a. Errors due to the pyranometer window

Typical thermoelectric pyranometers measure SWIR in the wavelengths between 0.3 and 2.8 μm. At the top of the atmosphere (TOA), a measurement in this window underestimates SWIR by approximately 3.6%; at the surface, the error depends on the atmosphere above the pyranometer due to the calibration procedure. Pyranometers are calibrated (at least indirectly) against an active cavity radiometer without a window, and consequently, the radiation from the wavelengths cut off by the pyranometer filter is taken into account under the atmospheric conditions prevailing when the pyranometer is calibrated: when the humidity at measurement time is larger than at calibration time, the pyranometer underestimates SWIR (M. Anklin 1997, personal communication). Calibration is done at clear-sky conditions, which do not represent the mean atmospheric conditions at most GEBA stations, and thus, in the mean, the pyranometer data in the GEBA underestimate SWIR. An upper limit for this underestimation is 20 W m⁻², the maximum difference of the absorption in the wavelengths outside the pyranometer window between moist and dry atmospheres. It is not possible to assess this error at all GEBA stations in the periods with measurements: as the GEBA stores only monthly means, the atmospheric conditions at the time of the single readings are not known.

A bias (such as the underestimation of SWIR due to the pyranometer window) that is not included in a statistical model enlarges the variance (section 2c). The underestimation due to the pyranometer window is therefore accounted for with a random (with zero mean) error in the mean of all stations in the GEBA database when the overall error of the SWIR monthly and yearly means is assessed: the random error accounting for the bias due to the pyranometer window is assumed to be (i) independent from the other random errors and (ii) 1% of the measured value.

b. Errors of single pyranometer measurements

Errors in pyranometer readings are also due to other sources than the pyranometer window. Measurements with a random error of 4 W m⁻² are feasible if a good instrument is properly maintained (Konzelmann and Ohmura 1995). In comparison experiments, the random error of single pyranometer readings was 2% of the measured value (Fröhlich and London 1986). Random errors cannot be corrected, but their statistical structure can be taken into account when the data are used. Often, pyranometer measurements are also afflicted with a systematic error (with nonzero mean). An example of a systematic error with a time-dependent mean is the error produced by a drifting instrument. Systematic errors can be detected and possibly corrected if a detailed station history is available.

Maintenance of the instruments, of their installation, and of the data acquisition system is crucial to the quality of the measurements. Errors (systematic and/or random) due to maintenance problems can therefore not be excluded. Errors in the single pyranometer readings propagate to the hourly, daily, monthly, and yearly means aggregated consecutively from the original data. There is no other possibility than to assume that all errors are random, since the GEBA station histories are not detailed enough to allow for a methodical detection of systematic errors.

Random errors of pyranometer measurements are estimated in sections 2c, 2d, and 2e for daily, monthly, and yearly means of SWIR. With these estimates, the random errors including the contribution due to the pyranometer window are assessed in section 2g.

c. Errors of daily means

The influence of the maintenance to the quality of pyranometer data was investigated in a long-term pyranometer comparison project jointly performed by the Swiss Meteorological Institute (SMI), Zurich, and the authors’ institute, the Swiss Federal Institute of Technology (ETH). In this project, SWIR was measured by both institutions from 1989 until 1992 at the same (Reckenholz) station, but completely independently. The instruments used in the experiment are both Moll–Gorczynsky–type thermoelectric pyranometers made by different manufacturers. The installation of the instruments, the maintenance schemes, and the data acquisition systems were chosen deliberately differently (Table 1) to simulate the differences between the institutions that measured and published the SWIR monthly means now stored in the GEBA database. Using the Reckenholz pyranometer measurements, the error of long-term pyranometer measurements at daily and monthly scales is estimated as follows.

If X(t) is written for the SMI time series, Y(t) for the ETH time series, E for expectations, and Var for variances, then X(t) = EX(t) + e_X(t) and Y(t) = EY(t) + e_Y(t), EX(t), EY(t) the true values and e_X(t), e_Y(t) independent random errors with zero mean, as only random errors are allowed. Since SWIR is measured at the same station, that is, EX(t) = EY(t),

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is obtained. Clearly, under these assumptions, any bias (systematic difference between the SMI and the ETH measurements) enlarges the errors, that is, Vare_X(t) and Vare_Y(t). VarD(t) is estimated with the mean square of the differences. From estimates of VarD(t) in (1), estimates of Vare_X(t) and Vare_Y(t) are assessed (possibly under additional suitable assumptions).

The absolute and the relative differences of the Reckenholz daily means, D(t) and D(t)/X(t), are plotted in the upper part of Fig. 1; the lower part contains a histogram (including a 1D scatterplot) of D(t), and box plots (median, upper quartile, and lower quartile; whiskers are drawn to nearest value not beyond a standard range from the quartiles, and points beyond are drawn individually) representing the monthly distributions of D(t). In the mean, the differences are positive (3.4 W m⁻²), their distribution is skewed, and except in April 1992, the relative differences are larger in winter than in summer. This annual cycle is due to the ventilation of the SMI pyranometer. This device prevents the dome of the instrument to be coated by dew and frost (if the temperatures are not lower than −2°C). It is concluded that the ETH measurements are biased in the winter months due to a missing ventilation. This bias enlarges the variance of the differences, since (1) assumes that the true values are equal. The exceptionally large differences in April 1992 are (there is no better choice) assumed to be random, since the measurements were as usual according to the station logs.

VarD(t) = 59 (W m⁻²)² and, since variances are positive, Vare_X(t) < 59 (W m⁻²)² and Vare_Y(t) < 59 (W m⁻²)². Thus, the mean square error (MSE) of the daily means of SWIR at Reckenholz station is less than 59 (W m⁻²)². This estimate does not include the random error due to the pyranometer window (section 2a), since both instruments were (indirectly) calibrated with the same standard and the atmospheric conditions were identical for both measurements at Reckenholz station.

d. Errors of monthly means

From the daily SMI and ETH means of SWIR observed at Reckenholz station, monthly means were calculated if more than 25 daily means were available. The ETH September 1989 mean is missing because only 16 daily means were available due to failures of the data acquisition system. The differences of the monthly means together with their histogram are plotted in Fig. 2; their variance estimated according to (1) is given in Table 2. It is concluded that the MSE of the monthly means of SWIR at Reckenholz station is less than 47.6 (W m⁻²)². The reduction of the MSE from daily means to monthly means is small [11.4 (W m⁻²)²] due to the following reasons. (i) The portion of the MSE produced by the bias due to the missing ventilation of the ETH instrument is not reduced by averaging the daily values. (ii) At Reckenholz station, the synoptic variability of SWIR is quite large, and thus missing daily means (occuring in the average twice per month independently at both stations) are a strong source of variability.

In the midlatitudes, daily means of SWIR are serially correleated at midlatitude synoptic scales. The serial correlation reduces the effective independent sample size to only about 10 when a monthly mean is calculated. In the tropical regions, the synoptic variability is very large but correlation scales are smaller; in the polar regions outside the polar night, the synoptic variability and the correlation scales are comparable to those of the middle latitudes in the winter half-year. Consequently, the monthly means of SWIR are often statistically less stable than one would expect from the number of daily means used.

Is the MSE calculated from a small sample of only 47 Reckenholz pairs of monthly means representative for the monthly means of SWIR in the GEBA database? From Table 2 it is concluded that the variance of the Reckenholz differences is approximately equal to the variance at the Moscow (Russia), Toronto (Canada), and Bracknell and London (United Kingdom) stations, whereas a larger variance was found for the Pretoria (South Africa) stations. These four pairs of stations were selected as being representative for the pyranometer measurements in countries with a large number of stations with measurements of SWIR for longer (decades) periods. The distances between the stations of these four pairs are a few kilometers (except for the U.K. pair, stations were selected because measurements before and after 1980 are available at both stations) (cf. Table 4, section 3b) and thus the radiative climates are slightly different. Consequently, the assumption EX(t) = EY(t), [now X(t) the time series of monthly means of SWIR at the first station in a pair, Y(t) at the second station] is no longer appropriate, and (1) is replaced by (2):

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The last line in (2) assumes that both stations in the Pretoria, Toronto, Moscow, and U.K. pairs contribute symmetrically to the variance of the differences. (At the Reckenholz station, the unventilated ETH instrument obviously contributes more to the variance of the differences than the SMI instrument).

The difference time series of monthly means at the pairs of stations in Table 2 are plotted together with their histograms in Fig. 2. The differences were calculated from monthly means retrieved from the GEBA database. From the U.K. difference time series follows that another maintenance scheme was introduced in 1980: the variance of this time series jumps from 54 to 34 (W m⁻²)², and the mean decreases from 8.5 to 5.1 W m⁻². These jumps are very unlikely due to a change of the radiative climate. The slight trends and/or jumps of the other difference time series are considered to be random; no knowledge about possible causes is available. For example, is the trend of the Toronto difference series due to a drifting instrument or an urbanization effect at only one station? If the variances of the difference time series are not due to natural phenomena, the MSEs of the monthly means of SWIR measured at the stations in Table 2 are (symmetric contributions assumed) half the estimates tabulated. Thus, the relative errors (root-mean-square error/mean of yearly means in years with measurements at both stations) are less than 5% at all stations in Table 2. As in the case of the daily means, the error due to the pyranometer window is not included in these estimates.

e. Errors of yearly means

The yearly means of SWIR in the GEBA database are calculated from the monthly means, if 12 (in polar regions, SWIR is assumed to be zero in the months falling in the polar night) monthly means are available. The error of the yearly means is estimated with the sample of yearly means observed at the stations in Table 2. In the following, X(t) is written for the time series of yearly means at the first station of each pair, Y(t) at the second station, and X (Y) are the means of all X(t) (Y(t)) in the years, where both X(t) and Y(t) are available. Then, according to (2), X′(t) = X(t) − X and Y′(t) = Y(t) − Y for the Pretoria, Toronto, Moscow, and U.K. stations, but, according to (1), X′(t) = X(t) − X and Y′(t) = Y(t) − X for the Reckenholz measurements. All [(X′(t), Y′(t)] are plotted in Fig. 3 using the symbols 1, 2, 3, 4, and 5 in the order of the stations given in Table 2. The moments of the yearly differences [D(t) = X′(t) − Y′(t)] are −0.4 W m⁻² and 15.8 (W m⁻²)². As in the case of the daily and monthly means, it is concluded that the MSE of the yearly means is less than 16 (W m⁻²)², and, if both stations contribute symmetrically to the variance of the differences, it is 8 (W m⁻²)². This assumption is suitable for the Pretoria, Toronto, Moscow, and U.K. stations. In the Reckenholz case the errors due to the missing ventilation of the ETH instrument propagate to a yearly bias of 3 W m⁻² in the mean and thus the assumption of symmetric contributions cannot be applied. Nevertheless, in the mean at the stations in Table 2, the MSE is 8 (W m⁻²)² and the relative random error 1.9% (the mean of SWIR at these stations is approximately 150 W m⁻²). As in the case of the daily and monthly means, the error due to the pyranometer window is not included in these estimates.

f. Quality control

The station histories stored in the GEBA database are not detailed enough to allow for a methodical detection of monthly means of SWIR afflicted with systematic errors. It is also hardly possible to detect random errors of up to 15% of the monthly mean to be checked because the spatial and interannual variabilities are both 15% in winter at midlatitude stations (section 4). More useful for the development of quality control procedures is the notion of gross errors. Gross errors are systematic or random. They are due to severe maintenance problems, instrument and data acquisition system failures, and/or data processing mistakes. Empirical formulas and statistical techniques were used to devise quality control procedures that detect values afflicted with gross errors when applied to the SWIR monthly means in the GEBA database (Gilgen et al. 1997; H. Gilgen and A. Ohmura 1998, unpublished manuscript).

Values suspected of being afflicted with error by a quality control procedure are flagged. The flagged values are checked against the data source and duly corrected if a typing or optical character reading error occurred when the data were inserted into the database. No other corrections are applied to the values, since only the station scientist, who has access to the original records and knows the history of the instruments used, is in a position to give a correct answer to the problem of definitively identifying erroneous values.

The GEBA climatologies of SWIR calculated in the period from 1950 to 1995 are not biased by the application of the quality control procedures at the global scale. At the regional scale and in subperiods, however, systematic gross errors due to countrywide maintenance and/or data processing problems have been detected by the quality control procedures (Gilgen et al. 1997; H. Gilgen and A. Ohmura 1998, unpublished manuscript).

g. Error inclusive the contribution due to the pyranometer window

If pyranometer measurements are compared with values of SWIR calculated by remote sensing algorithms or GCMs, the error of the pyranometer data has to be taken into account. The estimates in sections 2d and 2e (5% of the monthly means, 1.9% of the yearly means), however, do not include the error due to the pyranometer window (section 2a), if it is assumed that (i) the atmospheric conditions were identical at both stations in the pairs used for the estimation (Table 2) anytime when the single pyranometer measurements were made and (ii) the pyranometers were calibrated in the same session, that is, at the same time and site. The total random error including the contribution due to the pyranometer window of SWIR monthly and yearly means is assessed using the assumptions in section 2a. Under these assumptions both MSEs are added and the overall relative errors are calculated: they are 3.2% of the Pretoria monthly means, 3.8% of the Toronto monthly means, 5.0% of the Moscow monthly means, 4.7% of the U.K. monthly means, less than 5.4% of the Reckenholz monthly means, and 2.1% of the yearly means.

It is concluded from these percentages that, in general, (i) the relative random error of measurement is approximately 5% of the monthly means and (ii) approximately 2% of the yearly means of SWIR stored in the GEBA database. These estimates apply only for monthly or yearly means of SWIR that have not been flagged as being afflicted with error by the GEBA quality control procedures (section 2f). The GEBA database, however, stores monthly and yearly means afflicted with larger random errors that have not been caught by the GEBA quality control. An example are the measurements at the high-altitude alpine stations of Pian Rosa, Corvatsch, Jungfraujoch, and Weissfluhjoch in Table 4, discussed in section 3b.

a. Linear model for the trend and station effects

The variance of a climatological cell mean of SWIR is broken down into the contributions of the sources of variability listed above by using linear models (regression and analysis-of-variance techniques): the response-variable SWIR (y, in W m⁻²) is modeled as a linear combination of the predictor variables, time (t, in years), and station identification (s, labels A, B, C, . . .). Thus, the model for the ith yearly mean of SWIR in a grid cell with two stations A and B is written

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If the grid cell contains only one station, (3) reduces to

y_ia₀a₁t_ie_i(4)

This model assumes that (i) the decadal trend is linearly dependent with coefficient a₁ on time, (ii) the differences between the stations in the cell due to local climate effects are coefficients a_2A and a_2B (constant station effects), and (iii) the residuals e_i are normally (because tests are used) independent, distributed with zero mean and constant variance. The coefficients are estimated by minimizing the sum of the e²_i. The trend is calculated as a percentage of the cell mean in 10 yr. The coefficient a₁ is tested for zero slope with a two-sided t test. The total variation in the response (variance of the cell mean and total sum of squares) is broken down into the contributions due to (i) the trend, (ii) the station effects, and (iii) the residuals. The sum of contributions (i) and (ii) is the variation in the fitted values, that is, the variation accounted for by the model. Mean squares are calculated by weighting the sums of squares due to the trend and the station effects with the number of coefficients estimated (the sum of the squared residuals with the number of observations minus the number of coefficients estimated; degrees of freedom). The mean squares due to the trend and due to the station effects are divided by the mean square of the residuals to obtain the F statistics. The F statistics are large if the variation due to the trend or the station effects are large as compared with the residual variation. If the significance levels of the F statistics are lower than a chosen threshold, the trends (the station effects) are significant at the chosen level.

The estimates of the trend and the analysis-of-variance breakdown of the sum of squares in seven example grid cells are given in Table 3. The yearly means of SWIR measured at the GEBA stations in these grid cells are plotted in Figs. 4–7. The moments of the time series of yearly means of SWIR measured at these stations are given in Table 4 (variances have been calculated only from 10 or more yearly means). The mean squares of the residuals in the analysis-of-variance breakdown in Table 3 are due to the interannual variability and the error. The interannual variability is assessed in section 3d.

Assumptions (i), (ii), and (iii) are not violated in most cells in which the SWIR yearly means were analyzed with (3) or (4). This is concluded from plots of the data and the residuals. The example grids in section 3b, however, were chosen to illustrate the application of (3) and (4) and to show their limitations. Therefore, in three out of the seven example grid cells, the assumptions are violated.

b. Example grid cells

In Fig. 4, the yearly means of SWIR in grid cell [(10°E, 50°N), (15°E, 52.5°N)] are plotted. In this grid cell, SWIR decreases linearly in the period 1950–80. Since 1980, SWIR has increased. The positive trend since 1980 is partly due to the data available since 1991 at two stations in eastern Germany (Zinnwald and Chemnitz, plotted with symbols 5 and 6, respectively). Both linear models (with and without station effects) have been applied to the yearly means of SWIR in this grid cell. The results are given in Table 3. The decadal trend is slightly positive if estimated using model (4) without station effects and slightly negative if estimated using model (3) with station effects. Using (3), the standard deviation of the residuals is 6.7 W m⁻², whereas no reduction of the standard deviation of the mean (8.1 W m⁻²) is obtained using (4). In this grid cell, therefore, estimates obtained with (3) are better than estimates with (4). Obviously, however, (3) does not capture the reversal of the trend occurring around 1980 and thus assumptions (i) and (iii) of (3) are violated. In this grid cell and in general, t and s are not independent and estimates of the trend using (3) or (4) are different. Estimates of trends with (4) in cells with two or more stations are considered to be inferior to estimates with (3), which allows for constant station effects.

Figure 5 contains plots of the yearly means of SWIR measured in adjacent cells [(7.5°E, 47.5°N), (10°E, 50°N)] and [(10°E, 47.5°N), (12.5°E, 50°N)]. In cell [(7.5°E, 47.5°N), (10°E, 50°N)] are eight stations with measurements starting between 1975 and 1980 with positive trends, and only one station (Würzburg, symbol 0) with a negative trend (measurements at Würzburg nominally start in 1957; in the GEBA database, however, yearly means are available since 1962 due to missing monthly means). Consequently, assumptions (i) and (ii) of (3) are violated, since trends are different at the stations in this grid cell (the discussion of different trends at the stations in a grid cell follows in the next paragraph). The overall trend is positive, but not significant (cf. columns 6, 7, and 8 in Table 3). In cell [(10°E, 47.5°N), (12.5°E, 50°N)], Hohenpeissenberg and Weihenstephan stations (symbols 4 and 5) with negative trends dominate, which results in a decadal trend found to be significant at the 0.99 level. In this grid cell, the assumptions of (3) are not violated. The total sum of squares in these cells are 4762 and 7327 (W m⁻²)²; of these, 0% and 31% are accounted for by the trend, and 28% and 29% by the station effects (cf. columns 9, 10, 11, 12, and 13 in Table 3).

In Fig. 6, the yearly means of SWIR measured at stations in grid cell [(5°W, 50°N), (0°, 52.5°N)] are plotted. In this cell, there are two stations with negative trends; Efford and Aberporth, plotted with symbols 3 and d, respectively. Both stations are located on the coast. A third coastal station (Wareham, symbol 2) shows no trend, and for Sutton Bonington station (symbol e) only the mean of the period of measurement is available. At the other stations, small positive trends have been measured. An adequate model for the intracell variability in this grid cell should allow for individual trends at the stations, whereas (3) allows only for an overall trend and constant station effects. Clearly, the solution of the problem is an analysis of the SWIR data at the subgrid scale. At the grid scale, however, a small positive trend results in this grid cell.

Figure 6 contains also a plot of the yearly means of SWIR measured at stations in grid cell [(7.5°E, 45°N), (10°E, 47.5°N)]. According to Table 3 the variability in this grid cell is much larger than in the other example grid cells due to the surface properties: measurements have been made at Alpine stations as well as at stations north and south of the Alps. A large part of the variability is due to the measurements at Pian Rosa station (symbol 4). Pyranometer measurements at high-altitude alpine stations are very difficult and often impossible due to unfavorable weather conditions. At the other high-altitude stations (Corvatsch and Jungfraujoch, cf. Table 4), therefore, only the Jungfraujoch 1989 mean (symbol 7) is available out of a total of 6 yr of measurement. The lowest yearly means of SWIR radiation have been measured at stations in the Zurich region (symbols d, e, g, h). Long time series are available for the Locarno Monti and the Davos-Platz stations (symbols 5 and 8). The Locarno Monti station is located at the southern slope of the Alps, and Davos-Platz is in an inner alpine valley. At both stations, however, the yearly means of SWIR are quite similar. In this grid cell, a significant negative decadal trend and a large intracell variability have been estimated, reducing the variance of the mean [471 (W m⁻²)²] to a much lower mean square of the residuals [85 (W m⁻²)²]. This value is still large compared to the values in the other grid cells in Table 3;it is likely due to the measurements at the high-altitude stations, which are afflicted with an error larger than 2%. These measurements need an analysis at the subgrid scale. At the grid scale, however, a relatively large standard deviation of the residuals results.

In Fig. 7, yearly means of SWIR in the grid cells [(10°W, 37.5°N), (7.5°W, 40°N)] and [(10°E, 35°N), (12.5°E, 37.5°N)] are plotted. In both grid cells, the contribution of the intracell variability to the variance of the mean is small. In cell [(10°W, 37.5°N), (7.5°W, 40°N)] also the contribution of the trend is small and thus the mean square of the residuals [61 (W m⁻²)²] is even larger than the variance of the cell mean [58 (W m⁻²)²] due to the decreasing degrees of freedom.

c. Trends and station effects limiting the representativity of SWIR yearly means

The estimates in Table 3 obtained in the example grid cells give a range of possible values for the trends and station effects. A relative change of 2% in 10 yr produces a considerable bias if data measured 10 yr ago are used to estimate a present climatological mean of SWIR. For example, climatological means of SWIR in the United States are calculated from data measured in the period 1950–75. At the U.S. stations during this period, SWIR decreases (in the mean approximately by −3% in 10 yr, estimated in grid cells with more than 20 observations, cf. Fig. 8, later) and therefore the GEBA estimates of present SWIR at the U.S. stations are more than 6% too large. This result is obtained under the assumption that the trends of SWIR at the U.S. stations have not changed since 1975 (trends did not change at the Canadian stations).

An extreme station effect (18.5 W m⁻²) in the grid cell [(7.5°E, 45°N), (10°E, 47.5°N)] has been estimated for the yearly means of SWIR at the Pian Rosa station. This high-altitude station measures considerably more SWIR than the other stations in this grid cell. Extreme station effects are also observed in grid cells with islands and/or coasts. In Fiji, Suva/Laucala Bay station (178°27′E, 18°9′S, 6 m above mean sea level (MSL), on the southwest coast of Viti Levu Island) measures 195 W m⁻² SWIR in the average of the years 1985, 1986, and 1987, whereas Nandi station (177°27′E, 17°45′S, 6 m MSL, on the northeast coast of Viti Levu Island) receives 226 W m⁻² in the average in the same period. In Croatia and Bosnia, the mean SWIR measured at Split/Marjan station (16°26′E, 43°31′N, 122 m MSL, at the coast) is 184 W m⁻², whereas at Banja Luka station (17°13′E, 44°27′N, 153 m MSL, inland) only 147 W m⁻² have been measured. These means were calculated from 10 yearly means measured in the period 1964–84 at Split/Marjan station and from 17 yearly means measured during the period 1964–90 at Banja Luka station. In more homogeneous grid cells (no large altitude differences, no coasts, no islands), however, the estimates in Table 3 suggest that the error due to a station effect is less than 5%, if a cell mean is estimated using the yearly means measured at only one station.

The estimates of the station effects in Table 3 are in line with the results of several studies summarized in Fröhlich and London (1986).

d. Interannual variability

In the preceding example grid cells, the relative standard deviation of the residuals (quotient of columns 5 and 3 in Table 3) is (i) less than 5% in the grid cells where the assumptions of (3) are not, or are only slightly [(7.5°E, 47.5°N), (10°E, 50°N)], violated; (ii) between 5% and 6% in grid cells [(10°E, 50°N), (15°E, 52.5°N)], [(5°W, 50°N), (0°, 52.5°N)], where (3) is not adequate; and (iii) larger than 6% in grid cell [(7.5°E, 45°N), (10°E, 47.5°N)], with the high-altitude stations, which are possibly afflicted with a larger error. In the example grid cells with a relative standard deviation of the residuals less than 5%, the model (3) and an error of measurement of 2% are likely to be adequate and, therefore, the interannual variability is estimated as follows: the MSE corresponding to a measurement error of 2% is subtracted from the mean square of the residuals assuming that the error is independent from the interannual variability. The quotient of the root-mean-square interannual variability and the cell mean is given in column 16 in Table 3. It is concluded that in the midlatitudes, the relative interannual variability of SWIR is about 4%, twice the random error of measurement (approximately 2% as estimated in section 2g).

e. Representativity of a cell mean

How representative is a yearly mean of SWIR for a larger area and a longer period? As already mentioned above, a general answer cannot be given because (i) the GEBA station records are not detailed enough to allow for a methodical detection of systematic errors, (ii) possible trends are not known, and (iii) climatological cell statistics are estimated with different procedures chosen according to the amount of data available.

In the ideal case, SWIR is stationary in space and time and enough measurements are available. Then the climatological cell mean of SWIR is easily estimated without bias as the mean of all yearly means of SWIR measured at the stations in the cell in the last few decades. The variance of the cell mean contains the contributions of the natural spatial and temporal variability and of the measurement error.

In the best case, the climatological cell mean is estimated from a sample of yearly means measured at stations representative for some or all regions with different radiative climates in the grid cell and in a period starting a few decades before present. Examples for this case are given in Figs. 4–7 and Table 3. In such a cell (i) the standard deviation of the cell mean represents the total variability of the data, (ii) estimates of the trend and of the station effects are obtained using model (3), and (iii) an estimate of the interannual variability is obtained from the standard deviation of the residuals of the model as the error of measurement is known.

In the average case, the climatological mean is estimated from a sample of yearly means measured at only one station: station effects are not estimated; a trend is calculated only if there are more than 20 yearly means available, and the standard deviation of the cell mean is calculated only if more than 10 yearly means are available. These are small samples and thus the estimates are statistically unstable. In such a cell, the standard deviation of the cell mean underestimates the total variability of SWIR, since the intracell variability (the strongest source in the example grid cells in Table 3) does not contribute to the variance of the cell mean.

In the worst case, a climatological cell mean is estimated from only one yearly mean of SWIR measured some years before present. In this case, the yearly mean available is the estimate for the climatological cell mean and no other estimates are obtained from the data. In such a grid cell, therefore, the sources of variability are assessed under the following assumptions: (i) the proportions of the sources of variability are constant in average grid cells (no large altitude differences, no coasts, no island) and (ii) the sources of variability are independent. Using the estimates for the midlatitude example grid cells in Table 3 and assuming a cell mean of 100 W m⁻², the variance of the cell mean is 9 + 25 + 16 + 4 = 54 (W m⁻²)² (3% due to the trend, 5% due to the intracell variability, 4% due to the interannual variability, and 2% measurement error). The resulting standard deviation of the cell mean is 7.3 W m⁻². It is concluded that the error of a climatological mean of SWIR in an average cell in the middle latitudes is approximately 7%, if the cell mean is estimated from only one yearly mean of SWIR. In the low and high latitudes, however, no estimates are available because no grid cells with samples of yearly means of SWIR large enough are available.

a. Means

Figure 8 contains the numbers of yearly means of SWIR, their means, and their relative standard deviations. In a grid cell, a climatological cell mean of SWIR is calculated from the sample of yearly means of SWIR defined in section 3. The minimum sample size is 1. The cell mean is not corrected for the systematic bias due to a possible trend, since trends are estimated only in grid cells with at least 20 yearly means. The standard deviation of the cell mean is calculated only in cells where at least 10 yearly means are available. In grid cells with relative standard deviations larger than 7% (section 3e), either the sample size is small or one or more sources of variability analyzed in section 3 are stronger than estimated for cells in the middle latitudes. For example, in grid cell [(7.5°E, 45°N), (10°E, 47.5°N)] with yearly means plotted in Fig. 6 and the statistics given in Table 3, the measurements at Plateau Rosa station are likely to be erroneous.

In the low latitudes, less than 200 W m⁻² have been measured in the Amazon and Zaire river basins, at the Guinea coast, and in southeast Asia. Adjacent to these innertropical regions of minimal SWIR, 220 W m⁻² have been measured in the Caribbean, West Africa, East Africa, and India. More than 250 W m⁻² reach the surface in the desert and/or high-altitude regions of North America, North Africa, Arabia, South America, South Africa, and Australia.

In the mid- and high latitudes in the Northern Hemisphere, continental and high-altitude regions receive more SWIR in the annual mean than the regions with maritime climate. For example, at 50°N, 100 W m⁻² and less are measured at the west coasts of North America and Europe, whereas 150 W m⁻² reach the surface in the Great Plains and Mongolia. The minima of approximately 80 W m⁻² have been measured at stations located at the coast of the North Atlantic Ocean, the Norwegian Sea, and the Barents Sea. These regions are relatively warm (compared with other regions in these latitudes) due to the North Atlantic drift, and thus large cloud amounts and the humid atmosphere reflect and/or absorb a large part of the TOA insolation.

In the mid- and high latitudes in the Southern Hemisphere, South America at 40°S receives 200 W m⁻², and southeastern Australia and New Zealand receive 160 W m⁻². Values of 120 W m⁻² and less have been measured at the stations on the islands in the southern oceans, with annual means below 100 W m⁻² at the McQuarie Islands and King Edward Point stations. The Antarctic ice sheet, however, receives up to 140 W m⁻².

b. Trends

Figure 8 also contains the relative change of SWIR (percent in 10 yr) estimated in grids cells with 20 and more yearly means of SWIR, the relative change in the cells with significant (two-sided t test at 0.95 level) trends and the standard deviation of the residuals of models (3) or (4) defined in section 3a. In large regions, SWIR decreases or is stationary; only in a few small regions have positive trends of SWIR been observed. A decrease in SWIR was also found in the following studies.

At the global scale, Stanhill and Moreshet (1992) found a mean reduction of 5.3% in SWIR data measured at 200 stations for the period 1958–85. At the regional and local scale, trends in SWIR were found by Russak (1990) at stations in the Baltic region; by Ohmura and Gilgen (1991) at stations at the Atlantic coast in Europe, in Germany, and in the Baltic region; by Liepert et al. (1994) at seven (out of a total of 12 analyzed stations) in Germany; by Stanhill and Kalma (1995) at the Hong Kong station; and by Abakumova et al. (1996) at most stations in the former Soviet Union. These results are in line with the estimates mapped in Fig. 8, since most data used in these studies have been inserted into the GEBA database.F

Reasons for the observed changes of SWIR have been found at the local scale in the following papers. (i) Liepert et al. (1994) concluded from records of sunshine duration that the decrease of SWIR is due to an increased cloud cover and sea fog at three stations, but it is due to changes of the atmospheric turbidity (likely due an increased tropospheric aerosol content) at four stations. (ii) Stanhill and Kalma (1995) could not explain the decrease of SWIR at the Hong Kong station by changes in the cloud cover. (iii) For the Toravere (Estonia) and Moscow stations, however, Abakumova et al. (1996) found an increasing cloudiness as the main reason for the negative trend of SWIR based on records of direct and diffuse radiation and cloud observations at these stations. From these results it is concluded the reasons for the observed changes of SWIR are likely to be different at different stations in the same climatic region:further research at the local scale using radiation and auxiliary atmospheric data at higher resolution (hourly and daily means) is needed.

In the large regions with moderate and strong negative trends (relative changes ⩽−2% in 10 yr), the GEBA estimates of a climatological mean of SWIR are systematically larger than the present mean. In regions with positive trends, however, an underestimation results.