16A.4 Polarimetric Classification of Winter Weather Precipitation Type Using Thermodynamic Input from Numerical Models

16A.4 POLARIMETRIC CLASSIFICATION OF WINTER WEATHER PRECIPITATION TYPE USING THERMODYNAMIC INPUT FROM NUMERICAL MODELS

Terry J. Schuur, Alexander V. Ryzhkov, and Heather D. Reeves

Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma and NOAA/OAR/National Severe Storms Laboratory

1. INTRODUCTION related to the generation of supercooled liquid water (Hogan et al. 2002), 4) regions The classification of cold-season of high ZDR and KDP that are believed to be precipitation type at the surface is associated with dendritic growth and/or ice complicated by the broad range of crystal generation (Moisseev et al. 2008; precipitation types that might result from Andric et al. 2009; Kennedy and Rutledge processes that occur below the height of the 2011), and 5) an apparent tendency for ZDR radar’s lowest elevation sweep. For in the snow region to increase upon the example, a deep layer of subfreezing air onset of storm decay as regions of dry, near the surface might lead to either a aggregated snow (characterized by low ZDR) complete refreezing of drops (ice pellets) or are replaced by pristine ice crystals refreezing upon contact with the surface (characterized by high ZDR). (freezing rain). Both of these precipitation In this study, we present results from the types are difficult to determine using radar continued evolution of a polarimetric data alone. Existing classification schemes, classification algorithm that is designed to such as the polarimetric Hydrometeor take advantage of thermodynamic output Classification Algorithm (HCA, Park et al. from a numerical model in the classification 2009) currently being deployed on the WSR- process. An earlier version of the algorithm 88D network, also do not take full advantage described by Schuur et al. (2011) has been of observations made at several elevation modified to use output from the High- angles. This effectively eliminates the Resolution Rapid-Refresh (HRRR) model. possibility of observations made aloft to be In addition to providing more information to used in the classification process. An aid in the interpretation of polarimetric example of such signatures is summarized signatures, the thermodynamic information by Ryzhkov et al. (2011), who report on provides a mechanism to produce surface- recent observational work to identify based classification results at distant ranges repetitive polarimetric signatures associated from the radar, where low-level layers of with microphysical processes in winter warm/cold air that fall well below the lowest storms. Analyses of numerous case studies available radar data might result in revealed signatures such as 1) a low-level microphysical processes that would enhancement in ZDR that appears to be otherwise remain undiagnosed. The benefit related to the refreezing of melted or of adding the thermodynamic data is partially melted hydrometeors, 2) downward therefore twofold: 1) to enhance excursions of the bright band to the surface classification capabilities in regions where resulting in localized regions of heavy, wet polarimetric radar data are available, and 2) snow, 3) plumes of high ZDR associated with to extend classification capabilities to embedded updrafts and possibly also regions where it is not. The project also seeks to provide an algorithm framework Corresponding author address: Terry J. Schuur that allows ongoing observational work, as University of Oklahoma/CIMMS listed above, to be easily incorporated into National Weather Center future algorithm development with the long 120 David L. Boren Blvd., Norman, OK, 73072 term goals of improving automated E-mail: [email protected] precipitation type classification at both the surface and aloft, including the capability to across the model grid using T, Td, and p. If remotely diagnose conditions favorable for the surface wet-bulb temperature TWs > 3°C, liquid water generation. it is assumed that precipitation at the surface is rain. However, if TWs < 3°C, the vertical 2. ALGORITHM DEVELOPMENT profile of TW at that point is classified as belonging to one of the four different types The classification algorithm used in this shown in Fig. 1. H0, H1, and H2 in Fig. 1 paper is similar to that first reported on by depict the heights of the 0°C crossing points Schuur et al. (2011), except that it has been in the profiles. Making use of the studies by modified to use higher resolution model data Czys et al. (1996), Zerr (1997), and Rauber that is mapped to a radar-centric coordinate et al. (2001), the TW profiles are then used to system, thereby providing better resolution create a background classification that and improved diagnostic capabilities. The consists of six precipitation categories: 1) initial classification is performed using output snow (SN), 2) wet snow (WS), 3) freezing from the High-Resolution Rapid-Refresh rain (FR), 4) ice pellets (IP), 5) a (HRRR) model analyses, which are created combination of freezing rain and ice pellets by interpolating the 13-km grid-spaced (FR/IP), and 6) rain (RA). In this procedure, Rapid-Refresh analyses to a 3.1-km spacing the threshold for the maximum and minimum using a 16-point bi-linear interpolation acceptable TW profiles in the warm (TWmax) method. The analyses are produced every and cold (TWmin) layers, respectively, are hour by assimilating observed variables into derived from a visual inspection of the the 1-hr forecast from the previous cycle scatterplots presented by Figs. 5 and 6 of using a variational three-dimensional Zerr (1997). Following the flow chart analysis scheme. Vertical profiles of the presented in Fig. 2: wet-bulb temperature TW are calculated

(a) (b) Type 1 Type 2 H H

TWs 0 T 0 TWs3 T (c) (d)

H Type 3 H Type 4

H0 H0

TWmax H1 TWmax H1 TWmin H2 TWmin 0 0 TWs T TWs T

Fig. 1. Four types of vertical profiles of wet-bulb temperature (Tw) corresponding to four or more types of precipitation.

BEGIN

Yes No Yes Tw profile TWs > 3°C ? SN Type 1? RA

T > 2°C T < 2°C T No T No Wmax No Wmax W W and and profile profile T > -5°C? T < -5°C? Type 2? Type 3? Wmin Wmin

Yes Yes

Yes Yes No

0°C < TWmax < 2°C H0 < 1 km? and

TWmin < -5°C? FR IP FR/IP

Yes No Yes No

WS RA IP RA

Fig. 2. Flow chart showing logistic for determination of precipitation types depending on vertical profile of wet bulb temperature.

• When TWs > 3°C, the precipitation at the • For profile Type 4 (Fig. 1d), where TWs < surface is classified as RA. 0°C and the TW profile crosses the 0°C level two times, the precipitation at the • For profile Type 1 (Fig. 1a) where TW < surface is classified as FR if TWmax > 2°C 0°C throughout the entire depth of the and TWmin > -5°C and IP if TWmax < 2°C profile, the surface precipitation is and TWmin < -5°C. Otherwise the classified as SN. precipitation at the surface is classified as FR/IP. • For profile Type 2 (Fig. 1b), where 0° < TWs < 3°C and the TW profile crosses the Polarimetric radar data are then used to fine 0°C level one time, the precipitation at tune the initial classification by determining the surface is classified as WS if H0 < 1 whether or not it is consistent with the radar km. Otherwise, the precipitation at the observations. For example, a polarimetric surface is classified as RA. radar observation of a bright band would be inconsistent with a model-based surface • For profile Type 3 (Fig. 1c), where 0° < classification of dry snow. Radar data are TWs < 3°C and the TW profile crosses the also used to refine a precipitation type within 0°C level three times, the precipitation at a category, such as by using Z and ZDR the surface is classified as IP if 0°C < observations to discern between ice crystals TWmax < 2°C and TWmin < -5°C, where and dry snow. The algorithm outputs 9 TWmax is the maximum TW in the vertical classes of hydrometeors: crystals (CR), dry profile and TWmin is the minimum TW in snow (DS), wet snow (WS), ice pellets/sleet the vertical profile. Otherwise the (IP), freezing rain (FR), a mix of freezing rain precipitation is classified as RA. and ice pellets (FR/IP), rain (RA), heavy rain (HR), and hail (HA).

3. CASE STUDY EXAMPLES (FR/IP and IP categories, see Fig. 3e) also both indicate that this broad region had In this section, we examine algorithm conditions favorable towards the generation output for 3 winter storm events sampled by of ice pellets and/or a ice pellet/freezing rain the OU-PRIME radar on December 24, mix. It should also be noted that the 2009, January 28, 2010, and February 1, algorithm output also indicates that the 2011. In total, 31 volumes of radar data region of ice pellets had a “branch” that (corresponding to 31 hourly HRRR grids) extended well to the west of the OKC metro were processed for these 3 events. area. The radar modification of the Reconstructed RHIs of polarimetric variables background classification, as shown by Fig. with HRRR TW fields overlaid were then 3f, indicates that small pockets of low ρHV at produced for every 5° of azimuth. Here we the western periphery of this ice pellet show classification results and reconstructed region were reclassified to be wet snow. RHIs for each of the 3 winter events to Future work will need to include more illustrate current algorithm analysis and focused efforts to collect information on classification capabilities. In particular, we precipitation type in an attempt to better focus on some of the precipitation features validate these types of features in the that are summarized by Ryzhkov et al. algorithm output. (2011). The low-level increase in ZDR is further illustrated by Figs. 4 and 5, which show 3.1 December 24, 2009 reconstructed RHIs at the azimuths of 20° and 205°, respectively. The enhanced Z

On December 24, 2009, central and ZDR and drop in ρHV in Figs. 4a-c all Oklahoma experienced a historic winter provide a clear indication of an elevated storm that has become widely known warm layer that seems to be consistent in throughout Oklahoma as the “Christmas Eve both height and depth with the relatively Blizzard”. As the storm system moved into weak warm layer indicated by the HRRR TW Oklahoma from the southwest in the early field (Fig. 4d). The most notable feature in morning hours of December 24, 2009, many this RHI is the evolution of the ZDR field locations in central Oklahoma began to beneath the radar bright band. At just below experience light freezing rain. By mid to late 1 km in height, a rather remarkable increase morning, the light freezing rain had in ZDR (Fig. 4b) is seen to take place within a transitioned to sleet and light snow and, by layer of < -5°C air (Fig. 4d). As drops freeze mid afternoon, heavy snow with wind gusts within this layer, an accompanying drop in Z -1 exceeding 60 mph (27 m s ) was common (Fig. 4a) is also noted to take place (Fig. over much central Oklahoma, leading the 4a). This drop in Z is likely due to a change Norman office of the National Weather in the dielectric constant as the drops Service to issue a Blizzard Warning – a rare freeze. While we do not yet fully understand occurrence for the southern Great Plains. the microphysical process that might be Fig. 3 shows 0.5° elevation OU-PRIME responsible for the increase in ZDR in this data and algorithm classification results at layer, we have observed it in numerous the surface for 170019 UTC on December winter storms, so it appears to be a 24, 2009. At this time, sleet and light snow repeatable feature. The layer of high ZDR -1 driven by winds gusting to 40 mph (18 m s ) can also be observed in Fig. 5 at 205° was falling over much of central Oklahoma. azimuth for ranges < 20 km from the radar. Further towards the southeast, the radar As in Fig. 4, the low-level increase in ZDR data show relatively light reflectivities of Z < here also appears to be collocated with a 20 dBZ over a broad region where ZDR > 2 low-level layer of < -5°C air. At higher dB. This region seems to be consistent with altitudes, the model output (Fig. 5d) the newly discovered (and yet unpublished, indicates that the elevated warm layer but discussed extensively in previously narrows and eventually disappears at a submitted quarterly reports) low-level ZDR range of about 45 km from the radar. While signature that appears to be related to the the radar data shown in Fig. 4a-c seemed to refreezing of melted or partially melted be consistent in both height and depth with drops. The background vertical profile type the model-diagnosed elevated warm layer, (type 4, see Fig. 3d) and precipitation type the radar data along 205° azimuth show that

(a) (b)

(e) (f)

Fig. 3. OU-PRIME PPI radar data at 0.5° elevation angle (a-c) and corresponding algorithm output (d-f) at the surface for 170019 UTC on December 24, 2009. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, (d) vertical profile type, (e) background precipitation type, and (f) radar modified precipitation type. Vertical profile types in panel (d) can be compared to those shown in Fig. 1.

(a) (b)

Fig. 4. Reconstructed RHI through panels shown in Fig. 3 at 20° azimuth. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, and (d) TW from the HRRR model output. TW profiles are also overlaid on each of the plots. Three color bars at bottom of panels correspond to vertical profile type, background precipitation type, and radar modified precipitation type for each gate (colors corresponding to those in Fig. 3d-f), respectively.

(a) (b)

Fig. 5. Reconstructed RHIs through panels shown in Fig. 3 at 205° azimuth. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, and (d) TW from the HRRR model output. TW profiles are also overlaid on each of the plots. Radar bright band detections in panel (c) are indicated by the asterisks. Three color bars at bottom of panels correspond to vertical profile type, background precipitation type, and radar modified precipitation type for each gate (colors corresponding to those in Fig. 3d-f), respectively. the high ZDR and low ρHV bright band be used to distinguish between rain and signatures drop noticeably in height with freezing rain, very few modifications were range, suggesting that the model-diagnosed made to the background classification by the elevated warm layer is too high. The addition of radar data (Fig. 6f). Two disappearance of the elevated warm layer in exceptions are the result of an addition to both the radar data and model output, the code that resulted in several heavy rain however, which corresponds in the surface classifications when 35 < Z < 55 dBZ and a classification with the transition from ice few erroneous reclassifications of WS at pellets to snow, both occur at ranges of ranges of between approximately 70-100 km between approximately 35 to 45 km from the from the radar, which are likely due to beam radar. broadening effects of a very intense bright band signature. This is something that will 3.2 January 28, 2010 have to be examined in more detail with future algorithm development efforts. The second major storm of the 2009- Fig. 7 shows a reconstructed RHI 2010 winter season occurred on January 28, through Fig. 6 at 255° azimuth. When 2010. Unlike the Christmas Eve Blizzard, compared to the RHIs shown in Figs. 4 and this storm was primarily known as a severe 5 for the December 24, 2009 winter storm, it freezing rain event as a large swath of can be seen that the melting level for each freezing rain with an accumulation > 0.25 of the storms are at comparable heights, but inch (6.4 mm) extended from southwest to that the depth and intensity of the warm northeast Oklahoma. In particular, a broad layer for the January 28, 2010 event was region in southwest Oklahoma received > much greater. Combined with the slightly 0.75 inch (19.1 mm) of freezing rain with shallower and warmer near-surface layer of some locations receiving an accumulation of cold air, it can be easily seen why the between 1.0 and 1.5 inches (25.4 - 38.1 background classification for the December mm), causing widespread damage. Here 24, 2009 event was correctly assigned to the we compare the combined polarimetric radar ice pellet category while the background data and model output for this storm to that classification for the January 28, 2010 event of the very different Christmas Eve Blizzard, was correctly assigned to the freezing rain which was primarily a heavy sleet and snow category. This suggests that our TWmax and event. TWmin parameters, while possibly needing Fig. 6 shows 0.5° elevation OU-PRIME some fine tuning in the future, are close to data and algorithm classification results at being on target. The most notable feature the surface for 130011 UTC on January 28, when examining the radar data (Figs. 7a-c) 2010. At this time, heavy freezing rain was in the RHI is the intense bright band falling over much of southwest Oklahoma. signature, which tends to verify both the Because there are no distinguishable intensity and height of the elevated warm differences in polarimetric radar data layer at ranges close to the radar. The radar between rain and freezing rain, radar data data do suggest a very slight drop in the alone can not be used to diagnose where height of the elevated warm layer at greater one might expect a transition from rain to distances from the radar though, as noted freezing rain to take place. The vertical earlier, this may have been largely due to profile type (type 4, see Fig. 6d) over the beam broadening. central one-third of the analysis domain is consistent with either ice pellets or freezing 3.3 February 1, 2011 rain. The TWmax and TWmin parameters specified in the background classification The final winter storm system that we scheme, however, correctly assigned the examined as part of this years task is the background precipitation type (Fig. 6e) to be event of February 1, 2011. This event had freezing rain. We do not know whether the some similarities to the Christmas Eve thin line of FR/IP on the northern fringe of Blizzard of December 24, 2009 in that it the area of FR was consistent with exhibited periods of light freezing rain, heavy observations or not. Because this was sleet, and snow with winds that occasionally primarily a freezing rain event at this time, exceeded 40 mph (18 m s-1). Fig. 8 shows and also because radar data alone can not 0.5° elevation OU-PRIME data and (a) (b)

(e) (f)

Fig. 6. OU-PRIME PPI radar data at 0.5° elevation angle (a-c) and corresponding algorithm output (d-f) at the surface for 130011 UTC on January 28, 2010. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, (d) vertical profile type, (e) background precipitation type, and (f) radar modified precipitation type. Vertical profile types in panel (d) can be compared to those shown in Fig. 1

(a) (b)

Fig. 7. Reconstructed RHIs through panels shown in Fig. 6 at 255° azimuth. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, and (d) TW from the HRRR model output. TW profiles are also overlaid on each of the plots. Radar bright band detections in panel (c) are indicated by the asterisks. Three color bars at bottom of panels correspond to vertical profile type, background precipitation type, and radar modified precipitation type for each gate (colors corresponding to those in Fig. 6d-f), respectively.

algorithm classification results at the surface region can be better understood by for 060403 UTC on February 1, 2011. Over examining Fig. 9, which shows a the 3 hour period prior to this time, reports in reconstructed RHI through Fig. 8 at 85° OKC indicated that the precipitation type azimuth. A comparison of radar Z, ZDR, and had transitioned from light freezing rain to ρHV bright band signatures with the HRRR sleet that was sometimes accompanied by TW fields along several RHIs and over a thunder. several hour period (not shown) suggests At approximately 0600 UTC, the first that the model-diagnosed elevated warm reports of snow were recorded in the OKC layer was too high and too intense for this metro area. At this time, Fig. 8 shows that event. This can also be seen in Fig. 9, most of the precipitation had moved off to which clearly shows that the top of the the east of central Oklahoma. Though Z in radar-observed radar bright band falls well this region was generally much higher than below the top of the model-diagnosed that observed in the December 24, 2009 elevated warm layer. This is particularly event, an extensive region with ZDR > 2 (Fig. evident in Fig. 9 at ranges of between 20 8b) that was similar to that seen in the and 40 km from the radar, where a December 24, 2009 event was also noticeable dip in the bright band signature observed over a broad area that had a suggests that heavy wet snow is reaching background precipitation type of FR/IP (Fig. the surface. Such localized regions of 8e). In this case, however, it appears that heavy wet snow are sometime hard to much of this high ZDR signature might be forecast and are likely the product of attributable to a “downward excursion” of the feedback between microphysics and radar bright band, resulting in a wet snow thermodynamics, such as localized cooling signature at the surface (see area of WS due to enhance melting and evaporation. classified in Fig. 8f). The origins of this (a) (b)

(e) (f)

Fig. 8. OU-PRIME PPI radar data at 0.5° elevation angle (a-c) and corresponding algorithm output (d-f) at the surface for 060403 UTC on February 1, 2011. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, (d) vertical profile type, (e) background precipitation type, and (f) radar modified precipitation type. Vertical profile types in panel (d) can be compared to those shown in Fig. 1. (a) (b)

Fig. 9. Reconstructed RHIs through panels shown in Fig. 8 at 85° azimuth. Panels represent (a) radar reflectivity, (b) differential reflectivity, (c) correlation coefficient, and (d) TW from the HRRR model output. TW profiles are also overlaid on each of the plots. Radar bright band detections in panel (c) are indicated by the asterisks. Three color bars at bottom of panels correspond to vertical profile type, background precipitation type, and radar modified precipitation type for each gate (colors corresponding to those in Fig. 8d-f), respectively.

Table 1: Criteria used for the modification of the background classification based on the radar determination of an elevated warm layer/bright band.

Elevated warm layer Yes Yes Yes Yes Yes Yes Background class SN All class except for RA IP FR/IP RA o o Condition TWmin< -5 C TWmin>-5 C Median BBH < 1km Surface ID (final) IP FR/IP WS IP FR/IP RA

Elevated warm layer No No No No No No Background class SN IP FR/IP RA FR WS Condition ZDR>0.6 and Z<20 dBZ otherwise Surface ID (final) CR DS IP FR/IP RA FR WS

4. CONCLUSIONS AND FUTURE supercooled drizzle in absence of the DEVELOPMENT melting layer aloft.

Observational analyses have revealed 5. ACKNOWLEDGEMENTS several repeatable polarimetric signatures in winter weather events that appear to provide We would like to thank the dedicated faculty, information on microphysical processes staff, and students of the University of such as the refreezing of water drops in a Oklahoma Atmospheric Radar Research low-level cold layer, downward excursions of Center for their work in collecting the OU- the radar bright band, and elevated layers of PRIME radar data used in this analysis. high ZDR and KDP that appear to be related to Part of this work was supported under an dendritic growth. Concurrent with the MOU with MIT Lincoln Laboratory through observational analyses, work has continued the FAA’s NEXRAD Program Office. to improve automated techniques of Additional funding was provided by combining polarimetric radar data with NOAA/Office of Oceanic Atmospheric thermodynamic output from numerical Research under NOAA/University of models to improve classification of Oklahoma Cooperative Agreement precipitation type in winter storms. Several NA17RJ1227, U. S. Department of changes have been made in the algorithm Commerce, and by the U.S. National over the past year in order to retain a higher Weather Service, Federal Aviation vertical resolution of the model output, Administration, and Department of Defense enhance the algorithm design to make it program for modernization of NEXRAD easier to test future concepts, and improve radars. algorithm diagnostic capabilities. The algorithm was tested on a total of 31 6. REFERENCES volumes of radar data on 3 winter storm events that were sampled by the OU-PRIME Andric, J., D. Zrnic, and V. Melnikov, 2009: radar. Overall, the algorithm appears to Two-layer patterns of enhanced ZDR in demonstrate some skill at classifying clouds. 34th Conference on Radar precipitation type at the surface. Future Meteorology. Williamsburg, VA, Amer. work, however, will need to include the Met. Soc., P2.12. collection of more comprehensive ground- Czys, R., R. Scott, K. Tang, R. Przybylinski, based observations for the purpose of and M. Sabones, 1996: A physically validating the algorithm results. based nondimensional parameter for In the coming year, comprehensive discriminating between locations of analysis of cold-season storms with high freezing rain and sleet. Wea. icing potential will be continued. The rapidly Forecasting, 11, 591-598. expanding network of polarimetric WSR-88D Hogan, R., P. Field, A. Illingworth, R. Cotton, radars will provide opportunities to capture and T. Choularton, 2002: Properties of cases with documented icing (PIREPs) embedded convection in warm-frontal suitable for analysis of polarimetric radar mixed-phase cloud from aircraft and signatures. In addition to the wet bulb polarimetric radar. Quart. J. Roy. temperature, which is utilized exclusively in Meteorol. Soc., 128, 451 – 476. the current winter HCA, the following Kennedy, P. C., and S. A. Rutledge, 2011: meteorological fields will also be analyzed. S-band radar dual-polarization Relative humidity will be explored to detect observations of winter storms. J. Appl. the areas of supersaturation with respect to Meteor. Clim. 50, 844-858. ice / water and winds retrieved from the Moisseev, D., E. Saltikoff, and M. Leskinen, model and radar will be examined to assess 2009: Dual-polarization weather radar possible impact of advection on polarimetric observations of snow growth processes. signatures. The current winter HCA has 34th Conference on Radar Meteorology. been designed to identify freezing rain / Williamsburg, VA, Amer. Meteor. Soc., drizzle associated with melting in an 13B.2. elevated warm layer. Special emphasis will Park, H.-S., A. V. Ryzhkov, D. S. Zrnic, and now be given to the “supercooled warm rain K-.E. Kim, 2009: The hydrometeor process” responsible for generation of classification algorithm for the polarimetric WSR-88D: Description and relation to aircraft icing and freezing application to an MCS. Wea. rain. 35th Conference on Radar Forecasting. 24, 730-748. Meteorology, Pittsburg, PA, American Rauber, R. M., L. S. Olthoff, M. K. Meteorological Society, Boston, Ramamurthy, and K. E. Kunkel, 2001: P13.197. Further investigations of a physically Schuur, T. J., Park, H.- S., A. V. Ryzhkov, based, nondimensional parameter for and H. Reeves, 2011: Classification of discriminating between locations of precipitation types during transitional freezing rain and ice pellets. Wea. winter weather using the RUC model Forecasting, 16, 185-191. and polarimetric radar retrievals. J. Appl. Ryzhkov, A. V., H. D. Reeves, T. J. Schuur, Meteor., In review. M. R. Kumjian, and D. S. Zrnic, 2011: Zerr, R. 1997: Freezing rain, an Investigations of polarimetric radar observational and theoretical study. J. signatures in winter storms and their Appl. Meteor., 36, 1647-1661.