Inhomogeneities arising from the use of five different methods to calculate daily mean temperatures are studied. The inhomogeneities are artificially imposed on the 20th century part of the Zwanenburg/De Bilt (1706-present) temperature time series in the Netherlands. Three approaches for removing the inhomogeneities from the daily temperature data are compared. In the first approach monthly adjustments are derived. In the second approach daily adjustments (for each calendar day) are derived that preserve the monthly adjustments. The third approach used the so-called objective Lamb weather types for deriving weather-type dependent daily adjustments. The homogenized and non-homogenized daily temperatures are compared using, among others, the day-to-day variability and the number of days above the 90th and below the 10th percentile. It is shown that the method for calculating the daily mean temperatures is of crucial importance. Also the choice of the common period used for calculating adjustments is rather important. Furthermore, there is no benefit in using daily adjustments derived from monthly adjustments. Finally, there is some benefit in using atmospheric circulation for weather-type dependent homogenization. The use of an adequate method to calculate the daily mean temperatures is, however, much more important.

Several climate change and variability studies have identified the need for homogenized daily time series in order to study the frequency and intensity of extreme climatic events. However, homogenization of daily climate series requires the development of new methodologies, because the traditional monthly-based adjustments are too coarse for daily data. In a review of homogenization methods for climate data, Peterson et al. (1998) already suggested that future work on homogenization should include improvement of adjustment methodologies, adjustments of daily data, and evaluating the impact of adjustments on extreme events.

Many studies have been undertaken to homogenize annual or monthly climatological time series (Peterson et al., 1998; HMS, 1996; Szalai et al., 1998; Slonosky et al., 1999; Vincent, 1998; Vincent and Gullett, 1999; Karl and Williams, 1987; Jones et al., 1986). In most studies inhomogeneities are traced in annual series and, subsequently, monthly adjustments are determined and applied to homogenize the series. Recently, in the EU-project IMPROVE (Improved understanding of past climate variability from early daily European instrumental sources), an attempt was made to derive daily adjustments by using daily measurements of cloudiness.

Inhomogeneities in climate time series arise from non-climatic factors like changes in station location, changes in methods to calculate means, changes in observation practices, changes in instruments and in station environment. Each of these changes may require a separate homogenization strategy. The changes may cause stepwise and/or gradual biases in the climatological time series, making these series unrepresentative of the climate of the concerning area.

In the present paper, inhomogeneities caused by changes in methods to calculate daily mean temperature are artificially imposed on the 20th century hourly data set of De Bilt in the Netherlands. Three approaches for removing these inhomogeneities are compared. Two of them are traditional approaches invoking monthly (12 values) or daily (365 values) adjustments to the data. The third method exploits the potential of the objective Lamb weather types for deriving weather-type dependent daily adjustments for daily temperature data is studied. The study is part of a long-term project aiming at homogenizing the complete Zwanenburg/De Bilt climatological time series (1706-present) at a daily base.

De Zwanenburg/De Bilt time series consists of six stations pasted together (Delft: 1706-1727; Rijnsburg: 1727-1734; Zwanenburg: 1735-1800 and 1811-1848; Haarlem: 1801-1810; Utrecht: 1849-1897; and De Bilt: 1898-present). The last 150 years, the daily mean temperatures are calculated using the arithmetic mean of 24 hourly values. For earlier dates daily mean temperature was mostly calculated from three temperature readings per day, where the time of measurement may vary. The inhomogeneities in the monthly time series, caused by using different methods to calculate the daily mean temperature, were usually removed by calculating monthly or daily adjustments for a common period. The adjustments were applied such that the older periods were adapted to the most recent period.

In this paper, we imitated the above-mentioned process to study the homogenization of daily temperature data, using the hourly temperatures of De Bilt (1901-1995). A reference temperature T_ref is defined as the arithmetic mean of 24 hourly values. Five alternative methods for calculating daily mean temperature are defined. The transition of one to each other in a time series may introduce inhomogeneities and biases with respect to T_ref. Three approaches for homogenization are compared. The first two of these approaches follow from the current practice for homogenizing temperature series on daily or monthly basis. In the third approach, daily weather types are used to find weather-type dependent adjustments.

The advantage of using manipulated modern daily data of De Bilt (1901-1995), is that the common period equals in fact the whole record length (1901-1995). Therefore, the errors can also be calculated for the whole record length.

The so-called objective Lamb weather types were used as a measure for daily weather. The objective Lamb weather classification scheme, also known as the Jenkinson scheme, was initially developed (Jenkinson and Collison, 1977) for the UK and the North Sea. From daily MSLP data on a regular 5° latitude by 10° longitude grid, extending back to December 1880, the following air flow indices were derived daily for both areas: (1) the direction of the flow; (2) the strength of the flow; and (3) the total shear vorticity. The latter is a measure of the rotation of the atmosphere. Positive vorticity corresponds to a low pressure area (cyclonic) and negative vorticity corresponds to a high pressure area (anticyclonic). The values of the three air-flow indices determine the weather type of the day considered. Sub-division gives a total of 27 weather types: anticyclonic, cyclonic, 8 directional types, 16 hybrid types and one type denoted as undefined. It was shown by Jones et al. (1993), that for the UK area the resulting scheme quite well reproduced the seasonal counts of the basic Lamb Weather Types. An important advantage of this objective scheme with respect to the latter is that it can be applied to other parts of Europe as well. As shown in Figure 1, we centered the grid near the Netherlands at 50°N, 5°E to obtain weather types for De Bilt.

Table 1 defines the reference temperature T_ref and the five alternative methods for calculating the daily mean temperature. The function f in this table equals the model function of Parton and Logan (1981) that describes the temperature on an arbitrarily time of the day using the times of sunrise and sunset and T_x and T_n and their times of occurrence. For the diurnal course of the temperatures, the function consists of a sinus function during the day and an exponential function during the night.

The model function of Parton and Logan (1981) can be rearranged such that T_x and T_n are found from two temperature measurements on arbitrarily times of the day. Van Engelen and Geurts (1983) applied this strategy and used a third measurement for a final correction. We also adopted this strategy.

Three approaches (a,b,c) were compared to remove the inhomogenities introduced by the changes in methods to calculate daily mean temperature. An extra subscript a, b or c was added to T₁,...,T₅ to denote an approach.

Approach (a)     Monthly adjustments were calculated and applied to T₁,...,T₅ using the, arbitrarily chosen, artificial common period 1991-1995 with T_ref in the hourly data set. The resulting homogenized temperatures were denoted T_1a,...,T_5a. In practice, common periods of 1 to 5 years have been used to calculate monthly adjustments. Monthly adjustments may, however, be rather sensitive to the choice of the overlapping period. Figure 2 illustrates this for T₁-T_ref using the 19 non-overlapping 5-year periods in 1901-1995. Of course, for shorter common periods the monthly adjustment are even more sensitive to the choice of the period.

Approach (b)     Daily adjustments were calculated and applied to T₁,...,T₅ for each calendar day using the monthly adjustments. An iterative cubic spline interpolation procedure was used that preserves the monthly adjustments as proposed by Harzallah and Sadourny (1995). The resulting homogenized temperatures were denoted T_1b,...,T_5b. An example of this approach is shown in Figure 3 for T₁.

Approach (c)     Daily adjustments were calculated using the weather types and applied to T_1b,...,T_5b. The resulting homogenized temperatures were denoted T_1c,...,T_5c. For each month and each weather type, the mean of errors T_1b-T_ref,...,T_5b-T_ref was calculated (for the whole period 1901-1995). These mean errors were subsequently used to adjust T_1b,...,T_5b giving T_1c,...,T_5c.

Figure 4 shows the frequency of the weather types for the 1901-1995 period. The anticyclonic type is denoted by (A), the cyclonic by (C), the directional types by their respective wind direction (NE, E, SE, S, SE, S, SW, W, NW), and the hybrid types by combinations of A or C with the directional types. UN denotes that the type is undefined and MIS that the type could not be calculated because of missing values of the mean seal level pressure. The frequency of weather types ranges between 24.5% (A) and 0.7% (CNE and CN).

Figure 5 shows for T_1b that the mean error (T_1b-T_ref) per weather type depends on the season. Therefore, the relationship between the weather types and the errors was calculated for each month separately. Because some of the weather types oc-cur only 0.7% of the days, the whole series (1901?1995) was used to derive the relationships between the weather types and the errors. Obviously, in practice such an ideal situation does not occur.

To compare the homogenized and non-homogenized temperatures with T_ref, we used three measures: (1) a direct comparison of the daily values using the bias (BIAS) and root mean squared error (RMSE); (2) a comparison of the day-to-day variability; and (3) a comparison of the number of days below the 10th and above the 90the percentiles for. The results for these measures are successively pre-sented below.

Table 2 presents the BIAS and RMSE, with respect to T_ref. The table shows that the non-homogenized temperatures T₃, T₄ and T₅ have a relatively small BIAS compared to T₁ and T₂. It is also seen that applying the monthly corrections (sub-script a) is especially advantageous for T₁ and T₂. On the other hand, the BIAS becomes larger instead of smaller for T₃. Apparently, the fact that the common period 1991-1995 is not representative for the whole period becomes noticeable here. The weather type correction (subscript c) automatically reduces the BIAS to zero because the reference and common period are identical (1901-1995).

Except for T₁ and T₂, Table 2 shows that the effect of using daily or monthly ad-justments on RMSE is small. There is no apparent positive effect of using daily adjustments based on monthly adjustments (subscript b), as compared to using only monthly adjustment, for both BIAS and RMSE. The positive effect of the weather type correction on RMSE is noticeable for all temperatures. This effect is, however, much smaller than the mutual differences in RMSE caused by using different methods for calculating the daily mean temperature. Finally, there is a clear positive effect, both in terms of BIAS and RMSE, of using the 22 UTC tem-peratures (T₂, T₅) instead of the 20 UTC (T₁, T₄) temperature.

Because it is known that there are some inhomogeneities in the De Bilt series, even in the period 1901-1995, the calculations were also carried out for the rela-tively homogeneous period 1971-1995. Because the differences with the results above were small, only the 1901-1995 period is discussed in the remainder of this paper.

An important measure of daily temperature variability is the so-called day-to-day variability. To calculate the day-to-day variability the absolute values of the lag-1 differences were calculated for the homogenized and non-homogenized tempera-tures and averaged for each month.

Table 3 presents the day-to-day variability for each month for a selection of the homogenized and non-homogenized temperatures. The results are expressed as a percentage differences from the day-to-day variability of T_ref calculated as 100(T_x-T_ref)/T_ref, where x denotes the concerning temperature series. The values for the simulations using monthly and daily adjustments are not shown because they hardly differ from the corresponding values for T₁,...,T₅. In general, the table shows a small decrease of the percentage differences because of the weather type correction. As in Section 3.1, this effect is much smaller than the mutual differ-ences in RMSE caused by using different methods for calculating the daily mean temperature. Especially the good performance of T₅ and, to a lesser extent, T₄ is striking. For T₁, T₂ and T₃ the day-to-day variability is overestimated. This is a well-known phenomenon that occurs when less than 24 hourly values are aver-aged to calculate the daily mean temperature.

Extreme events were calculated by counting the number of days in a month above the 90th percentile and days below the 10th percentile as calculated for the refer-ence temperature. First, the percentiles were calculated for each calendar day by linearly interpolating between order statistics of T_ref for that day (95 values). Sec-ond, to reduce the effect of sampling variability, smooth approximations of the percentiles were used instead of the raw values. Smoothing was done with the so-called supersmoother (Härdle, 1990).

Table 4 presents the BIAS and RMSE for the monthly counts. Results are given for a selected number of homogenized and non-homogenized temperatures. The table shows that the effect of the weather type correction is, in general, a decrease of both BIAS and RMSE. The performance of T_5c is clearly the best. It is notewor-thy that the RMSE of days above the 90th percentile is always lower than the RMSE of days below the 10^th percentile.

In this paper we compared three methods for removing inhomogeneities using hourly data of De Bilt (1901-1995). The inhomogeneities were artificially im-posed on the De Bilt series using 5 methods for calculating daily mean tempera-ture. The homogenized and non-homogenized temperatures were compared with the reference temperature. It appeared that the benefit of using daily temperature adjustments, derived from the monthly adjustments, is negligible. The length and choice of the common period, used to calculate the monthly adjustments, is much more important.

For inhomogeneities caused by using several methods for calculating daily mean temperature, the potential of the objective Lamb weather types for weather-type dependent homogenization is present but small. A drawback of the weather types may be that they are a representation of the atmospheric circulation at only one fixed time of the day. Another problem is that they are not available for the re-mote past. Possibly the use of wind speed and cloudiness may be more successful. These two variables are often measured three times a day, also before the year 1900.

The adapted model of Parton and Logan (1981) to calculate daily mean tempera-tures has a good predictive skill. This model may also be further improved, e.g. by taking into account the last observation of the previous day and the first observa-tion of the next day.

One source of inhomogeneities in temperature time series may by the use of sev-eral methods for calculating daily mean temperatures. In this paper these inho-mogeneities were studied using the hourly data for De Bilt (1901-1995). It was demonstrated that method for calculating the daily mean temperatures is of crucial importance. It is also shown that the choice of the common period used for calcu-lating adjustments is rather important. Furthermore, there is no benefit in using daily adjustments derived from monthly adjustments. Finally, there is some bene-fit in using the objective Lamb weather types for weather-type dependent homog-enization. The use of an adequate method to calculate the daily mean temperatures is, however, much more important.

For future studies dealing with homogenization of daily temperature time series, we recommend a further exploration of weather-dependent homogenization. For this purpose, other variables like cloudiness, wind speed and direction may be used. It is may also be profitable to develop a weather-dependent version of the model of Parton and Logan (1981).

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