INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 29: 185–196 (2009) Published online 23 May 2008 in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/joc.1714
Radar-guided interpolation of climatological precipitation data Arthur T. DeGaetano* and Daniel S. Wilks Northeast Regional Climate Center, Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, NY, USA
ABSTRACT: A refined approach for interpolating daily precipitation accumulations is presented, which combines radarbased information to characterize the spatial distribution and gross accumulation of precipitation with observed daily rain-gauge data to adjust for spatially varying errors in the radar estimates. Considering the rain gauge observations to be true values at each measurement location, daily radar errors are calculated at these points. These errors are then interpolated back to the radar grid, providing a spatially varying daily adjustment that can be applied across the radar domain. In contrast to similar techniques that are employed at hourly intervals to adjust radar-rainfall estimates operationally, this refined approach is intended to provide high-spatial-resolution precipitation data for climatological purposes, such as drought and environmental monitoring, retrospective impact analyses, and (when time series of sufficient length become available) assessment of temporal precipitation variations at high-spatial-resolution. Compared to the Multisensor Precipitation Estimators (MPEs) used operationally, the refined method yields lower crossvalidated interpolation errors regardless of season or daily precipitation amount. Comparisons between cross-validated radar estimates aggregated to monthly totals with operational (non-cross-validated) Parameter-elevation Regressions on Independent Slopes Model (PRISM) precipitation estimates are also favourable. The new method provides a radar-based alternative to similar climatologies based on the spatial interpolation of gauge data alone (e.g. PRISM). Copyright 2008 Royal Meteorological Society KEY WORDS
radar; rainfall; rainfall estimation; rain gauge
Received 31 January 2008; Revised 19 March 2008; Accepted 22 March 2008
1.
Introduction
Given that the approximately 10 000 rain gauges in use across the conterminous United States collectively cover an area slightly larger than a tennis court (only 4 × 10−9 percent of the total US land area), it is not surprising that there is a rich climatological literature on approaches to interpolating gauge rainfall. On the global scale, examples include Legates and Willmott (1990) and Chen et al. (2002) which focus on monthly or longer accumulations. An array of approaches has been applied to precipitation interpolation on national scales (e.g. Eischeid, et al., 2000; Kyriakidis et al., 2001; Hewitson and Crane, 2005; Sharples et al., 2005). These procedures vary in both their statistical methodology and base time interval (i.e. daily or monthly). In the United States, the Parameter-elevation Regressions on Independent Slopes Model (PRISM) (Daly et al., 1994, 2007) has emerged as a de facto standard for national- and local-scale precipitation interpolation of monthly and longer accumulations. PRISM interpolations are based on the assumption that locally the distribution of precipitation is primarily influenced by elevation and * Correspondence to: Arthur T. DeGaetano, Northeast Regional Climate Center, 1119 Bradfield Hall, Department of Earth and Atmospheric Sciences, Cornell University, Ithaca NY 14853, USA. E-mail:
[email protected] Copyright 2008 Royal Meteorological Society
aspect. In general, homogeneous local areas, or facets, are defined based on slope orientation. Within PRISM the slope of the linear climate–elevation relationship can change among facets based on the available station data. Weighting of the data points is also possible to represent the effects of variables other than elevation. Conversely, on shorter time scales (primarily daily and sub-daily), radar-based rainfall-estimation techniques have emerged as valuable tools for real-time flood forecasting, forecast validation, and weather-related impact assessments. Rainfall rate can be estimated from radar reflectivity using the Z –R relationship Z = A Rb ,
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where Z is the radar reflectivity, R is the rainfall rate, and A and b are constants which are often optimized to reflect different locations or weather types (e.g. Wilson and Brandes, 1979; Austin, 1987). Even if the optimal Z –R relationship could be selected a priori for a particular location or weather event, radar rainfall estimates are subject to other errors resulting from miscalibration, attenuation, misidentified frozen hydrometeors, anomalous propagation, and range degradation (Wilson and Brandes, 1979; Doviak and Zrnic, 1993; Fulton et al., 1998). Various methods have been proposed to correct
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these errors (Fulton et al., 1998; Anagnostou and Krajewski, 1999; Seo et al., 2000). Observed rainfall data have been used to adjust the radar reflectivity estimates, resulting in improved accuracy of radar-based rainfall estimates (e.g. Wilson, 1970; Brandes, 1975; Schuurmans et al., 2007). Although the rain-gauge values are typically considered the ‘ground truth’, errors exist in these data as well. Most notably, for high rainfall rates and in frozen-precipitation events, rain gauges may underestimate precipitation because of gauge-induced wind turbulence and/or inefficiencies in the design of automated tipping-bucket rain gauges (Crum and Alberty, 1993; Groisman and Legates, 1994). Non-automated rain gauges can also be inconsistent with radar estimates due to sampling time differences and human observation error. Operational radar-rainfall estimates disseminated by the US National Weather Service (NWS) use rain-gaugebased adjustments to correct the mean-field bias. The mean-field bias is defined as the average of the ratios of the gauge amount to radar amount over observation points in the spatial domain (e.g. the radar umbrella) for some time step (Smith and Krajewski, 1991; Seo et al., 1999). This adjustment is part of the NWS Multisensor Precipitation Estimators (MPEs) procedure. In this process, radar values are mapped on the polar stereographic hydrologic rainfall analysis project (HRAP) grid (∼4 km × 4 km). Satellite-based rainfall estimates provide supplemental
information in areas of poor radar coverage. Optimization methods outlined by Seo (1998a,b) are used to create a field of estimated precipitation. A mean-field bias correction is applied over each NWS River Forecast Center (RFC) domain (Figure 1 shows two such domains). This adjustment can be performed hourly at individual RFCs (Fulton et al., 1998; Seo, 1998a,b; Seo et al., 1999; Seo and Breidenbach, 2002). Seo and Breidenbach (2002) found that mean-field bias corrections reduced the mean-squared error (MSE) by 27% in the cool (October–March) season and 26% in the warm (April–September) season. However, the meanfield bias does not correct errors varying over smaller scales. Although the MPE product is widely used in weather and flood forecasting applications, the use of these data to provide high spatial resolution-precipitation climatologies has been limited. Potential for using these data for climatological applications is assessed in this study via comparisons of archived MPE precipitation estimates and conventional gauge-only precipitation interpolations, with radar-based precipitation estimates to which additional daily spatially varying adjustments are introduced. Hereafter, this new approach is termed radar-guided interpolation. While the notion of combining radar and gauge data is not new, previous approaches have focussed on hydrological modelling as opposed to longer term climatological data development and as such have not provided
Figure 1. Map of rain gauge stations used (dots) and coverage of the MPE from the Middle Atlantic (lower box) and Northeast River Forecast Centers (upper box). Copyright 2008 Royal Meteorological Society
Int. J. Climatol. 29: 185–196 (2009) DOI: 10.1002/joc
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a rigorous comparison of this general approach with more conventional climatological spatial interpolation techniques. Such comparisons are included in Section 4 of the present work, following a description of the data sources and the study domain (Section 2) and description of spatially varying radar adjustments (Section 3). Section 4 also illustrates the procedure and results for three individual daily cases. A summary follows in Section 5.
2.
Domain and data
The study area consists of the 12 northeastern states of the United States indicated in Figure 1. Precipitationgauge data are taken from approximately 650 Cooperative Observer (www.nws.noaa.gov/om/coop/) stations located by the dots in Figure 1. The actual number of stations varies daily due to missing and erroneous reports. The chosen stations all record daily observations between 0700 and 0900 local time, which is the most common reporting period, to ensure a consistent accumulation interval for comparison with the radar data. The data cover the period from August 2005 through December 2006. The radar domains (quasi-rectangular regions indicated in Figure 1) of the Northeast River Forecast Center (NERFC) and the Mid-Atlantic River Forecast Center (MARFC) encompass the study area. Hourly radar MPE precipitation estimates were obtained from ftp://ftp.emc.ncep.noaa.gov/mmb/precip/st2n4.arch. Hourly values were summed up to give daily radarderived precipitation totals consistent with a 0800–0800, local time, observation period. Data from this source blend the MPE estimates from multiple regional forecast centres into a single national product. Both the radar and gauge data were pre-screened to remove suspect data. Gauge reports of no precipitation were set to missing if both the corresponding radar pixel amount and each of the surrounding radar pixels indicated precipitation >2.5 mm. Gauge reports >2.5 mm were set to missing if the corresponding radar pixel amount was zero and each of the surrounding radar pixels indicated precipitation 5 mm (Figure 5(b)). A similar pattern characterizes the MPE error field (not shown). The error pattern for the weighted-regression interpolation is similar, although the area of −5 mm errors in central New York is broader. As in Figure 4, some of the areas of largest errors occur in association with the highest precipitation totals and extend to areas where the station precipitation gradients are sharp. Others, such as the >15 mm errors along the New York/Pennsylvania border, do not. This area is centred on a station that reported no precipitation during the 11–13 July period. It is likely that this observation is erroneous, given that the closest stations reported rainfall on one or more of these days. Figure 6 illustrates the performance of the radar-based interpolation technique during a lake-effect snow event. On 13 October 2006 snow fell downwind (to the east) of Lakes Erie and Ontario, producing a historic lakeeffect snowfall event in western New York. The highest negative errors are centred on the high precipitation area to the east of Lake Ontario, an indication that the radar consistently underestimated the liquid-equivalent precipitation. Relatively high negative errors are also centred on the precipitation maxima to the northeast of Lake Erie. Farther downwind the errors are sharply positive, perhaps an artifact of the low rain -gauge Copyright 2008 Royal Meteorological Society
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Figure 4. Maps of (a) daily observed (rain gauge) rainfall (mm) on 27 June 2006 with the corresponding error (mm) at station locations based on (b) MPE and (c) radar-guided interpolation. In panels b and c, dashed contours represent areas where interpolation underestimates the observations. Dark shading is used to show negative errors < − 45 mm with light shading used for errors < − 30 mm. Shading also denotes errors >15 mm. In panel a, precipitation totals >90 mm are shaded, with darker shading denoting accumulations >110 mm.
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Figure 5. Maps of (a) daily observed (rain gauge) precipitation (mm) on 12 July 2006 with the corresponding error (mm) at station locations based on (b) radar-guided interpolation. In panel b, dashed contours represent areas where interpolation underestimates the observations with shading used to denote errors >15 and < − 15 mm. In panel a, shading is used to show precipitation amounts >35 mm.
density in the area (Figure 1). Unlike the concentrated bull’s eye of high precipitation to the east of Lake Erie that characterizes the gauge analysis (Figure 6(a)), the IDW radar-guided interpolations show a broad swath of relatively high precipitation that extended to the southern shore of Lake Ontario (Figure 7(a)). This is in agreement with the pattern of snowfall obtained from an independent spotter network (Figure 7(b)). Precipitation amounts in the rain event in northern Vermont are both over and underestimated by the radar-guided interpolation. 4.3. Monthly precipitation totals In many climatological applications, such as drought monitoring, monthly precipitation accumulations are of Copyright 2008 Royal Meteorological Society
interest. In this regard, interpolations based on PRISM have increasingly become standard in the USA. Thus, at this temporal scale it is natural to judge the benefit of the radar-guided interpolation in relation to PRISM. Unfortunately cross-validation results are not available for PRISM. Rather, PRISM precipitation estimates at a station are influenced by the observed precipitation at that site. This characteristic gives PRISM an inherent advantage when comparing it to methods in which the interpolation algorithm has been blinded to the data at the target locations. Nonetheless, Figure 8 indicates that the cross-validated IDW radar-assisted MSEs are quite competitive in comparison to the non-cross-validated PRISM values. In terms of MSE, the average MSE Int. J. Climatol. 29: 185–196 (2009) DOI: 10.1002/joc
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Figure 6. Maps of (a) daily observed (rain gauge) liquid-equivalent precipitation (mm) on 13 October 2006 with the corresponding error (mm) at station locations based on (b) radar-guided interpolation. In panel b, dashed contours represent areas where interpolation underestimates the observations with shading used to denote errors >9 and < − 9 mm. In panel a, dark shading is used to show precipitation amounts >21 mm with light shading used for precipitation >15 mm.
ratio is 0.93, indicating lower MSE for the PRISM values. In the summer months, when the nature of precipitation is more frequently convective, the IDW radar-assisted interpolation MSE is smaller than that of PRISM despite the inclusion of data from the target stations in the PRISM interpolations. For MPE, the MSE ratios are consistently >1 illustrating the benefit of the additional daily spatially varying adjustment. As is the case for daily values, MSEs for the weighted-regression interpolations are intermediate between the IDW radarassisted interpolations and the MPE. It is difficult to tell how much of the apparently better MSEs for PRISM interpolations can be attributed to their in-sample validation. As noted above, it is not possible to re-compute cross-validated PRISM interpolations. Computing in-sample IDW interpolations is problematic, because calculating a weight for the interpolation point itself using Equation (3) involves division by zero. However, in-sample weighted-regression interpolations can be computed because the weight associated with zero distance in Equations (4) and (5) is finite. This calculation produced a reduction of MSE of approximately 10% relative to the cross-validated results reported in Table I, suggesting that the radar-guided interpolations are of the Copyright 2008 Royal Meteorological Society
least comparable accuracy to the corresponding PRISM estimates for monthly accumulations. Similarly, based on the in-sample weighted-regression analysis, the effect of retaining the validation stations may have been to reduce the PRISM bias by approximately 9%. The monthly IDW radar-guided interpolations are essentially unbiased and show little month-to-month variability with respect to the bias (Figure 8). Weightedregression interpolations are also nearly unbiased, although these interpolated values tend to underestimate the station values during summer. Both the MPE and PRISM values are also nearly unbiased during the colder months. However, in summer the PRISM bias becomes positive indicating that the PRISM interpolations tend to be higher than those reported at the station locations.
5.
Summary and conclusions
The spatial interpolation of daily station-based rain gauge observations, guided by radar-estimated rainfall data, has been described. The approach allows for spatially varying adjustment, and clearly improves upon the conventional MPE radar-based product, which includes largescale bias corrections to radar-estimated precipitation Int. J. Climatol. 29: 185–196 (2009) DOI: 10.1002/joc
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Figure 7. Maps of (a) radar-based interpolated liquid-equivalent precipitation (mm) on 13 October 2006 and (b) independent spotter network snowfall (cm). In panel a, shading shows precipitation amounts >12 mm.
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accumulations. The best results were achieved using a simple IDW interpolation of the radar-minus-gauge field, with the two interpolation parameters being allowed to vary daily in response to the current meteorological situation, through a cross-validation procedure. A more Copyright 2008 Royal Meteorological Society
elaborate weighted-regression approach, using grid point elevation as its predictor, yielded less accurate interpolations on average, possibly because some elevation information may already be present in the raw radar reflectivities upon which the initial MPE radar fields are based. Int. J. Climatol. 29: 185–196 (2009) DOI: 10.1002/joc
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One of the anticipated uses of the method is in the construction of monthly climatological precipitation summaries, at high-spatial-resolution, by summing the daily interpolated precipitation fields. For this purpose, the present results were compared to those arrived at through the use of the PRISM system (Daly et al., 1994, 2007) which is becoming the de facto standard for spatial interpolation of real-time monthly climatological fields in the USA. This comparison is difficult to make fairly, because the PRISM estimates include validation data as part of the fitting procedure, whereas the radar-guided interpolation performance statistics have been fully cross validated. However, differences in MSE for interpolations based on the weighted-regression approach, fitted with and without the validation data, suggest that the radar-guided precipitation interpolation described here performs comparably to PRISM on the monthly time scale. An additional attribute of the radar-guided interpolation procedure is its ability to flag erroneous rain gauge observations on the basis of their very large crossvalidated interpolation errors. This capacity is another aspect of the potential usefulness of the method in operational climatology. Despite the limited geographic scope of the locations considered here, comparable results likely extend to most US regions east of the Rocky Mountains. The study domain was selected such that it encompassed features that could potentially affect the interpolation, such as coastal and lake influences, radar coverage issues resulting from the proximity to international borders, and topography. The computational expense of multiple cross-validation trials (i.e. doubly cross-validated daily optimization of the inverse distance weighting parameters for over 600 withheld station analyses) impeded an analysis over a wider area. Planned future work will evaluate the utility of the radar-guided interpolation methodology, either in its original or modified form, in the mountainous western USA. Real-time daily gridded precipitation fields derived from radar-guided interpolation are currently being used in a number of applications ranging from crop modelling to long-term flood and drought monitoring. In addition, the resulting data fields have been archived since 1 January 2005, providing a resource for other climatological analyses. An intriguing use of the data in the future is the analysis of precipitation extremes. Although, during summer the average error for the highest precipitation amounts (>76 mm) is on the order of 5%, a more rigorous analysis on a larger sample of extremes is necessary to promote this application. The interpolated precipitation data are available through the Northeast Regional Climate Center and the Cornell Center for Advanced Computing at http://compag.tc.cornell.edu/sciencegateway/ Acknowledgements This article represents an extension of Eric Ware’s M.S. thesis at Cornell University. We thank Brian Belcher for computer programming support and Patricia Wnek, Copyright 2008 Royal Meteorological Society
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Joseph Ostrowski, Jeff Ouellet, and Robert Shedd, at the Mid-Atlantic and NERFC for their assistance in acquiring radar data. D. J. Seo provided invaluable assistance during the thesis phase of this work. This work was supported through the Cornell Initiative on Computational Agriculture, funded by a Special Grant of the USDA-CSREES. Partial support was also obtained through NOAA contract EA133E07CN0090. References Anagnostou EN, Krajewski WF. 1999. Real-time radar rainfall estimation. Part 1: algorithm formulation. Journal of Atmospheric and Oceanic Technology 16: 189–197. Austin PM. 1987. Relation between measured radar reflectivity and surface rainfall. Monthly Weather Review 115: 1053–1070. Brandes EA. 1975. Optimizing rainfall estimates with the aid of radar. Journal of Applied Meteorology 14: 1339–1345. Chen M, Xie P, Janowiak JE, Arkin PA. 2002. Global land precipitation: a 50-yr monthly analysis based on gauge observations. Journal of Hydrometeorology 3: 249–266. Cleveland WS, Devlin SJ. 1998. Locally weighted regression: an approach to regression analysis by local fitting. Journal of the American Statistical Association 83: 596–610. Craven P, Wahba G. 1979. Smoothing noise with spline functions: estimating the correct degree of smoothing with the method of generalized cross validation. Numerische Mathematik 31: 377–403. Crum TD, Alberty RL. 1993. The WSR-88D and the WSR-88D operational support facility. Bulletin of the American Meteorological Society 74: 1669–1687. Daly C, Neilson RP, Phillips DL. 1994. A statistical-topographic model for mapping climatological precipitation over mountainous terrain. Journal of Applied Meteorology 33: 140–158. Daly C, Smith JI, McKane R. 2007. High-resolution spatial modeling of daily weather elements for a catchment in the Oregon Cascade Mountains, United States. Journal of Applied Meteorology and Climatology 46: 1565–1586. Doviak RJ, Zrnic DS. 1993. Doppler Radar and Weather Observations. Academic Press: San Diego, CA. Eischeid JK, Pasteris PA, Diaz HF, Plantico MS, Lott NJ. 2000. Creating a serially complete, national daily time series of temperature and precipitation for the western United States. Journal of Applied Meteorology 39: 1580–1591. Fulton RA, Breidenbach JP, Seo DJ, Miller DA, O’Bannon T. 1998. The WSR-88D rainfall algorithm. Weather and Forecasting 13: 377–395. Groisman PY, Legates DR. 1994. The accuracy of United States precipitation data. Bulletin of the American Meteorological Society 75: 215–227. Hewitson BC, Crane RG. 2005. Gridded area-averaged daily precipitation via conditional interpolation. Journal of Climate 18: 41–57. Kyriakidis PC, Kim J, Miller NL. 2001. Geostatistical mapping of precipitation from rain gauge data using atmospheric and terrain characteristics. Journal of Applied Meteorology 40: 1855–1877. Lall UY, Moon Y-I, Kwon H-H, Bosworth K. 2006. Locally weighted polynomial regression: parameter choice and application to forecasts of the Great Salt Lake. Water Resources Research 42: W05422, Doi: 10.1029/2004WR003782. Legates DR, Willmott CJ. 1990. Mean seasonal and spatial variability in gage-corrected global precipitation. International Journal of Climatology 10: 111–127. Nuss WA, Titley DW. 1994. Use of multiquadric interpolation for meteorological objective analysis. Monthly Weather Review 122: 1611–1631. Price DT, McKenney W, Nalder IA, Hutchinson MF. 2000. A comparison of two statistical methods for spatial interpolation of Canadian monthly mean climate. Agricultural and Forest Meteorology 101: 81–94. Rogalus MJ, Ogden FL. 2007. Comparison of GCIP and stage III radarrainfall estimates of the Mississippi river basin for 1997. Journal of Hydrology 341: 177–185. Schuurmans JM, Bierkens MFP, Pebesma EJ, Uijlenhoet R. 2007. Automatic prediction of high-resolution daily rainfall fields for multiple extents: the potential of operational radar. Journal of Hydrometeorology 8: 1204–1224. Int. J. Climatol. 29: 185–196 (2009) DOI: 10.1002/joc
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