Comparison of methods for spatially estimating station temperatures in a quality control system

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 28: (28) ublished online August 27 in Wiley InterScience ( Comparison of methods for spatially estimating station temperatures in a quality control system Jinsheng You, a Kenneth G. Hubbard a * and Steve Goddard b a High lains Regional Climate Center, University of Nebraska, Lincoln, Nebraska, USA b Department of Computer Science and Engineering, University of Nebraska, Lincoln, Nebraska, USA ABSTRACT: The inverse distance weighting (IDW) and spatial regression test () methods provide data estimates for a station of interest based on the measurements at neighbouring stations. This paper evaluates the performance of the two approaches across the USA in estimating maximum and minimum daily temperature where the estimates are compared to actual measured data. The performance of these approaches was assessed using the coefficient of efficiency, explained variance, root mean square error, systematic and non-systematic errors. The t-test and variance test were also used to compare the performances of the two methods. In addition, two other versions of the IDW were tested. The first IDW modification was intended to determine the importance of adding a lapse rate correction to the surrounding stations. The second IDW modification used the intermediate estimates from the method and therefore, by comparison to, showed the relative importance of using weights. The spatial regression approach was found to be superior to all versions of the IDW method especially in the coastal and mountainous regions. The spatial regression approach successfully resolves the systematic differences caused by temperature lapse rate with elevation, which is not accounted for in the inverse distance weighting method. Both the and the IDW methods are found to perform relatively poorly when the weather station density is low. Copyright 27 Royal Meteorological Society KEY WORDS temperature estimates; spatial interpolation; quality control; quality assurance; lapse rate Received 8 September 26; Revised 27 Apri 27; Accepted 28 Apri 27. Introduction Quality assurance procedures described by Guttman and Quayle (99) have been applied to quasi-automatically check weather data from the cooperative climatological stations in the National Climatic Data Center (NCDC) for validity. Internal consistency checks such as the threshold method and the step change test were designed for the review of single station data to detect potential outliers (Wade, 987; Meek and Hatfield, 994; Eischeid et al., 995). Recently, quality assurance procedures that rely on the use of multiple stations have proven useful, e.g. spatial tests compare a station s data against the data from neighbouring stations (Wade, 987; Gandin, 988; Eischeid et al., 995; Eischeid et al., 2; Shafer et al., 2; Hubbard, 2a). Spatial tests employ the data from neighbouring stations to make an estimate of the variable at the station of interest. The estimate can be formed by weighting according to the distance separating the locations (Guttman et al., 988; Wade, 987), or through other statistical approaches (Eischeid et al., 995; Eischeid et al., 2; Hubbard et al., 25). * Correspondence to: Kenneth G. Hubbard, High lains Regional Climate Center, University of Nebraska, Lincoln, Nebraska, USA. khubbard@unlnotes.unl.edu The spatial regression test () used herein (Hubbard et al., 25) does not assign the largest weight to the nearest neighbour, but instead assigns the weights according to the strength of the relationship as quantified by the root mean square error (RMSE) values between the station of interest and each neighbouring station. Research has demonstrated the performance of the in identifying seeded errors (Hubbard et al., 25). The and inverse distance weighting (IDW) methods provide separate estimates of a station s data based on surrounding stations. This is critical to the process of identifying suspect data. Both the IDW and methods are undertaken to ensure quality data in the Applied Climate Information System (ACIS) (Hubbard et al., 24). The estimates are used to form a continuous data set by filling in for missing values. A comparison of these two methods is made in this paper. The predicted results from the two methods are compared with the measured values at each station and the results presented for the continental USA. One modification was added to the IDW method to adjust the surrounding station values to the elevation of the station of interest by applying a temperature lapse rate. As discussed below, the involves both finding the best-fit estimates based on the surrounding stations and using the best-fit-based weights. To determine the relative benefit of the best-fit estimates and weights, a Copyright 27 Royal Meteorological Society

2 778 J. YOU ET AL. second modification of the IDW was made which uses the same best-fit estimates as the but weights from the IDW method. 2. Data and methods 2.. Data The tests in this study were conducted on data from the continental USA for 22. The data were retrieved from stations within the NOAA Cooperative (COO) Observer Weather Data Network, a regional automated weather data network (Hubbard, 2b), and other networks through the ACIS, a distributed data management system (rcc-acis.org). This study includes the estimation of maximum (T max ) and minimum (T min ) air temperature for the time period. The COO data was QC d at NCDC prior to archival. Currently the NCDC and the regional climate centres archive the T max and T min in degrees Fahrenheit. To be consistent with the wide spread use of this data in Fahrenheit and consistent with the database, we use degrees Fahrenheit in this paper Spatial regression test The (Hubbard et al., 25) is a quality control approach that checks whether the variable falls within the confidence interval formed from surrounding station data during a time period of length n (n = 6 for this study, Hubbard and You, 25). Stations within a rectangular box ( longitude latitude) centred on the station of interest are selected and a linear regression performed for each station paired with the station of interest and centred on the datum of interest. For each surrounding station, a regression-based estimate is formed: x i = a i + b i y i () where y i is the particular measurement at the ith surrounding station, x i is the regressed intermediate estimates of the station of interest based on y i,anda i and b i are parameters of the linear regression function. The weighted estimate (x ) is derived by utilizing the standard error of estimate (s) also known as RMSE in the weighting process. x = N N x i s 2 i / s i 2 (2) N is the number of stations that have R 2 greater than.5 within a rectangle box ( longitude latitude) centred on the station of interest. If N<2, no estimates were conducted for the station of interest in this study. The weighted standard error of estimate (s ) is calculated: /s N 2 = N s i 2 (3) To account for possible systematic time shifting of observations (this occurs when an observer consistently records his observation on the day before or after the actual date of observation), the surrounding station s data are each shifted by ± day and the regression repeated. The shift (,, +) that results in the lowest standard error of estimate is then taken into Equations (2) and (3). The estimated confidence intervals are based on s and we test whether or not the station value (x) falls within the confidence intervals. x fs x x + fs (4) If the relation in Equation (4) holds, then the corresponding datum passes the. Increasing f decreases the number of potential Type I errors (valid extreme values that are flagged). Unlike distance weighting techniques, this approach selects those stations that compare most favourably to the station of interest, and these may or may not be the closest stations. In our analysis, we use the value of 3. for f (as used in Hubbard et al., 25) Inverse distance weighting method The IDW method is a simple distance weighted estimate of the value at the target station. The assumption here is that surrounding stations should receive more weight if they lie in closer proximity to the target station than other neighbours. This estimate is given by ˆx = n [y i w i ]/ n w i (5) where ˆx is the predicted variable, y i is the particular measurementatthe ith surrounding station and the weight function w i is derived from the inverse of the distance between the target station and the ith surrounding station. The five nearest stations are used (n = 5), a number which has proven to provide satisfactory results (Hubbard and You, 25). The performance of the IDW method was found to give only slight improvements when as many as 3 stations were used. The improvement was less than.5 F of RMSE for more than 95% of the stations (Hubbard and You, 25). The orographic effect on air temperature was accounted for, by using a lapse rate for the IDW method (Leemans and Cramer, 99; Dodson and Marks, 997). A reference air temperature of the station of interest from a specific station can be obtained through a lapse rate (γ ) applied to the elevation differences and the measurements at the neighbouring station: x i = y i (z z i )γ (6) Here z is the elevation of the station of interest and z i the elevation of ith neighbouring station. The air temperature can be estimated by substituting y i in Equation (5) by the reference estimates x i. The lapse rate takes a value 6.5 C/km (equivalent to.7 F/km) Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

3 COMARISON OF METHODS FOR SATIALLY ESTIMATING STATION TEMERATURES 779 in this study. The results obtained by this modification were labelled as IDW lapse. One other modification of the IDW method (or to the method) is introduced here to apply the inverse distance weights to the estimates obtained from Equation (). The weighted estimate is obtained by substituting the estimates from Equation () for y i in Equation (5). The results obtained in this modification are labelled as Idw erformance measures The coefficient of efficiency (E) (Nash and Sutcliffe, 97) was used as a measure of fit between the actual and predicted data. E is given by: [ m ] m / m E = (x i x) 2 ( ˆx i x i ) 2 (x i x) 2 (7) Where x i is the measured variable, ˆx i is predicted variable, x is the arithmetic mean of x i for all events i = tom. The calculation of E is a procedure which essentially is the sum of the deviations of the observations from a linear regression line with a slope of. If the measured variable is predicted exactly for all observations, the value of E is. Low values of E show high deviations between measured and predicted values. For the case where E is negative, the predictions are very poor and average or climatic values would provide a better estimate than the predictions. R 2 is the explained variance. Values of R 2 are widely used as an index of agreement, and so are included here. However, R 2 is not always instructive and, as Willmott (98) cautions, should not be used alone to assess the accuracy of estimates. The E value is more sensitive to the presence of a systematic model error than are R and R 2. Other measures of model performance included in this paper are the systematic (E s ) and non-systematic (E u ) components of the RMSE. E s = E u = RMSE = [ m [ m ] ( ).5 2 ˆri x i /m ] ( ).5 2 ˆx i ˆ ri /m (8) (9) (E 2 s + E2 u ) () where ˆ ri is calculated from the slope (b) and intercept (a) of the regression of the predicted ˆx and observed x (such that ˆ ri = a + (b x i )) In-depth statistical evaluation method In this study, two tests were conducted for both the mean and the variance of differences between the observations and estimations for each method of the method pair. The t-test (based on unequal variance) and variance test were performed for a given confidence level (95%) to determine if results from the two methods were significantly different. Here we use Method to represent and Method 2 to represent IDW in the test. The test procedure is as follows:. Use the t-test to determine if the mean offset (between observations and estimates) from Method is smaller than the offset for Method 2 for both the T max and T min. We define the deviations as x = Est(Method ) o and x2 = Est(Method 2) o, where o is the observation and Est(Method ) and Est(Method 2) are estimated from Methods and 2, respectively. Now we have the hypothesis: H :µ x <µ x2 () The confidence level in these tests is.95. We accept the hypothesis if the p-value of the test is smaller than.5. For the variance of the offset we also have the test: H :σ x <σ x2 (2) The hypothesis is also tested at a confidence level of.95 and the hypothesis is accepted when the p-value is less than Results Estimates were made for all days when observations were available at the stations. The estimates were compared to the original observations. All coefficients and the two statistical tests were applied to evaluate the performance of the IDW and the methods. We initially compare the performance of the methods by the t-test and variance. We then show detailed analyses of E and R 2. The spatial distribution patterns of these coefficients are plotted and a short discussion is provided. 3.. General performance of the methods evaluated using t-test and variance test For the continental USA, the daily maximum and minimum air temperature are estimated for all stations available through ACIS for 22 using the and the IDW methods, respectively. The t-test and variance test were carried out for the paired methods (Table I). The spatial patterns of the results between the and IDW methods (namely, method and method 2 respectively,) applied in Equations () and (2)) were mapped as shown in Figure. For those areas with a p-value smaller than.5, we will accept that Method offers superior performance on the basis of the lower mean offset or lower variance of offset in hypothesis (). We also test the reverse of the hypothesis shown in Equations () and (2) (H :µ x >µ x2, H :σ x >σ x2 ) on a confidence Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

4 78 J. YOU ET AL. Table I. Fraction of stations where better performance was found using the t-test and variance test (95% significance). > IDW a < IDW b T max t-test.84. Variance test.7.4 T min t-test.58.2 Variance test.36.4 a Means that the method is significantly better than the IDW method. b Means that the method is significantly inferior to the IDW method. level of.95. For those areas having a p-value lower than.5, we will conclude that Method 2 offers superior performance. As shown in Figure, the red dots are those stations where the method is better than the IDW for either the t-test or the variance test of T max or T min. The method is significantly better than the IDW method for T max with better performance at 84% of all stations based on the t-test and at 7% of all stations as indicated by the variance test (also Table I), while for T min, the fractions become 58 and 36%. The provides superior performance, with a few exceptions, in the complex terrain of the mountain west and the acific coast (Figure ). We conclude that the is clearly superior to the IDW method for T max while superiority is not clear for T min. The comparison of the spatial patterns (Figure ) and the results taken together in Table I lead us to favour the method. The variance test results of T min show that the and IDW methods have similar performance in the Rocky Mountains and other major mountains. In this region, T min is more localized to the topography and lower elevation sites may experience inversions at the time of observation for T min while higher stations are generally windier and have fewer inversions. The mixing is generally stronger for the times associated with the observation of T max. This would explain the stronger spatial correlation structure for T max and the weaker correlation structure for T min ; thus the regression approach is more efficient in predicting T max than T min General performance of the methods evaluated using E and R 2 The values of E and R 2 based on comparing the target station measured values and the corresponding estimates were then plotted on maps. The method that exhibits the larger E or R 2 is considered to be more representative. The values of coefficients are mapped in Figure 2(a) E for, (b) E for IDW, (c) R 2 for, and (d) R 2 for IDW. We found the value of E to be greater than.9 in general (Figure 2(a) and (b)) for both methods. A similar response can be identified for the distribution of R 2 (Figure 2(c) and (d)) for the two methods for T max and T min. Both methods provide good estimates of the T max and T min and only a small fraction of the area has t test for Tmax t test for Tmin variance test for Tmax Comparison results -: IDW better than : Cannot judge : better than IDW variance test for Tmin Figure. The mean test (using t-test) and variance test between the method and IDW method. This figure is available in colour online at Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

5 COMARISON OF METHODS FOR SATIALLY ESTIMATING STATION TEMERATURES 78 Figure 2. Interpolated spatial patterns for both the Tmax and Tmin : (a) coefficient of efficiency (E) for, (b) E for IDW, (c) R 2 for, and (d) R 2 for IDW. Data are from the COO observation network for 22. This figure is available in colour online at an E or R 2 less than.5. A more detailed analysis is given for the E associated with Tmax in the following discussion. The differences between E for the two methods were plotted for both Tmax and Tmin on maps (Figure 3). Copyright 27 Royal Meteorological Society Over much of the USA, the approach is only slightly better than the IDW method with the difference of E less than.2. The differences of E are greater than.2 along the western coastal regions and in some parts of the mountainous regions, which is Int. J. Climatol. 28: (28)

6 782 J. YOU ET AL. Figure 3. Interpolated spatial patterns (for both the Tmax and Tmin ) of the difference between and IDW coefficients for (a) E() E(IDW), (b) RMSE() RMSE(IDW), (c) Es () Es (IDW), and (d) Eu () Eu (IDW). This figure is available in colour online at consistent with our findings in the t-test and variance test (Figure ) that is a better method in these regions. For Tmax, E for most stations is greater than.8 for both methods as shown in the cumulative distribution of Copyright 27 Royal Meteorological Society E (Figure 4). The distribution of E differs for the and IDW methods for both Tmax and Tmin. The curve for E for the method falls to the right of the same curve for the IDW method. The peak of the method is at.975 to. with 25% of the stations falling in this range. Int. J. Climatol. 28: (28)

7 COMARISON OF METHODS FOR SATIALLY ESTIMATING STATION TEMERATURES Tmax IDW Tmax Tmin IDW Tmin E Es Tmax IDW Tmax Tmin IDW Tmin Tmax IDW Tmax Tmin IDW Tmin RMSE Tmax IDW Tmax Tmin IDW Tmin R 2 Eu Tmax IDW Tmax Tmin IDW Tmin Figure 4. Cumulative distribution function of coefficients (E, R 2, RMSE, E s,ande u ) for the two methods for daily data from the COO observation network for 22. Values of E( T max ) exceed.95 for about 85% of all stations while for E(IDW T max ), the stations exceeding.95 represent roughly 5% of the stations. Clearly this indicates the superiority of. Values of E and R 2 are generally higher in areas east of the Rocky Mountains (Figure 2). The differences between the and the IDW method in the mountainous areas are discriminated by the E coefficient. On the contrary, the R 2 indexresultedinrelativelymore differences between the and IDW methods in the Mest region where the time of observation rather than complex terrain results in systematic differences in observations. The method is allowed to shift the data sequence, and where the times of observation are different, may enhance the best-fit of the regression between the measurements and the reference data from surrounding stations. Thus, uncertainties associated with time of observation were partially resolved by the method. The R 2 approach is relatively weak in identifying the stations where systematic errors are significant as in Sierra Nevada Mountains, Rocky Mountains and Appalachian Mountains General performance of the methods evaluated using error coefficients The distributions of all other indices such as E u, E s,and RMSE, indicate that is more efficient in predicting the maximum temperature than IDW (Figures 3 and 4). The method is superior to the IDW especially in areas where it resolves the behaviour of measurements from stations located in complex terrain. It is also Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

8 784 J. YOU ET AL. better in resolving the Type I errors brought about by differences in times of observation. A more detailed analysis of the errors in the estimates of T max is given below. Figure 3 also shows that the method significantly reduces the errors between the estimates and the measurements. The systematic errors, E s, for the mountainous stations are much lower for the method than for the IDW approach. For many stations, the systematic error for the is reduced by 2 F compared to the IDW method. In a few areas, this difference is reduced by 5 F. The method can account for most of the systematic errors since the regression function in this method provides an offset that implicitly adjusts for differences in measured variables caused by topographical effect such as lapse of temperature with elevation or inversion. Since the regression for application of the covers a period of days, any significant changes in inversion behaviour or frequency with time of year were presumably resolved in this study down to about 6 days (the window of application). The differences in non-systematic errors (E u )between the two methods convey a similar message. The method results in lower non-systematic errors than the IDW method. However the distribution patterns of the differences of E u are different from the distribution patterns of the difference of E s. The IDW method has a significantly larger E u for many stations in the Mest states such as Nebraska, South Dakota, North Dakota, Wyoming, Kansas, Montana, and Colorado. Some stations in the eastern United States also have considerable difference between E u for these two methods. These larger differences arise mainly in areas where different approaches were applied to stations with different times of observation, which was found to significantly affect the quality assurance results. As previously explained, the method provides a mechanism for shifting the measurements at neighbouring stations to gain the best-fit while IDW does not. The differences between RMSE indicate that the method has lower errors than the IDW method (areas in the RMSE maps that are negative in Figure 3). The RMSE for the IDW method exceeds the RMSE of the method by 2 F for many regions and exceeds it by 5 F in some areas. Only a few isolated stations have slightly smaller RMSE for the IDW method. The two methods have similar responses for estimating the minimum air temperature as well as the maximum air temperature; and the method outperforms the IDW method on the basis of the values of E, R 2, RMSE, E s, and E u. The advantage of the method is slightly greater in the case of maximum air temperature when compared to minimum air temperature. The systematic errors for both the T max and T min show that the method outperforms the IDW, especially in the mountainous west and along the coasts. The non-systematic errors for the two estimates of T max and T min indicate different patterns than seen in the systematic errors. The distribution of non-systematic errors is similar for the and IDW methods for the estimates of T min and the errors are significantly different for T max. The large non-systematic errors in the IDW method for the maximum air temperature are not present in the T min analysis. These phenomena are consistent with the fact that T min is more localized than T max and is more continuous and has smaller differences between the previous and the following days than T max when a front passes. The potential differences in T max or T min between nearby stations which have different times of observation are more significant for T max than for T min as shown in the Mestern states, e.g. Kansas, Colorado, Nebraska, South Dakota and North Dakota A few examples A few stations were selected from the coastal area and the mountainous region to illustrate the type of results associated with the different methods at the local level (Figures 5 and 6). The coastal station selected was San Francisco, CA, while the mountainous stations selected were Silver Lake Brighton and Snake Creek owerhouse in Utah. Contrasts in elevation are significant for these three stations, with San Francisco at 53 m, Snake Creek owerhouse at 832 m and Silver Lake Brighton at 2664 m. Silver Lake Brighton is located along a mountain ridge, while Snake Creek owerhouse is located in a high mountain-valley. Despite the large difference in elevation, these two stations are only a few miles apart. The slope of the regression line between observed and estimated values using the method falls between.98. for most stations. In contrast, the estimates obtained using the IDW method overestimate the maximum temperature for the high elevation station and underestimate the maximum air temperature for the mountain-valley station. This situation is typical of what we observed in mountainous regions such as Sierra Nevada Mountains, Rocky Mountains and Appalachian Mountains. The Silver Lake Brighton, UT, station is a ridge station with many surrounding stations located in mountain valleys. Snake Creek owerhouse, UT, a neighbouring station to Silver Lake Brighton, is situated in a valley. The IDW method on average overestimates.5 F fort max and 7.5 F fort min, respectively, at Silver Lake Brighton. Similarly, T max is underestimated by.7 F andt min is overestimated by 4.7 F forsnake Creek owerhouse, UT (Figure 5). A similar response can be identified for the estimates of the minimum air temperature. Here, we need to note that the trends for the IDW method at Snake Creek owerhouse station are opposite for the T max and T min. This result may be because the minimum temperature is more localized than the maximum temperature for the valley stations. The IDW method can provide reasonable estimates when the elevation of the station of interest is close to the elevation of neighbourhood stations and no gradients are induced by topographical or maritime influences. Table II lists the E value of the two methods for several western coastal stations for the maximum air Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

9 COMARISON OF METHODS FOR SATIALLY ESTIMATING STATION TEMERATURES y =.684x R 2 =.9439 T max y =.252x R 2 =.9232 y =.9922x R 2 = SILVER LAKE BRIGHTON, UT y =.9938x R 2 =.9694 y =.9594x R 2 = SNAKE CREEK OWERHOUSE, UT T min y =.933x R 2 =.8524 y =.993x R 2 = SILVER LAKE BRIGHTON, UT y =.367x R 2 =.892 y =.9839x R 2 = Snake Creek owerhouse, UT y =.4x R 2 =.5899 y =.9968x R 2 = SAN FRANCISCO, CA y =.9968x R 2 = SAN FRANCISCO, CA y =.976x R 2 = Figure 5. Comparison of observed to estimated for both and IDW methods for daily data in 22. temperature. These methods are not as effective for the coastal stations as for the plains stations (also example at San Francisco in Figure 5). The E value is relatively low at many of the stations shown. However, the method is significantly better than the IDW method, the latter resulting in a negative E value at several locations. Both the and the IDW methods are strongly affected by the density of stations. Many of the low values of E occur in the regions where weather stations are sparsely distributed such as in the deserts in California, Nevada, Arizona, New Mexico, etc. The performance was also diminished in the sparsely populated mountainous regions in Wyoming, Idaho, and Montana making it difficult to attain a high density of COO stations. The cold regions in Maine and the wetlands in Florida have similar isolated stations where both methods give poor performance as shown in Figure 2. Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

10 786 J. YOU ET AL Comparison of and IDW methods with the other two IDW modifications The IDW method with lapse rate modification to account for the elevation effects on air temperature and the IDW method with best-fit estimates were also implemented over all stations across the continental USA. The RMSE barplots of the, IDW, and the two modified IDW methods are shown in Figure 6. Both the IDW method and the IDW Lapse method use five stations for the estimation. The method and the Idw method use the same number of stations. The estimating techniques based on the regressed intermediate values ( and Idw) outperform the general IDW method and the IDW method with lapse rate modifications. This is likely because the regression technique can implicitly account for systematic temperature differences caused by topographical differences. For RMSE less than 2 F, the qualified an additional % of the total stations compared to the Idw method for both T max and T min. The method also has 5% more stations than the Idw method when RMSE is less than 3 F. The differences indicate that the weighting method also plays an important role in estimating T max and T min even when the intermediate estimates are generated using the same regression techniques. Table II. E for the and the IDW methods for estimates of the maximum temperature at western coastal stations. E() E(IDW) San Francisco, CA Berkeley, CA San Francisco Oceans Lompoc.58. Cachuma Lake Using a lapse rate in the IDW does not greatly improve the performance of the IDW. Both the normal IDW method and the IDW lapse have a very similar fraction of total stations falling in a specific RMSE bin. However, the lapse rate modification can to some extent, improve the IDW method in the mountainous regions. For example, the RMSE at Silver Lake Brighton, UT, has been reduced from 2. to 4. F and from 8. to 3.4 F fort max and T min, respectively. At this station, the has the best performance with RMSE equal to 2.9 and 3. F fort max and T min, repectively. The Idw has slight larger RMSE of 3.3 and 3.5 F fort max and T min, respectively. % 9% 8% 7% 6% 5% 4% 3% 2% % % % 9% 8% 7% 6% 5% 4% 3% 2% % % Tmax Idw IDW IDW Lapse Methods Tmin Idw IDW IDW Lapse Methods RMSE (F) (5,] (4,5] (3,4] (2,3] (,2] [,] RMSE (F) (5,] (4,5] (3,4] (2,3] (,2] [,] Figure 6. Cumulative bar plot of fraction of stations associated with the four methods having RMSE in the ranges shown. The RMSE values for a few stations are greater than F for IDW and IDW Lapse method and are not shown in the bar plot. Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)

11 COMARISON OF METHODS FOR SATIALLY ESTIMATING STATION TEMERATURES Discussion and conclusions Compared with the IDW method, the performs better in most locations including the plains, mountains, and coastal regions. In the plains, the relative advantage is not as large. In the mountainous regions, the IDW method displays significant bias when the neighbouring stations and the station of interest are located in a valley and on a ridge, respectively. The compensates with a large offset for maximum temperature due to the elevation differences. The approach significantly outperforms the IDW method in the west coast regions. This is because accounts for the systematic differences in air temperature along the coast. Using the RMSE weights is better than using the inverse distance weights in estimating T max and T min which indicates that weights are important even when the regressed intermediate values are used in both cases. The method is recommended over the Idw method. Both the and IDW approach provide similar estimates of the maximum temperature and the minimum air temperature for many stations, especially in the plains. This is reasonable because in the plains, the air temperature is more affected by the air masses than by the topographical features. The temperature lapse with elevation leads to a possible poor performance of IDW in complex terrain. The is more efficient in representing the offsets between the stations that have different elevations; the estimates using the method have much lower systematic error than those obtained using the IDW method. The method is also superior to the IDW method in the regions where the stations have different times of observation. There were regional differences in how well the IDW worked for T max and T min. When using the IDW method, less nonsystematic error exists in the estimates of the minimum air temperature than for the estimates of the maximum air temperature. Using lapse rate modification can improve the performance of IDW in the mountainous regions; however, the improvement is not comparable to the that associated with using the regression techniques over the IDW method. Both the and the IDW methods are affected by the density of the stations. Errors in the estimates increase as the station coverage becomes sparser. The performance of both methods can be improved to some extent in these regions by enlarging the inclusion neighbourhood (Hubbard and You, 25). However, more analysis of the estimates by the two methods in these regions is suggested for operational considerations. References Dodson R, Marks D Daily air temperature interpolated at high spatial resolution over a large mountainous region. Climatic Research 8: 2. Eischeid JK, Baker CB, Karl T, Diaz HF The quality control of long-term climatological data using objective data analysis. Journal of Applied Meteorology 34: Eischeid JK, asteris A, Diaz HF, lantico MS, Lott NJ. 2. Creating a serially complete, national daily timeseries of temperature and precipitation for the Western United States. Journal of Applied Meteorology 39: Gandin LS Complex quality control of meteorological observations. Monthly Weather Review 6: Guttman NV, Quayle RG. 99. A review of cooperative temperature data validation. Journal of Atmospheric and Oceanic Technology 7: Guttman N, Karl C, Reek T, Shuler V Measuring the performance of data validators. Bulletin of the American Meteorological Society 69(2): Hubbard KG. 2a. Multiple station quality control procedures. Automated Weather Stations for Applications in Agriculture and Water Resources Management, AGM-3 WMO./TD No. 74. High Lains Regional Climate Center, Lincoln: 248. Hubbard KG. 2b. The Nebraska and high plains regional experience with automated weather stations. Automated weather station for Application in Agriculture and Water Resources Management. High lains Regional Climate Center: Lincoln, AGM-3 WMO/TD No. 74; 248. Hubbard KG, You J. 25. Sensitivity analysis of quality assurance using spatial regression approach A case Study of the maximum/minimum air temperature. Journal of Atmospheric and Oceanic Technology 22(): Hubbard KG, DeGaetano AT, Robbins KD. 24. Announcing a modern ACIS. Bulletin of the American Meteorological Society 85(6): Hubbard KG, Goddard S, Sorensen WD, Wells N, Osugi TT. 25. erformance of quality assurance rocedures for an ACIS. Journal of Atmospheric and Oceanic Technology 22: 5 2. Leemans R, Cramer R (eds). 99. The IIASA database for mean monthly values of temperature, precipitation, and cloudiness on a global terrestrial grid. Research Report RR-9-8. November 99. International Institute for Applied Systems Analysis: Laxenburg; 6. Meek DW, Hatfield JL Data quality checking for single station meteorological databases. Agricultural and Forest Meteorology 69: Nash JE, Sutcliffe JV. 97. River flow forecasting through conceptual models. Journal of Hydrology : Shafer MA, Fiebrich CA, Arndt DS, Fredrickson SE, Hughes TW. 2. Quality assurance procedures in the Oklahoma mesonetwork. Journal of Atmospheric and Oceanic Technology 7: Wade CG A quality control program for surface mesometeorological data. Journal of Atmospheric and Oceanic Technology 4: Willmott CJ. 98. On the validation of models. hysical Geography 2: Copyright 27 Royal Meteorological Society Int. J. Climatol. 28: (28)