ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS

INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 25: 1809 1817 (2005) Published online 7 October 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/joc.1220 ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS BOMIN SUN a, * and THOMAS C. PETERSON b a NOAA National Climatic Data Center and STG Inc., Asheville, North Carolina, USA b NOAA National Climatic Data Center, Asheville, North Carolina, USA Received 14 February 2005 Revised 3 May 2005 Accepted 3 May 2005 ABSTRACT Temperature normals have been estimated for stations of the newly developed US Climate Reference Network (USCRN) by using USCRN temperatures and temperature anomalies interpolated from neighboring stations of the National Weather Service Cooperative Station Network (COOP). To seek the best normal estimation approach, several variations on estimation techniques were considered: the sensitivity of error of estimated normals to COOP data quality; the number of neighboring COOP station used; a spatial interpolation scheme; and the number of years of data used in normal estimation. The best estimation method we found is the one in which temperature anomalies are spatially interpolated from COOP stations within approximately 117 km of the target station using a weighting scheme involving the inverse of square difference in temperature (between the neighboring and target station). Using this approach, normals of USCRN stations were generated. Spatial and temporal characteristics of errors are presented, and the applicability of estimated normals in climate monitoring is discussed. Copyright 2005 Royal Meteorological Society. KEY WORDS: temperature normals; USCRN; COOP 1. INTRODUCTION A climate normal is defined as the arithmetic mean of a climatological element calculated over three consecutive decades (World Meteorological Organization, WMO, 1989). WMO recommends the official 30- year normals periods that end in 1930, 1960, and 1990, for which periods the WMO published World Climate Normals. Many WMO members, including the United States, update their normals at the end of each decade by using the preceding 30 years data. The most recent one uses the period covering 1971 2000. Climate normals are generally used as the base to classify climatic characteristics for given regions, and have also been used in a variety of other applications, including agriculture, commerce, industry, and transportation. This study will estimate temperature normals for US Climate Reference Network (USCRN) sites, a National Oceanic and Atmospheric Administration (NOAA) sponsored climate and weather observing network. The USCRN started deploying stations in 2001. As of July 2005, 60 stations were deployed. When fully deployed, the USCRN should include more than 100 stations to capture both the national climate trends and variations for temperature and precipitation (Vose and Menne, 2004). In this work, normals of near-surface air temperature (T min,t max,andt mean ) at USCRN stations are estimated using USCRN measurements combined with station data from the Cooperative Station Network (COOP, National Weather Service, 1989). After these normals are derived, current USCRN observations can be put into a historical perspective for operational climatemonitoring activities. This greatly increases their value for applications. Estimation of normals also provides a way to integrate the USCRN network with other surface-observing networks. Section 2 describes the strategy for estimating normals for the USCRN stations. Naturally, our goal is to have the errors of estimated normals as small as possible. In Section 3, a series of error evaluations * Correspondence to: Bomin Sun, NOAA/National Climatic Data Center, Asheville, NC 28801, USA; e-mail: Bomin.Sun@noaa.gov Copyright 2005 Royal Meteorological Society

1810 B. SUN AND T. C. PETERSON will be described, which will provide the guidance to select the best normal estimation approach. Section 4 discusses the applicability of estimated normals in operational climate monitoring. Results of the USCRN normal estimation are exhibited in Section 5, where the USCRN normals are estimated using the best approach described in Section 3. 2. STRATEGY OF NORMAL ESTIMATION The basic assumption in the normal estimation process is that the monthly temperature anomaly at a particular location, e.g. at a USCRN site, is approximately equal to the monthly temperature anomaly interpolated from surrounding National Weather Service Cooperative Station Network (COOP) stations (Figure 1). The anomaly is the departure from the normal. This assumption can be expressed as T ij uscrn ˆT ij coop (1) where T ij represents the monthly anomaly temperature at a target station, ˆT ij denotes the average anomaly interpolated from neighboring COOP stations, and i and j indicate a particular month and year. USCRN normals at a given station can thus be estimated from Ñ ij uscrn T ij uscrn ˆT ij coop (2) Where Ñ ij represents the estimated normal and T ij denotes the temperature at the month i and year j. To minimize the error of estimated normals, we need to understand the sensitivity of error to COOP data homogeneity; the number of neighboring stations; and the spatial interpolation method. We also need to understand how the error changes with the number of years of data used so that we can predict the magnitude of error when more years of USCRN data are available. All these factors were investigated by using monthly data of 1971 2003 from all 4629 COOP stations, which have normal values (Figure 1). This strategy allows us to evaluate the errors of estimated normals and find the best approach to estimate USCRN normals. The error is the difference between the estimated Paired CRN Single CRN COOP Figure 1. Data for 1971 2003 from 4629 COOP stations are used in normal estimation. As of July 2004, 60 USCRN stations were deployed

ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS 1811 normal and true normal, which was averaged from COOP data of 1971 2000. The COOP normal and its error estimated from a particular month of a year are thus expressed in Equations 3 and 4 respectively. Ñcoop ij T coop ij ˆT ij coop error ij = Ncoop i Ñ coop ij (3) (4) where Tcoop ij and Ñcoop ij are the monthly temperature and estimated normal at a target COOP station, Ncoop i is the normal calculated from data of 1971 2000 for the month i at the target COOP station, and ˆT ij coop is the anomaly at the target COOP station interpolated from neighboring COOP stations. We calculated estimated normals and their errors for each month in each year of the focus period at each individual station (Equations 3 and 4). There are 33 estimated normals and 33 related errors in 1971 2003 for a given month and station. The sample size for the n-year error for that month and station should be equal to all of the n-year combinations from those 33 values. The term n-year error refers to the error of normal estimated by using n years of data. In this study, all combinations with n consecutive years were included as samples for the n-year error. For example, samples of the 2-year error include cases of 1971 and 1972, 1972 and 1973,..., 2002 and 2003. The sample size used to estimate the n-year error is therefore equal to (34 n). As will be shown in Section 3.1, errors of estimated normals are sensitive to COOP data quality. There still can be undetected bad data points in the COOP datasets even though they have undergone quality assurances and/or homogeneity adjustments. Those bad COOP data points can produce outlying values of estimated normals and related errors, which would bias their arithmetic means. In this article, median errors are used to represent the error characteristics. At individual stations, the median values of n-year error are determined from 34 n combinations. These station median values are displayed in Figure 7 to demonstrate the spatial characteristics of uncertainty in estimated normals. A median error value derived from all the 4629 stations (Figure 1), i.e. the total sample for the n-year error is 4629 34 n, is used to represent the overall error characteristics for the contiguous United States. These median values are the basis for the calculation in Figures 2, 3, 4, and 5. Error of estimated normal (deg.c) 0.9 0.8 0.7 0.6 0.5 0.4 TD3200 Official Normal dataset Menne-Williams dataset 0.3 1970 1975 1980 1985 1990 1995 2000 years Figure 2. Sensitivity of error of estimated normals to COOP data homogeneity. Three COOP datasets are compared. Normals are estimated by using 24 neighboring COOP stations and the arithmetically averaging interpolation scheme. Errors in the figure are overall median values for the contiguous United States derived from all of its 4629 stations (see Section 2 for details)

1812 B. SUN AND T. C. PETERSON Error of estimated normal (deg.c) 0.40 0.35 0.30 0.25 July T min January T max July T max 0.20 0 20 40 60 80 100 number of stations Figure 3. Sensitivity of errors of estimated normals to the number of neighboring stations used. The short vertical lines point to the number of stations corresponding to the minimum error values. A weighting scheme involving the inverse of square difference in temperature between the neighboring and target station is used in normal estimation. The normals are estimated by using 3-year data. Same as Figure 2, the errors in this figure are overall median errors for the contiguous United States Error of estimated normal (deg.c) 0.40 0.35 0.30 0.25 Inverse diff. square Arith. average Inverse distance 0.20 0 20 40 60 80 100 number of stations 300 250 200 150 100 50 distance (km) Figure 4. Sensitivity of error of estimated normals to spatial interpolation method. Three interpolations are compared. The right y-axis indicates the distance within which the neighboring COOP stations are located. Same as Figure 3, normals are estimated by using 3-year data and errors are overall median error values for the contiguous United States 3. ERROR EVALUATIONS 3.1. COOP data homogeneity To evaluate the sensitivity of error to data homogeneity, the following three versions of COOP data were used. (1) Cooperative summary of the day (surface land daily data) (TD3200, National Climatic Data Center, 2003). NCDC s quality assurance checks were conducted on this dataset. The assurance system used, however, differs for observations before and after 2000 (Angel et al., 2003). (2) NCDC s official 1971 2000 monthly normal dataset (TD9641C, National Climatic Data Center, 2002). This dataset was produced from TD3200, which has undergone extensive quality checks, estimation of missing data, time of observation bias adjustment (Karl et al., 1986), and detection and adjustments of nonclimatic change points. The technique outlined in Peterson and Easterling (1994) and Easterling and Peterson (1995) was used to adjust temperature change points. This method involves comparing

ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS 1813 1.2 Error of estimated normal (deg.c) 1.0 0.8 0.6 0.4 0.2 10th/90th percentile 50th percentile 25th/75th percentile 0.0 0 5 10 15 20 25 30 number of years Figure 5. Dependence of the error of estimated normal on the number of years of data used. The normal is estimated using 24 neighboring COOP stations. A weighting scheme involving the inverse of square difference in temperature between the neighboring and target station is used in normal estimation. The percentile values are derived from all of the 4629 stations over the contiguous United States, e.g. the total sample for the n-year error case is 4629 (34 n) (where n represents the number of years of data used in normal estimation) the record of the target station with a reference series generated from neighboring stations. Where significant discontinuities are detected, the difference in average annual temperatures before and after the inhomogeneity is applied to adjust the mean of the earlier block with the mean of the latter block of data. (3) 1959 2003 Serially Complete Adjusted Monthly Dataset produced by M.J. Menne and C.N. Williams at NCDC (the Menne Williams dataset, personal communication). Quality control and inhomogeneity adjustments similar to those in TD9641C and a technique of multiple change point test statistics (Menne and Williams, 2005) were applied to TD3200 to produce this dataset. Figure 2 shows the year-to-year variability of error calculated from each of the above three COOP datasets. The yearly error from TD3200 is on average 30 to 40% larger than that from the other two datasets. Also, a significant downward trend in 1971 2000 and an apparent discontinuity in 2000 are exhibited in the error from TD3200. Data in TD3200 were recorded by instrument systems, which changed with time (e.g. Quayle et al., 1991). The error characteristics in TD3200 most probably result from its lack of homogeneity adjustments. Errors from the Menne Williams dataset show a stable yearly variability, which is quite similar to that from TD9641C. The error values from Menne Williams, however, are slightly smaller compared to those of the latter. This might indicate that the change point detection method used in the Menne Williams dataset is better. Errors in Figure 2 are for. Except for the magnitude of error values, comparison results from the three datasets for other months and for T max (not shown) are similar. All these results indicate that normal estimation is sensitive to the COOP data quality. The Menne Williams dataset appears to be the most homogeneous dataset available to us and was therefore used in all further error evaluations and USCRN normal estimation. 3.2. Number of neighboring stations Neighboring stations refer to nearby stations whose temperature anomalies are used to estimate the normals at a target station. Errors in T min and T max for both January and July show similar variations with respect to the number of neighboring stations used (Figure 3): they decrease rapidly with the increase of neighboring stations from one to around five, they continue to decrease but more gradually, and then reach a minimum value and afterwards increase slowly. The number of neighboring stations corresponding to the minimum error, the so-called optimal number, varies with month and with T min and T max. For example, the January and July numbers for T min are 22 and 32 and for T max are 18 and 23 respectively.

1814 B. SUN AND T. C. PETERSON The median errors in Figure 3 represent the overall error characteristics for the contiguous United States. One might expect that the optimal number should vary with geographic regions. After conducting calculations for all of the 4629 stations, we noticed that the optimal number varies with location and it does not show strong regionally dependent patterns. We therefore chose to use the average number of the above four numbers, 24, to estimate normals at all COOP stations for all months as the differences between the errors associated with the number of 24 and the minimum errors are negligible. As illustrated in Figure 4, these 24 stations are located on average within about 117 km of their target stations. Normal estimation in this study is based on the data from the COOP network (Figure 1), in which the separation distance on average is about 24 km between pairs of two closest stations. Stations in the eastern United States, however, are more densely distributed than in the western United States. This leads to the error in the east, which is overall smaller than in the west, as will be shown in Figure 7. It is anticipated from Figure 3 that estimated normals would be less accurate if a less dense network than COOP was used. 3.3. Spatial interpolation scheme In normal estimation, a spatial interpolation scheme is required to interpolate the temperature anomaly at a target station from anomalies of neighboring COOP stations (Equations 2 or 3). Figure 4 compares errors of normal estimated from three commonly used interpolation schemes: arithmetically averaging, inverse distance weighting, and Inverse Weighting of Square of Temperature Difference (IWSTD) between the neighboring and target station. The error patterns generated from these schemes are spatially similar (not shown); however, the third one gives the smallest error value. For example, the error associated with the use of 24 stations for IWSTD is 0.25 C, about 5% smaller than the other two methods. A difference in temperature (or temperature anomaly) between two stations of a climate region generally increases with their separation distance. The situation, however, can be different if the stations are located in an area with very different surface characteristics or a complicated topography. In these circumstances, station separation distance might be a less appropriate measure of temperature (or temperature anomaly) difference. This helps explain that normals estimated from inverse distance weighting or arithmetically averaging were not as accurateas IWSTD, which assigns more weights on the neighboring stations with temperatures closer to the temperature of the target station. IWSTD is also better than other schemes we tested, including the Spatial Regression Test (Hubbard et al., 2004), an interpolation scheme newly developed for quality assurance purposes. 3.4. Number of years of data Error of estimated normals shown in Figures 3 and 4 were produced by using 3-year data. Figure 5 demonstrates the dependence of errors on the number of years of data used in normal estimation. Besides the median error (the thick black curve), the 10th, 25th, 75th, and 90th percentile errors are also shown to give better understanding of the error characteristics. Two conclusions can be drawn from the information shown in Figure 5. First, as expected, error values decrease with the increasing number of years of data used. The errors, however, are reduced faster when the starting number of years of data used in normal estimation is only a few. For instance, compared to the error associated with the use of 1-year data, the error is reduced by about 40% if 5 years of data are used in normal estimation. Second, as shown in the 25th, 75th, 10th, and 90th percentile error curves, 50% of cases have the 1-year error values within the range 0.06 0.67 C and 80% of cases within the range 0.03 1.08 C. This is a result of a higher variability associated with the data of a smaller time period. Actually, these error ranges also decrease when more years of data are used (Figure 5). The normal in Figure 5 was estimated by using IWSTD. It is noted (not shown) that this scheme produces the smallest error from the various schemes compared if the number of years of data used is less than 20. Otherwise, the arithmetically averaging or distance inverse weighting can do a better job in normal estimation. To summarize, the best normal estimation approach we found from these evaluations includes the use of 24 neighboring stations, a spatial interpolation scheme involving the inverse weighting of square difference in temperature (between the neighboring and target station), and the use of Menne Williams dataset, the most homogeneous COOP dataset available to us so far.

ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS 1815 0.5 ratio of error to anomaly 0.4 0.3 0.2 0.1 July T min January T max July T max 0.0 0 5 10 15 20 25 30 number of years Figure 6. Ratios of error of estimated normal to anomaly. Normals associated with the error were calculated using the same approach as the one for Figure 5. The anomaly is the median value of the absolute anomalies of 1971 2003. Overall median ratio values for the contiguous United States are used in this figure. They were derived from the sample of 4629 (34 n) (where n is the number of years data used in normal estimation) 4. APPLICABILITY IN OPERATIONAL CLIMATE MONITORING The usefulness of estimated normals in operational climate monitoring depends not only on the potential error but also on the typical magnitude of the climate anomaly being monitored, namely, on the ratio of error to anomaly. Here, the anomaly is the median value derived from the absolute COOP anomaly values of 1971 2003. This anomaly value measures the typical magnitude of year-to-year climate variability. Figure 6 shows the error-to-anomaly ratio against the number of years of data used in normal estimation. The error was calculated from our best normal estimation approach described in Section 3. The ratios in Figure 6 use the overall median values for the contiguous United States, derived from ratios of all of its 4629 stations. Apparently, with more years of data, the ratios for T min and T max for both January and July decrease in the way the errors do (Figure 5). Interestingly, the January error-to-anomaly ratios are around 0.2 or smaller even if only a few years of data are used in normal estimation. For July, 4-year and 10-year data are required for the ratios of error-to-anomaly of T max and T min to reach 0.2 respectively. 5. RESULTS OF USCRN NORMAL ESTIMATION Normals of the USCRN stations were estimated by using the best approach stated in the last paragraph of Section 3. USCRN started observations in 2001. Depending on locations, normals of USCRN stations were therefore estimated (Equation 2) by using 1-year, 2-year, or 3-year data from 2001 to 2003. The corresponding errors and error-to-anomaly ratios were assigned from values calculated using the 1971 2003 Menne Williams COOP data alone (Equation 4). To investigate how large the errors at USCRN sites might become with more years of USCRN data available, Figure 7 was produced. It shows errors of the estimated normal for based on using 1-year, 3-year, 5-year, and 10-year data, respectively. It is apparent from Figure 7 that errors in the western United States (west of 105 W) are larger than those in the eastern part. This pattern is also seen in other months and in all interpolation methods tested. This indicates that estimated normals at USCRN stations in the west generally have an error larger than that in the east. The errors, however, are not spatially homogeneous in either the western or eastern United States. As shown in Figure 7, the largest errors of the contiguous United States are present over the state of Colorado, where the 1-year-data and 3-year-data errors reach over 0.9 and 0.6 C respectively; errors in northern parts of North Dakota, Minnesota, and Wisconsin and Northeast regions are larger than those in other areas of eastern

1816 B. SUN AND T. C. PETERSON 1-year data 3-year data 5-year data 10-year data 0.00 0.25 0.50 0.75 1.00 >1.0 Figure 7. Errors of normals for estimated using the same approach as the one for Figure 5. Errors at individual stations are median values derived from the sample of 34 n, where n denotes 1, 3, 5, and 10, respectively, the number of years of data used in normal estimation United States. These error characteristics coincide with the station density distribution (Figure 1): areas with higher (lower) station densities correspond to smaller (larger) errors. As expected, the magnitude of the error is reduced dramatically across the United States when more years of data are used. The error reaches around 0.2 C in most of the eastern United States and around 0.4 C in most of the western United States when 5 years of data are used. The current product of USCRN estimated normals (not shown) was generated by using USCRN and COOP data from 2001 to 2003. To indicate the uncertainty and applicability of estimated normals, errors and errorto-anomaly ratios (described in Sections 4 and 5) are also provided for all individual USCRN stations. For example, at the North Carolina State Horticultural Crops Reservation Center, Asheville, NC, the estimated T min normal for October based on 3 years data is 6.0 C, and its error and error-to-anomaly ratio are 0.28 and 0.24 C respectively. This estimated normal product will be updated when more data are available for more recently commissioned USCRN stations. 6. SUMMARY In this study, a temperature normal at a particular target location, i.e. a USCRN station, was estimated from the temperature at the target station and the temperature anomaly interpolated from neighboring COOP stations. Errors of estimated normals depend on the quality of COOP data, on the number of neighboring stations, on the spatial interpolation method, and on the number of years of data used. This study indicates that temperature normals can be estimated with a high accuracy by using 24 neighboring stations, a weighting scheme involving the inverse of square difference in temperature between the neighboring and target station with less than 20 years in length. Using this approach, normals of the USCRN stations were estimated using data from 2001 2003. Winter T min errors are generally larger than those of other seasons. They are also larger than T max errors. Spatially, errors in the western United States are larger than those in the eastern part. Errors decrease

ESTIMATING TEMPERATURE NORMALS FOR USCRN STATIONS 1817 nonlinearly with the increase in the number of years of data (about 40% of the errors are reduced within the first 5 years of data). In terms of the applicability of the estimated normals in operational climate monitoring, the error-to-anomaly ratios in winter are 0.2 or smaller even if only a few years of data are used. In contrast, 4 to 10 years of data are required for summer ratios to reach that level. ACKNOWLEDGEMENTS The NCDC s official 1971 to 2000 monthly normal dataset was provided by Thomas Whitehurst, and the 1959 to 2003 Serially Complete Adjusted Monthly Dataset was provided by Claude Williams and Matthew Menne. We are grateful to constructive comments from Sharon LeDuc, Trevor Wallias and Alan McNab. Suggestions from the two anonymous reviewers are acknowledged. This work has been funded by NOAA s US Climate Reference Network Program. REFERENCES Angel WE, Urzen ML, Del Greco SA, Bodosky MW. 2003. Automated validation for summary of the day temperature data (TempVal). 83rd AMS Annual Meeting, combined preprints CD-ROM, 9 13 February 2003, Long Beach CA, 19th Conference IIPS [International Conference on Interactive Information and Processing Systems for Meteorology, Oceanography, and Hydrology], American Meteorological Society: Boston, Mass, File 15.3, 4 pp. (February 2003). Easterling DR, Peterson TC. 1995. A new method for detecting and adjusting for undocumented discontinuities in climatological time series. International Journal of Climatology 15: 369 377. Hubbard KG, Goddard S, Sorensen WD, Wells N, Osugi TT. 2004. Performance of quality assurance procedures for an applied climate information system. Journal of Atmospheric and Oceanic Technology in press. Karl TR, Williams CN Jr, Young PJ, Wendland WM. 1986. A model to estimate the time of observation bias associated with monthly mean maximum, minimum and mean temperatures for the United States. Journal of Climate and Applied Meteorology 25: 145 160. Menne MJ, Williams CN Jr. 2005. Detection of undocumented change points: On the use of multiple test statistics and composite reference series. Journal of Climate in press. National Climatic Data Center. 2002. Monthly normals of temp, precip, HDD, & CDD, 1971 2000 [i.e., Monthly station normals of temperature, precipitation, and heating and cooling degree days (old title)] (Climatography of the US # [i.e., no.] 81 [online], (http://nndc.noaa.gov/?http://ols.nndc.noaa.gov/plolstore/plsql/olstore.prodspecific?prodnum=c00115-pub-s0001). Documentation, Monthly station normals of temperature, precipitation, and degree days, and precipitation probabilities and quintiles, 1971 2000, TD9641C, (http://www4.ncdc.noaa.gov/ol/documentlibrary/datasets.html), 21. National Climatic Data Center. 2003. Cooperative summary of the day [online], (http://ols.nndc.noaa.gov/plolstore/plsql/olstore. prodspecific?prodnum=c00122-man-s0001), Documentation, Cooperative summary of the day(dsi[i.e., old TD series]-3200), 18 pp, (http://www4.ncdc.noaa.gov/ol/documentlibrary/datasets.html), 18. National Weather Service. 1989. NWS Observing Handbook No. 2, Cooperative Station Observations 1st Edition, Government Printing Office; 83. Peterson TC, Easterling DR. 1994. Creation of homogeneous composite climatological reference series. International Journal of Climatology 14: 671 679. Quayle RG, Easterling DR, Karl TR, Hughes PY. 1991. Effects of recent thermometer changes in the cooperative station network. Bulletin of American Meteorological Society 72: 1718 1723. Vose RS, Menne MJ. 2004. A method to determine station density requirements for climate observing networks. Journal of Climate 17: 2961 2970. World Meteorological Organization. 1989. Calculation of Monthly and Annual 30-year Standard Normals, WCDP-No. 10, WMO-TD/No. 341, World Meteorological Organization: Geneva.