostic.” In the prognostic method, we want to know where the precipitation measured aloft will eventually reach the ground. For this we need to estimate the hydrometeor trajectories forward in time, and consequently we need prognostic wind information. On the other hand, a diagnostic method focuses on the determination of fall streaks using vertical wind shear information. Fall streaks are precipitation patterns composed of hydrometeors falling from the same cloud (or the same generating element within a cloud). Following a fall streak from the radar observation to ground level tells where the precipitation is reaching ground at the instant of the measurement. For further discussion on fall streaks and trajectories the reader is referred to Marshall (1953).
Both methods use a single radar plan position indicator (PPI) scan for advection adjustment. In the prognostic case, this means that precipitation observed farther away from the radar generally reaches the ground later than that observed closer. For this reason the corrected field does not represent any single observation time, but instead the corrected field time stamp is a function of range from radar. In the diagnostic case the fall streaks are generally obtained from a simplified constant shear model for vertical wind speed (Mittermaier et al. 2004), and this may lead to uncertainties, especially when the wind field is evolving quickly. However, the most significant issue is that both methods attempt to correct a single PPI scan, in which case the evolution of the precipitation field is ignored.
The method presented here sidesteps some of the issues by using a different approach to wind advection adjustment. Instead of bringing a single PPI scan to ground level, we first define a ground level grid with given spatial resolution. For each cell in the ground level grid, we compute the estimated trajectory of the falling hydrometeors using 4D model winds and melting layer information. The computation is done from the ground up and backward in time, and the trajectory-corrected radar reflectivity value is obtained from the location and time where the trajectory intersects the lowest elevation angle PPI scan for the first time. The method is illustrated in Fig. 4. As the interception typically occurs not only in a different location, but also in the past relative to the ground level field time stamp, a time series of radar PPIs is needed for any given ground level field. This way the 4D trajectory adjustment method also takes into account the past evolution of the precipitation field. Precipitation from a newly developed structure may not have reached the ground at the time of the radar scan, in which case surface precipitation estimation using assumed fall streaks fails. As the 4D method also uses radar fields from the past, no assumptions are made regarding the persistence of radar echoes. The presented trajectory adjustment method is not an adjustment of the PPI scan at its location in space but a methodology to derive ground level estimates from a series of PPI scans. The use of multiple radar observations also eliminates the problem of having a ground level field with varying temporal representativity.
Illustration of the 4D trajectory adjustment method. Instead of obtaining the radar measurements from bins immediately over each ground location (solid lines) they are obtained using the computed trajectories (dashed lines). The corrected bin is generally at another location and in an earlier radar scan, an arbitrary time step being indicated by dots. Far away from the radar the corrected bin would be beyond the maximum measuring distance Rmax, and is therefore unavailable. Vectors indicate the wind profile.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
The number of radar observations needed for each ground level field depends on the maximum fall time of the hydrometeors in the area where the adjustment is applied. This in turn depends on the vertical temperature profile, which affects the fall speed of descending hydrometeors through phase transitions.
3. Data sources in the current implementation
The method is tested by using it in conjunction with the operational radar composite at FMI (Saltikoff et al. 2010). In the current implementation, the following data are used by the adjustment scheme:
4D wind field.
Time series of radar PPI scans.
Melting level height for phase transition estimation.
Radar-measuring geometry.
Ground topography.
The 4D wind fields and melting level information needed in the advection adjustment scheme are obtained from the NWP High-Resolution Limited-Area Model (HIRLAM; Undén et al. 2002), version MB71, which runs operationally at FMI. The model fields are available in 10-km spatial and 1-h temporal resolution. The vertical resolution of the model spans from tens of meters near the surface to approximately 300 m at 5-km height, the practical maximum height considered for the radar composite. The vertical structure of the wind should therefore be represented with enough resolution for our purposes (e.g., see Mittermaier et al. 2004).
Hydrometeor phase must be estimated during the fall time, as it significantly affects the fall speed used for trajectory computation. The melting level height information provided by HIRLAM is used to determine hydrometeor phases, after which the hydrometeor fall speeds are adjusted accordingly. The fall speed scheme used by the adjustment algorithm is the one described in Fig. 1. Ground topography is also obtained from the HIRLAM model in 1-km spatial resolution.
The advection adjustment is applied to the VPR-corrected 500-m pseudo–constant altitude plan position indicator (CAPPI) at a 1-km spatial and 5-min temporal resolution using eight operational FMI radars. The composite geometry needed for trajectory computation can be obtained from the composite definition (Saltikoff et al. 2010).
In the implementation, the trajectory-corrected field is computed for an area that is slightly larger than that of the operational composite. This is necessary, as we want to be able to adaptively deform the observed precipitation field according to the prevailing wind field beyond the limits of the fixed composite.
4. Effects of trajectory adjustment
The effect of the trajectory adjustment scheme on the radar composition in snowfall is demonstrated in Fig. 5. The extents of the composites are illustrated with colored lines. The red line represents the nominal maximum range of the composite, approximately determined by 250-km range circles centered on each radar. The green line represents the maximum composite range when hydrometeor trajectories are taken into account. As previously described, advection causes the area covered by the composite to skew with the prevailing wind field, moreso when wind is strong and melting level height is low. Upwind (south and southwest) the effective maximum measuring range is reduced as precipitation landing near the nominal maximum range originates from beyond the limits of the base composite. Likewise, downwind (northern areas) the effective maximum range is extended beyond that of the base composite.
Example of the trajectory-corrected instantaneous radar composite of radar reflectivity factor (dBZ) in a snowfall case from 9 Jan 2011. (a) The uncorrected composite and (b) the composite after trajectory adjustment. The red line depicts the nominal composite area, while the green line depicts the trajectory-corrected area. Some advection masking is observed near the southern edge of the composite, while extension is apparent near the eastern border of the composite. Reflectivity values vary from 10 dBZ to approximately 45 dBZ.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
The effects of advection masking and extension can be quantified as the relative amount of composite pixels where only trajectory-corrected or -uncorrected precipitation is observed compared to the amount of composite pixels where precipitation is observed in both. The ratio describes the effect of advection masking in the entire composite domain. The percentages have been calculated as a function of accumulation time for a frontal snowfall event in Fig. 6a. Each pixel is taken to observe precipitation in the accumulation period if the intensity exceeds an equivalent of 0.1 mm in 24 h. It is observed that after 12 h of accumulation, approximately 6% of the precipitation area is affected by advection masking, while 12% experiences advection extension. Asymmetry of the wind field is the likely cause of the discrepancy between the two.
(a) Relative amount of advection masking (dashed line) and extension (solid line) in a snowfall case from 27 Dec 2010 in terms of composite pixels. (b) The relative amount of precipitation between corrected and uncorrected fields in where both fields are available.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
Figure 6b presents the relative precipitation amount in pixels where both trajectory-corrected and -uncorrected precipitation are available as a function of accumulation time. The differences from the 100% level are mainly caused by evolution in the precipitation field. These differences diminish with accumulation time, demonstrating the fact that accumulation products are unlikely to benefit from advection adjustment in the domain as a whole, provided that the observations are made sufficiently close to the radars. As a result of small-scale effects, the local differences may persist over extended periods of time.
When visually comparing trajectory-corrected and directly measured radar precipitation fields in areas where both fields are available (where edge effects do not affect observations), it is observed that the corrected field has a tendency to lag behind the directly observed field. This observation is in agreement with the fall streak shape described by Mittermaier et al. (2004), as the fall streaks tend to bend backward relative to the observed precipitation aloft.
The differences between the directly measured and trajectory-corrected fields are most prominent in areas farthest away from the radar, as the beam height directly contributes to precipitation fall times and consequently advection distances. Typical observed maximum fall times, located near the edge of the radar composite, are on the order of 1.5 h. In practical terms, this implies that trajectory adjustment should benefit precipitation estimation in areas were there is little overlap by neighboring radars, with areas covered by a single radar benefiting the most. As the effective measuring area is extended downstream, certain areas previously beyond radar maximum range will enjoy coverage at least occasionally.
When compared with high temporal resolution in situ precipitation observations, trajectory adjustment should improve the correlation between radar reflectivity and surface precipitation rate. An example of this is presented in Fig. 7, where surface snowfall is observed by an optical present weather sensor (Vaisala FD12). The temporal representativity has somewhat increased after the adjustment is applied. Furthermore, a number of gauge–radar comparisons from a snowfall event on 9 January 2011 are presented in Fig. 8. In the observed case the adjustment seems to improve the accumulation estimation compared to direct radar measurements. However, in some cases the adjustment may even make the accumulation estimation worse. The causes that contribute to the performance of advection adjustment need further study.
A comparison of directly observed and trajectory-corrected radar reflectivities with present weather sensor observations. Radar-measuring distance is approximately 100 km. In particular, the observed gap in snowfall is more accurately described by the corrected reflectivity time series.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
Gauge–radar accumulation comparisons from four FMI weather stations both with and without advection adjustment. The stations are (a) Lohja, (b) Hyytiälä, (c) Joutsa, and (d) Viitasaari, located in southern Finland. Station accumulation data are obtained using either OTT Pluvio or Vaisala VRG weighing gauges. Precipitation event is a snowfall case from 9 Jan 2011.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
5. Discussion
Applying the trajectory adjustment method to the FMI composite reveals significant differences between the directly observed and trajectory-corrected fields. To determine whether the differences are physically meaningful, we must examine the assumptions made in the adjustment model. In the current implementation the wind fields are produced with 10-km spatial and 1-h temporal resolution. This limits the validity of the adjustment method to wind patterns of similar or greater scale, which in turn means that the method is most accurate in frontal precipitation. However, the method is not dependent on the source of wind information, and it could benefit from the introduction of a model with higher resolution if the high-resolution wind fields remain coherent enough. Also, simultaneous observations from multiple Doppler radars can be used to estimate the local three-dimensional wind field (Ray et al. 1980), and this wind field in turn could be used as the source of wind data for the adjustment method. This type of wind data is however rarely available from an operational standpoint and was not considered in this paper.
As the model fields are produced by an operational NWP model in the current implementation, they are forecasts instead of analyzed fields. From this it follows that the quality of the adjustment can get worse when using an older forecast, however the extent of this remains unclear. Wind verification statistics in Fig. 9 show that RMSE for wind speed at the first 8 h of forecast, which is the maximum age of any used forecast, is approximately 2.5 m s−1. The magnitude of precipitation advection at the synoptic scale is unlikely to be severely affected by the fact that the wind fields are forecasts.
HIRLAM NWP wind forecast verification statistics from January 2011 for (left) direction and (right) speed. The model version used in the adjustment is MB71, denoted by the green lines.
Citation: Monthly Weather Review 140, 3; 10.1175/MWR-D-11-00045.1
It should be noted that the adjustment scheme assumes the precipitation measured aloft reaches ground. For this reason overhanging precipitation is not accounted for, and the corrected precipitation field can in such cases be unrealistic. Overhanging precipitation is present in approximately 11% of Finnish precipitation cases (Pohjola and Koistinen 2004). Trajectory adjustment is however essential when attempting to identify overhanging precipitation using ground-based measurements. A discrepancy between ground level precipitation and that measured aloft can be caused by the fall streak shape, which must be corrected for before any comparisons are made. Only after adjustment can the true overhanging precipitation be identified.
Mittermaier et al. (2004) argued that VPR correction should in fact be applied along a fall streak when there are inhomogeneities in the precipitation field. In the current scheme at FMI the VPR correction is applied before the trajectory adjustment, meaning the slanted trajectories of the falling hydrometeors are not taken into account. This may pose problems when advection distances are large, as hydrometeors may enter a different VPR regime during their fall time. The significance of this effect remains unknown and it was not studied further as there are currently no tools to handle it in an operational manner.
While the effect of the advection adjustment is apparent when comparing instantaneous precipitation fields, the effect will generally diminish when accumulating precipitation over longer time periods. When considering sufficiently large areas, the corrected and directly measured radar accumulations should approach one another with accumulation time, the evolution of the precipitation field being the sole source of discrepancy between the two fields. Should no evolution take place, the two accumulation fields would be identical when the entire precipitation pattern has passed over the measuring area. Such a model is, however, highly idealized, and local differences may persist over long time periods. For example, this is commonly the case in the areas near the radar-measuring area edge where either directly measured or trajectory-corrected field is often unavailable.
The amount of wind advection displacement relative to the spatial resolution of the precipitation product is a rough measure of the importance of advection adjustment. Advection can therefore be important even when measuring close to the radar if the desired product is relatively high resolution. This is the case in urban hydrology applications as described by Collier (1999). The wind field should also be estimated with similar resolution.
Fall speeds are of extreme importance when computing hydrometeor trajectories. The current scheme uses statistical values for both rain and snow, but the fall speed scheme could be improved through the use of polarimetric capabilities of modern radars. In particular, different types of snow (aggregate, graupel) have significantly different fall speeds (Zawadzki et al. 2001) and if the snow type can be identified, the fall speed could be adjusted accordingly. This is an obvious future improvement for the method. Polarimetric radars can also be used to more accurately estimate the melting level height.
When radar data is missing from the composite, the altered radar geometry must be taken into account in the trajectory computations. Generally, missing data in the radar time series produces bands of missing precipitation in the trajectory-corrected field at certain ranges from the radar. Missing data can be handled by obtaining the corrected value further from the past in the radar time series. In other words, the corrected radar data is obtained from the time and location where the trajectory intersects a valid radar measurement bin. An additional higher elevation angle can be used to “catch” trajectories that have passed the first intercept point due to missing data.
6. Conclusions
When applied to the operational FMI radar composite, the 4D trajectory adjustment scheme exhibits clear differences when compared to the unaltered composite. The most significant difference is the deformation of the radar coverage area according to the prevailing wind field. The effective measuring area is in essence advected downwind and the magnitude of deformation is determined by precipitation phase, wind field, and ground topography. In Finnish conditions, deformations of nearly 100 km have been observed. This forces us to reevaluate the way we define the areas covered by the radar composite.
The main conclusion of the paper becomes evident in Fig. 3. When taking the trajectories of the falling hydrometeors into account, even in a somewhat simplistic manner, the resulting radar precipitation fields at ground level at a fixed time moment can be drastically different from directly observed precipitation patterns at the lowest elevation PPI scan at the same time moment. While this is qualitatively known among radar experts, common users may think that a single radar image truly represents ground level precipitation. Of course an instantaneous single radar measurement represents the worst appearance of advection effects. Compositing data from PPI scans in a network of several radars and application of accumulated precipitation amounts instead of instantaneous intensities will, in relative terms, suppress most of the error effects in quantitative precipitation estimation (QPE) due to advection. Still, the outer edge of any network is analogous to a single radar case.
As precipitation advection distances can be large, trajectory adjustment is likely to benefit any application that uses instantaneous observations of radar reflectivity for ground level products. This is especially true in areas that experience snowfall and poor radar coverage. Productwise, snowfall-related products such as radar-based visibility nowcasting are likely to be futile without an advection adjustment scheme.
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