Land surface air temperature (SAT) is one of the most important variables in weather and climate studies, and its diurnal cycle is also needed for a variety of applications. Global long-term hourly SAT observational data, however, do not exist. While such hourly products could be obtained from global reanalyses, they are found to be unrealistic in representing the SAT diurnal cycle.
Global hourly 0.5° SAT datasets are developed here based on four reanalysis products [Modern-Era Retrospective Analysis for Research and Applications (MERRA for 1979–2009), 40-yr ECMWF Re-Analysis (ERA-40 for 1958–2001), ECMWF Interim Re-Analysis (ERA-Interim for 1979–2009), and NCEP–NCAR reanalysis for 1948–2009)] and the Climate Research Unit Time Series version 3.10 (CRU TS3.10) for 1948–2009. The three-step adjustments include the spatial downscaling to 0.5° grid cells, the temporal interpolation from 6-hourly (in ERA-40 and NCEP–NCAR reanalysis) to hourly using the MERRA hourly SAT climatology for each day (and the linear interpolation from 3-hourly in ERA-Interim to hourly), and the bias correction in both monthly-mean maximum (Tmax) and minimum (Tmin) SAT using the CRU data.
The final products have exactly the same monthly Tmax and Tmin as the CRU data, and perform well in comparison with in situ hourly measurements over six sites and with a regional daily SAT dataset over Europe. They agree with each other much better than the original reanalyses, and the spurious SAT jumps of reanalyses over some regions are also substantially eliminated. One of the uncertainties in the final products can be quantified by their differences in the true monthly mean (using 24-hourly values) and the monthly averaged diurnal cycle.
Land surface air temperature (SAT) is one of the most important variables in weather, climate, and climate change studies. Surface station observations and globally gridded data based on these station measurements have been widely used (e.g., Meehl et al. 2007; Hansen et al. 2012). The inhomogeneity in the distribution of these stations has caused their observations to be less representative horizontally. For instance, while the high-resolution (10′ × 10′) global monthly temperature dataset from the Climate Research Unit (CRU) includes 12 783 SAT stations, most stations are located over relatively flat areas at low to midlatitudes (New et al. 2002). The point SAT measurements do not always accurately represents the regionally averaged climate variability (e.g., Jones et al. 1997; Le Treut et al. 2007). Changes in instruments, station siting, movement of station sites, and land use/land cover change (including urbanization) also affect the accuracy of station data in assessing the global and regional climate change (e.g., Jones et al. 1990; Pielke et al. 2007; Fall et al. 2011).
Station data of daily maximum (Tmax) and minimum (Tmin) temperature are used to compute daily and monthly-mean SAT based on (Tmax + Tmin)/2 in some countries, while the averaging method is different in other countries (e.g., Mitchell and Jones 2005). The averaging method may also change with time (e.g., in Australia; Jones and Moberg 2003). On the other hand, the widely used SAT data (e.g., the CRU data) include Tmax and Tmin (rather than hourly SAT or SAT at fixed hours). A cornerstone in climate change research is the increase of SAT in the past century and the faster increase in Tmin than in Tmax (e.g., Karl et al. 1991, 1993; Easterling et al. 1997; Trenberth et al. 2007; Zhou et al. 2010). On the other hand, it is widely recognized that the monthly-mean SAT varies according to the time (i.e., specific local hour) of recording Tmax and Tmin values (e.g., Baker 1975; Blackburn 1983; Karl et al. 1986; Aguilar et al. 2003). The change of the observational time over stations also introduces errors in computing the temperature trends (Jones et al. 1986). McNider et al. (2012) cautioned against the use of mean SAT as a climate metric since it contains Tmin, which reflects a redistribution of heat by changes in atmospheric turbulence rather than by an accumulation of heat in the atmospheric boundary layer. They suggested Tmax alone as a more robust climate metric. These points can be clearly illustrated by the histograms of the timing of daily Tmin and Tmax occurrences in Fig. 1 based on hourly observations. While Tmax and Tmin under a clear-sky condition over midlatitudes usually occur in the early afternoon and around sunrise, respectively (e.g., in top panels of Fig. 1), the timing of the occurrences can be widespread under other conditions. Therefore, while daily Tmax and Tmin still have a clear physical meaning, their monthly mean (i.e., the average of values at different times of each day) is difficult to interpret physically, as emphasized in Zeng and Wang (2012).
There has been a major technological shift in the past few decades in temperature measurements from mechanical thermometers requiring human readings of Tmax and Tmin to automated electrical thermometers for observations at hourly and shorter time intervals. It has long been recognized (e.g., Brooks 1921) that the monthly mean based on ½(Tmax + Tmin) is different from the true monthly-mean temperature, which is defined as the integral of the continuous temperature measurements in a month and can be very accurately represented using hourly data. Figure 2 shows clearly that the 24-hourly daily mean is usually smaller than (Tmax + Tmin)/2 (e.g., for 236 days over Tucson, Arizona, in 1998), and that the differences have a wide distribution (including positive values). Over those four stations within one year, the annual mean differences between two varies from −0.07° (Cabauw) to −0.71°C [Amazonian Rainforest Meteorological Experiment (ARME)], and the standard deviation of the daily differences varies from 0.47° (Cabauw and ARME) to 1.1°C (Tucson). More extensive data are also available from the U.S. Climate Reference Network (USCRN, http://www.ncdc.noaa.gov/crn/) on the timing of daily Tmax and Tmin occurrences and the differences between 24-h daily mean and (Tmax + Tmin)/2. While the Tmax and Tmin data are widely available, the hourly data do not exist. The question is then, how can we develop global hourly SAT data for the historical period?
Besides in situ Tmax and Tmin measurements, another data source is the atmospheric reanalysis products with complete temporal and spatial coverage based on the assimilation of data from different sources (e.g., satellite remote sensing, radiosondes) using the same forecasting system. However, reanalysis products have difficulty in reproducing the monthly mean and diurnal variation. For instance, Fig. 3 shows that the monthly (July) SAT differences between reanalyses and in situ data vary from 2.8°C over a boreal forest site [old jack pine (OJP)] to −1.4°C over a semiarid site (Tucson). The standard deviation (STD) of the hourly differences at the same hours (i.e., 0000, 0600, 1200, and 1800 UTC) for all reanalyses and observations varies from 3.2° (Tucson) to 0.2°C (OJP). Even though the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Int) have relatively fine temporal resolutions, they still have difficulty in capturing the observed diurnal variations. Some of these differences are due to the quantities and qualities of the assimilated observations in each reanalysis (e.g., Wang and Zeng 2012). In general, mean biases can be easily removed, as has been done in previous data development studies (Ngo-Duc et al. 2005; Qian et al. 2006; Sheffield et al. 2006). However, these studies did not consider the adjustment of Tmax and Tmin; therefore, the adjusted diurnal amplitude of SAT is still biased from the observation.
The purpose of this work is to evaluate various reanalysis products in reproducing the SAT diurnal variations and to develop global hourly 0.5° × 0.5° SAT datasets based on the reanalyses and CRU data. Here, we focus on the reanalysis evaluation, development of a new method for data adjustment, and preliminary assessment of our products. Section 2 describes the multireanalysis products and in situ CRU Time Series, version 3.10 (TS3.10), data used in this study, while section 3 compares different reanalyses with in situ measurements. Section 4 presents the data development procedure, followed by the evaluation of our final products using in situ measurements over various sites in section 5. Conclusions and further discussions are given in section 6.
2. Reanalysis and in situ data
The 2-m air temperature data from four reanalysis products are used, including the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis 1 (NRA1; Kalnay et al. 1996), the 40-yr ECMWF Re-Analysis (ERA-40; Uppala et al. 2005) and its more recent version (ERA-Int; Dee et al. 2011), and the National Aeronautics and Space Administration (NASA) Global Modeling and Assimilation Office (GMAO) MERRA (Rienecker et al. 2011). These datasets are derived using different forecasting models and different data assimilation methods but constrained by similar observational data from various sources. Even if these reanalyses use the same data source, their assimilation system and model deficiencies may lead to the rejection of different percentages of that input data. Rienecker et al. (2011) introduced the MERRA products and also presented a good summary of observational data (including the instrument) used in each reanalysis. While the assimilation system is “frozen” for each reanalysis, temporal inhomogeneity can still exist because of changes in the observational systems, particularly before the satellite era (Thorne and Vose 2010; Dee and Simmons 2011). These reanalyses also cover different periods with different horizontal resolutions and temporal output frequencies (Table 1), including the longest period from NRA1 (1948–2009), the highest (i.e., hourly) output frequency from MERRA, and the highest horizontal resolution (0.5° × 0.67°) from MERRA. The details of each reanalysis product can be found in the cited references.
Since the reanalysis SAT data contain various uncertainties, the CRU TS3.10 monthly-mean Tmax and Tmin data (Mitchell and Jones 2005) are utilized to do the bias correction. The CRU TS3.10 data are monthly gridded data derived from station values over land and are available for the period of 1901–2009. This dataset (http://badc.nerc.ac.uk) covers 67 420 grid cells with a resolution of 0.5° × 0.5° over global land excluding Antarctica. Besides the above-mentioned datasets, hourly temperature data from four stations (Fig. 1) are also utilized.
3. Comparison of reanalyses with the CRU TS3.10 data
Early studies have evaluated some reanalyses with in situ measurements from various perspectives. Simmons et al. (2004) compared the SAT trends and low-frequency variability in CRU, ERA-40, and NRA1, and found that ERA-40 is generally more consistent with the CRU station data than NRA1. ERA-Int is the updated ERA-40 reanalysis system with an advanced bias-correction method and assimilates more satellite/in situ observations (Dee et al. 2011), which significantly improve the global hydrological cycle (Uppala et al. 2008) and river basin hydrometeorology (Betts et al. 2009). Mooney et al. (2011) indicated that winter temperature in ERA-Int is slightly closer to observations than ERA-40 over Ireland. Jones et al. (2012) showed that ERA-Int is considerably better than ERA-40 in comparison with the CRU data over land. Wang and Zeng (2012) also illustrated that ERA-Int is in better agreement with in situ SAT over the eastern Tibetan Plateau than others. Using the flux tower data over North America, Decker et al. (2012) found that SAT is best simulated by ERA-Int, followed closely by MERRA and ERA-40 on 6-hourly, monthly, and monthly averaged diurnal time scales. Complementary to these studies, the reanalyses products are compared with the CRU TS3.10 data in this section, focusing on the seasonal and interannual variability and trend. Note that the average SAT diurnal cycle from reanalyses has been evaluated using in situ hourly data over four sites in Fig. 3. Since there are very few stations available over Antarctica and Greenland, large uncertainties exist in both the reanalysis and CRU data over these regions. Therefore, these two regions are excluded in our analyses below.
To facilitate the comparisons in this section, all reanalysis products have been spatially downscaled to 0.5° × 0.5° resolution (to be discussed in section 4). As mentioned earlier, the monthly-mean SAT is computed from Tmax and Tmin in CRU, while it is computed from the available diurnal output from various reanalyses (i.e., 6-hourly in ERA-40 and NRA1, 3-hourly in ERA-Int, and hourly in MERRA).
Figure 4 (left panels) shows that for the annual mean SAT anomalies with respect to the common period (1979–2001) climatology over the three regions and over global land (60°S–60°N), most reanalysis products are more consistent with each other and with the CRU data after 1980 than in earlier years, reflecting the assimilation of satellite observations in the modern era into the reanalysis system. The differences in the annual mean SAT anomalies between each reanalysis and the CRU data vary significantly from year to year. Reanalysis products also show some abrupt (and unrealistic) jumps that request further investigations, such as the abrupt increase of SAT in 1967 over the southwestern United States, the Tibetan Plateau, and global land in NRA1, and the large SAT oscillations over the Amazon rain forest in MERRA. The abrupt decrease of SAT since 1967 over the Amazon in ERA-40 is consistent with the finding of Betts et al. (2005). ERA-Int does not show any significant jumps over the three regions and global land, and overall its annual SAT variations are more consistent with the CRU data than the others.
Figure 4 (right panels) shows that the biases in the monthly-mean SAT climatology between reanalyses and CRU averaged for the common period of 1979–2001 vary with season, with ERA-40 showing the overall least dependence on seasons. Representing the first generation of reanalysis, NRA1 significantly underestimates SAT over the three regions and global land. The performance of other reanalyses is region dependent. Over the southwestern United States, ERA-Int and MERRA give the lower biases, while ERA-Int and ERA-40 give the lower biases over the Tibetan Plateau. Over the Amazon, MERRA and ERA-40 give the lower biases, while ERA-40 gives the lowest bias over global land.
Figures 5 and 6 present the global distribution of seasonal SAT differences between reanalyses and CRU data averaged over the common period of 1979–2001 for December–February (DJF) and June–August (JJA), respectively. In the boreal winter (DJF) (Fig. 5), all four reanalyses are warmer (by up to 5°C) than CRU over Eurasian high latitudes east of 90°E and colder than CRU (by up to 6°C) over Greenland. One possible reason for such large biases is that the CRU data over Greenland were obtained from the interpolation of low-lying stations in the coastal areas (Brohan et al. 2006; Mitchell and Jones 2005). Further investigations on the cause of such large biases are still needed. Each reanalysis also has cold or warm biases (up to 5°C) over other regions (such as NRA1 over the Tibetan Plateau and MERRA over a part of South America). The globally (excluding Greenland and Antarctica) averaged biases vary from −0.36° (MERRA) to 0.62°C (NRA1), and the biases for ERA-Int (−0.05°C) and ERA-40 (0.23°C) are in between. In the boreal summer (JJA) (Fig. 6), all four reanalyses are warmer (by up to 5°C) than CRU over Oman, Yemen, and part of Saudi Arabia. NRA1 has a significant cold bias over the Tibetan Plateau and along the western coast of the American continents, with the global average bias being −0.84°C. MERRA has a warm bias over most regions and a remarkably cold bias over Greenland, leading to a global average bias of 0.84°C (excluding Greenland and Antarctica). ERA-Int has a cold bias over the tropical rain forests with a global average bias of −0.29°C.
We also computed the linear trends of seasonal SAT from CRU (Fig. 7) and the trend differences between each reanalysis and CRU (Figs. 8 and 9) for 1979–2001. While the common period of 23 years may be too short to assess the significance of SAT trends (which is not the purpose here), our evaluation of the trend differences is still useful for our understanding of the overall differences between reanalyses and the CRU data. In both DJF (Fig. 7a) and JJA (Fig. 7b), the warming trend prevails over most regions. There are some exceptions in DJF; for example, eastern Siberia shows a substantially cooling trend (up to −2°C decade−1). The warming trend is greatest over North America, and western and northern Europe in winter. The globally (excluding Greenland and Antarctica) averaged CRU SAT trend in DJF is 0.19°C decade−1, which is much smaller than that (0.24°C decade−1) in JJA.
Compared with CRU, the trend biases from different reanalyses show distinctly seasonal and spatial patterns (Figs. 8 and 9). In DJF (Fig. 8), all reanalyses show overall negative trend biases over most of the regions, and the globally (excluding Greenland and Antarctica) averaged trend differences vary from −0.05° (ERA-40) to −0.17°C decade−1 (NRA1). Although the spatial distributions of trend differences are different in MERRA and ERA-Int, their globally averaged trend differences from CRU are similar (about −0.1°C decade−1). In JJA (Fig. 9), the positive and negative trend differences largely cancel each other out in ERA-40 (Fig. 9c), leading to a globally averaged trend difference of 0.004°C decade−1 only. NRA1 shows the negative trend biases over large areas, with a global mean value of −0.15°C decade−1. The globally averaged trend differences (excluding Greenland and Antarctica) in ERA-Int and MERRA are in between, −0.1° and −0.04°C decade−1, respectively. MERRA also shows a large positive bias (over 2°C decade−1) over part of North Africa.
There are several reasons for the above-mentioned differences among the four reanalyses, and between reanalyses and the CRU data. Each reanalysis uses a different land–atmosphere coupled forecasting model for the data assimilation, a different data assimilation system, different types and percentages of data assimilated (e.g., Rienecker et al. 2011), and different horizontal and vertical resolutions (e.g., Table 1). For instance, ERA-40 and ERA-Int assimilate SAT to adjust soil moisture, while MERRA and NRA1 do not. As mentioned earlier, the monthly mean is computed using different numbers of data per day in the reanalyses and CRU, and this would affect the monthly mean (e.g., Figs. 2 and 3). Furthermore, the CRU data quality is affected by two factors: 1) the change of measurement instruments, change of station location, and local environmental change due to urbanization and agricultural activities (e.g., Pielke et al. 2007); and 2) the interpolation from station data to 0.5° × 0.5°, particularly over data-sparse regions (e.g., Greenland, where only sparsely located stations at coastal areas were used for SAT interpolation in CRU TS3.10).
4. Global hourly 0.5° × 0.5° SAT data development procedure
All four reanalyses have different spatiotemporal resolutions (Table 1) that are coarser than the one we intend to develop (i.e., hourly 0.5° × 0.5°). Our procedure for data development includes three steps: horizontal downscaling, temporal downscaling, and monthly bias correction.
First, a mapping approach is employed to downscale the SAT of each reanalysis from its native grid to 0.5° × 0.5°. When a 0.5° × 0.5° grid cell is within a native reanalysis grid cell, its SAT is directly taken from the reanalysis value. When a 0.5° × 0.5° grid cell is across two or more (with a maximum of four) native reanalysis grid cells, its SAT is computed from the area-weighted average value from all crossed native cells. Using common 0.5° × 0.5° grid cells facilitates the comparison among reanalyses and between reanalyses and the CRU data (e.g., Figs. 4–9).
To temporally downscale reanalysis SAT from its native resolution to hourly, linear or bilinear interpolation methods have been traditionally used, for example, to disaggregate data from 6- to 3-hourly (Qian et al. 2006; Sheffield et al. 2006). The linear interpolation approach is also used here to downscale SAT from 3-hourly to hourly for ERA-Int. However, the 6-hourly SAT data from NRA1 and ERA-40 (centered at 0000, 0600, 1200, 1800 UTC) do not adequately represent the diurnal variations (e.g., Fig. 3), and a linear interpolation of 6-hourly data would lead to incorrect Tmax and Tmin values and their timing. Therefore, a new interpolation approach is developed here based on the MERRA hourly SAT.
First, the diurnal cycle climatology for each day at each 0.5° × 0.5° grid cell (after the spatial downscaling) is computed using the MERRA hourly SAT (centered at 0000, 0100, …, 2300 UTC) linearly interpolated from the native values (centered at 0030, 0130, …., 2330 UTC) for the period of 1979–2009. It is then used to interpolate the 6-hourly SAT of ERA-40 and NRA1 to hourly:
where xi is the downscaled hourly NRA1 or ERA-40 SAT for a given day at a 0.5° × 0.5°grid cell; yi is the MERRA hourly climatology for that day; i = 0, 1, 2, 3, 4, 5 represents each hour within a 6-h time interval; xL and xR are the first (e.g., centered at 0600 UTC) and the following (e.g., centered at 1200 UTC) 6-hourly reanalysis SAT values; and yL and yR are the corresponding values from the MERRA hourly climatology. Mathematically, Eq. (1) represents a linear interpolation between the two biases of (xL − yL) and (xR − yR) from 6 hourly to hourly. However, because yi varies nonlinearly with time, Eq. (1) represents a nonlinear interpolation of 6-hourly ERA-40 or NRA1 values. Furthermore, xi = xL at i = 0, and xi = xR at i = 6 in Eq. (1). In other words, the original 6-hourly SAT values from ERA-40 or NRA1 are not adjusted and only the hourly values in between are nonlinearly adjusted in Eq. (1). For the hourly reanalysis data (i.e., MERRA), no temporal interpolation is needed.
Our last step in data development is the monthly bias correction of the spatially and temporally downscaled SAT values. Usually, the monthly-mean reanalysis SAT was adjusted to match the CRU monthly mean ½(Tmax + Tmin) (e.g., Ngo-Duc et al. 2005; Qian et al. 2006; Sheffield et al. 2006). However, this approach suffers from two deficiencies: 1) the diurnal amplitude is not adjusted and is still unrealistic (e.g., Fig. 3); and 2) as mentioned earlier, the monthly mean using different numbers of data per day from reanalyses is different from (Tmax + Tmin)/2 in CRU. A new approach (without these two deficiencies) is developed here based on the CRU monthly Tmax and Tmin values.
The interpolated hourly SAT value at a 0.5° × 0.5° grid cell (Ti, i = 0, 1, 2, …, 23 UTC) can be adjusted to obtain T′i from
where the subscripts “max” and “min” refer to the daily maximum and minimum values, respectively; and the subscripts “m” and “m,obs” refer to the monthly mean from a reanalysis and from CRU TS3.10, respectively. While Eq. (3) adjusts the daily maximum SAT by the monthly-mean bias, Eq. (4) adjusts the daily minimum SAT by adjusting the diurnal range that is always greater than or equal to zero. If the Tmin adjustment was the same as that for Tmax in Eq. (3), then the unrealistic situation of T′max < T′min would be found to occur over some grid cells with small diurnal ranges. Equations (2)–(4) ensure that the adjusted reanalysis SAT products have exactly the same monthly-mean Tmax and Tmin as CRU TS3.10 and at the same time provide hourly SAT values. Note that while all four reanalyses after our three-step adjustments give exactly the same monthly Tmax and Tmin (as CRU), they do have different daily and monthly means using 24 hourly values and different monthly-mean diurnal cycles, and these differences represent the uncertainty of our products.
5. Evaluations of the final products
Using the three-step adjustments in section 4, we have developed global hourly 0.5° × 0.5° SAT datasets based on the NRA1 (1948–2009), ERA-40 (1958–2001), ERA-Int (1979–2009), and MERRA (1979–2009) reanalyses (referred to as final products hereafter).
Figure 10 evaluates the performance of our adjustment method against the traditional approach using in situ hourly observations over four sites as used in Figs. 1–3. These flux tower sites (except the Tucson site) have been widely used in international land model intercomparison projects and have high-quality data. The traditional procedure includes the linear interpolation from 6-hourly ERA-40 SAT to hourly and the monthly-mean (Tmax + Tmin)/2 bias correction. To allow a fair comparison with in situ measurements, the in situ data (rather than the CRU data) were used to obtain daily Tmax and Tmin and their monthly averages, and the in situ data (rather than the MERRA hourly SAT) were used to obtain the monthly averaged SAT climatology in Eq. (1). Figure 10 shows that the averaged diurnal cycle based on the traditional approach yields incorrect maximum and minimum values and gives incorrect timing of these values over all four sites. In contrast, the results using our procedure are much more realistic (Fig. 10 and Table 2).
Since our final products already agree exactly with the monthly-mean Tmax and Tmin from CRU TS3.10 at each 0.5° × 0.5° grid cell, it is not easy to further evaluate them using in situ point measurements because of the inherent differences between point measurements and 0.5° × 0.5° gridcell average SAT, such as elevation variations in a grid cell and errors from the interpolation scheme used to obtain the CRU data. With this caution, Fig. 11 and Table 3 evaluate our hourly final products using the in situ measurements over the four sites. The monthly-mean Tmax and Tmin from in situ point observations are quite different from the CRU data over a 0.5° × 0.5° grid cell (Table 3). To allow a fair comparison between our final products and in situ measurements, our final products are readjusted based on the in situ monthly-mean Tmax and Tmin using Eqs. (2)–(4). The readjusted final products agree well with the in situ data in Fig. 11 with the mean biases of all products from the 24-h averages of in situ measurements varying from −0.19°C over a semiarid site (Tucson) to 0.32°C over a rain forest site (ARME). The standard deviations between the readjusted final products and the in situ data in Fig. 11 are less than 0.95°C at three sites (ARME, OJP, and Cabauw) and vary from 1.05° to 2.47°C at the Tucson site. Over the Cabauw site, the adjusted ERA-40 diurnal cycle has the correct timing of the Tmax and Tmin at 1400 and 0400 UTC, respectively. In contrast, Tmax and Tmin occur four hours too early (at 1200 and 0000 UTC, respectively) in the linear interpolation of the 6-hourly ERA-40 data in Fig. 10. This demonstrates the advantage of our interpolation method in Eq. (1). On the other hand, as mentioned earlier, Eq. (1) represents a nonlinear hourly interpolation between 6-hourly ERA-40 (or NRA1) values, and hence it may also introduce spurious features occasionally (such as the dip around 1200 UTC in the adjusted ERA-40 data and, to a lesser degree, in the adjusted NRA1 data over the Cabauw site in Fig. 11d).
Figure 4 is replotted here using the final hourly products (Fig. 12). The temporal variations of our final products are much more consistent with each other in Fig. 12 (left panels) than those of the original reanalysis products in Fig. 4 (left panels), and all the abnormal jumps in the original reanalyses in Fig. 4 (left panels) have been substantially eliminated in Fig. 12 (left panels). As mentioned earlier, while all adjusted reanalysis products have the same monthly-mean Tmax and Tmin, they do not necessarily have the same monthly means using 24 hourly values (Fig. 12, right panels). However, the differences among our final products in Fig. 12 (right panels) are much smaller in magnitude than those based on the original reanalysis products in Fig. 4 (right panels).
Because the final products have the same monthly Tmax and Tmin [and hence (Tmax + Tmin)/2] as the CRU data, the differences in the right panels of Fig. 12 essentially reflect the differences between the true monthly mean using 24 hourly values versus the monthly mean (Tmax + Tmin)/2. Over most regions, these differences are negative most of the time, consistent with the conclusions based on in situ observations in Fig. 2. For example, the average differences vary from −1.13°C for the adjusted MERRA product to −0.75°C for the adjusted NRA1 and ERA-Int products over the southwestern United States (top-right panel in Fig. 12). The global (60°S–60°N) mean differences vary from −0.21° for the adjusted NRA1 to −0.56°C for the adjusted MERRA (bottom-right panel in Fig. 12). Note that if we use the same numbers of SAT values per day as those in Fig. 4, then the monthly and annual mean values from our final products would be slightly different from those in Fig. 12 based on 24 hourly values per day, but the above conclusions would remain the same (figure not shown).
Since the four stations in Fig. 11 were used in our data development, we have also selected two additional sites for independent evaluations of our data: one in Australia (37.7°S, 144.8°E) in 1995 from the National Climatic Data Center (NCDC) global hourly datasets and another over Siberia (71.6°N, 128.8°E) in 2003 from the Coordinated Energy and Water Cycle Observations Project. The results are similar to those at the four stations in Fig. 11. For instance, the standard deviations between the readjusted final products and the in situ data for a figure similar to Fig. 11 vary from 0.35° to 0.55°C at the Australian site and vary from 0.60° to 1.54°C at the Siberian site.
We have also compared our products with the daily datasets over Europe (referred to as E-obs; Haylock et al. 2008). The 0.5°E-obs daily temperature data were developed using more station data than in the CRU data. Because of this difference and the difference in the interpolation method, the E-obs data may be regarded as more reliable than the CRU data over Europe. As an example, the standard deviation of daily temperature difference between our final products and the E-obs data at each 0.5° grid cell over Europe (i.e., in the E-obs domain) was computed in January and July 1990. In January 1990, the median (25th and 75th percentiles) of the standard deviations over Europe varies from 1.6°C (1.0°, 2.4°C) for ERA-40 to 2.3°C (1.7°, 3.1°C) for NRA1. In July 1990, the corresponding values are much smaller, varying from 0.8°C (0.6°, 0.9°C) for ERA-40 to 1.3°C (1.1°, 1.5°C) for NRA1. The ERA-Int and MERRA results are in between. The differences between the adjusted ERA-40 data and the E-obs data are smallest, partly because the ERA-40 data were used to assist in the E-obs data development (Haylock et al. 2008).
6. Conclusions and further discussions
For historical and technological reasons, daily Tmax and Tmin have been measured and used to compute daily and monthly means for over a century in some countries. The averaging method, however, is different in other countries, and it may also change with time in the same country. The widely used global SAT data (e.g., the CRU data) include Tmax and Tmin only (rather than hourly SAT or SAT at fixed hours), and the global Tmax and Tmin data have become a fundamental data record for climate research. However, Tmax (or Tmin) does not occur around a similar time at a specific location (e.g., early afternoon for Tmax or around sunrise for Tmin); instead, the timing of the occurrence of Tmax (or Tmin) varies from day to day. Partly for this reason, the true daily or monthly mean using 24 hourly surface air temperature (SAT) values is different from (Tmax + Tmin)/2, as has been recognized for decades. This difference is negative on average over most locations, but it could be positive or negative for a given day at a specific location.
A logical choice to provide the diurnal information in combination with the in situ Tmax and Tmin data from CRU TS3.10 would be the various reanalyses that assimilate observational data from different sources with the same forecasting model and data assimilation system to provide complete and continuous fields globally. However, reanalysis SAT is strongly affected by the land surface model and the atmospheric boundary layer turbulence parameterization (e.g., McNider et al. 2012), and hence it is less constrained by observations than some other quantities (e.g., the geopotential height at 500 hPa). Therefore, four reanalyses (NRA1, ERA-40, ERA-Int, and MERRA) are found to be deficient in reproducing the diurnal Tmax and Tmin, the monthly SAT climatology, and the annual mean SAT trend over global land. They also contain spurious jumps in the SAT time series at some regions. For the common period of 1979–2001, the SAT differences and SAT trend differences between reanalyses and the CRU TS3.1 data vary spatially and seasonally.
The monthly-mean reanalysis bias can be corrected using the CRU (Tmax + Tmin)/2, but this approach does not remove the reanalysis bias in the diurnal temperature range (Tmax − Tmin). The linear interpolation from 6-hourly to hourly SAT fails to reproduce the daily Tmax and Tmin (which do not occur around a fixed time). In this study, we have developed three-step data adjustments, including 1) area-weighted spatial downscaling from the horizontal resolution of each reanalysis to a common 0.5° × 0.5° grid; 2) temporal interpolation from 6 hourly (in ERA-40 and NRA1) to hourly based on the MERRA hourly SAT climatology for each day (without adjusting the 6-hourly values themselves), linear interpolation from 3 hourly to hourly (in ERA-Int), and no interpolation for the MERRA hourly SAT; and 3) monthly bias correction in both Tmax and Tmin.
Evaluations with in situ measurements over four locations demonstrate that our innovative adjustments represent significant improvements over traditional methods. In this way, we have developed global hourly 0.5° × 0.5°SAT datasets for the period of 1948–2009 based on four reanalyses constrained by the monthly CRU TS3.10 Tmax and Tmin data: NRA1 (1948–2009), ERA-40 (1958–2001), MERRA (1979–2009), and ERA-Int (1979–2009). These final products have exactly the same monthly Tmax and Tmin as CRU TS3.10. They agree with each other much better than the original reanalyses, and the spurious SAT jumps of reanalyses have also been substantially eliminated. They are also overall consistent with in situ point measurements over four locations (used in data development) and two additional independent locations. Compared with the 0.5° daily temperature data over Europe (Haylock et al. 2008), the median of the standard deviations of the daily temperature differences between our final products and these regional data varies from 1.6° to 2.3°C in January 1990 and is much smaller (0.8°–1.3°C) in July 1990.
There are several uncertainties in our data products, which will be the focus in our subsequent study. While our final products have the same monthly Tmax and Tmin (as the CRU data), they do not necessarily have the same true monthly mean using 24 hourly values. One of the uncertainties can be quantified by the differences in the true monthly mean and the monthly averaged diurnal cycle among our final products. The second uncertainty of our final products is directly related to the uncertainty of CRU TS3.10 monthly Tmax and Tmin data, particularly over regions with very limited station data (e.g., Greenland). Another uncertainty is related to the temporal downscaling of the NRA1 and ERA-40 6-hourly data to hourly in Eq. (1) using the MERRA hourly climatology for each day computed from 1979 to 2009, as this causes somewhat similar diurnal patterns on the same day in all years in the adjusted NRA1 (or ERA-40) product (figure not shown).
Since our final products have exactly the same monthly Tmax and Tmin as the CRU data but also provide hourly SAT, they represent value-added products to the broad user community of the CRU and reanalysis SAT data. In particular, there are three important types of applications of our products: 1) definition of the daily and monthly mean based on hourly SAT as the fundamental climate data record; 2) evaluation of the SAT diurnal cycle of weather and climate models; and 3) use of the hourly SAT and other variables to force land surface models in the offline simulation of energy, water, and carbon cycle as well as dynamic vegetation. Since no temporal interpolation is needed for the MERRA hourly SAT output, the adjusted MERRA hourly 0.5° × 0.5° SAT data (1979–2009) are recommended if the user is interested in a single product only. In general, the use of all final products is encouraged so that data uncertainties can be quantified to a certain degree. The trend analysis using each of our products is also much more reliable than using the original reanalysis. As mentioned earlier, while our final products have the same monthly Tmax and Tmin (as the CRU data), they do not necessarily have the same true monthly mean using 24 hourly values (e.g., right panels of Fig. 12). Therefore, the trend analysis of a single time series combining different final products for different periods (e.g., ERA-Int from 1979 to 2009, ERA-40 from 1958 to 1978, and NRA1 from 1948 to 1957) is not appropriate.
More detailed analysis of the final products, including the uncertainty quantifications, will be provided in a subsequent paper. Since the beginning of this project, a new version of the CRU SAT data has become available. Besides MERRA, the NCEP Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) also provides hourly output that can be used for the diurnal temperature adjustment of 6-hourly data. These data will also be used in the future development of our products (version 2).
Based on these results and discussions, we suggest that reanalysis centers save the hourly (rather than the 3 or 6 hourly) two-dimensional near-surface fields in future reanalysis activities, as has been done by MERRA and CFSR. For the surface station observing community, it is time to save hourly observations and provide Tmax and Tmin [and hence (Tmax + Tmin)/2] as well as the true daily and monthly means using 24 hourly data for the weather and climate data record, as has been done by the U.S. Climate Reference Network.
The first author (AW) was supported by Department of Science and Technology of China (Grant 2009CB421403), and the National Science Foundation of China (Grant 41275110), while the second author (XZ) was supported by NASA (Grant NNX09A021G), the NSF (Grant AGS-0944101), and DOE (Grant DE-SC0006773). Drs. Xiaodong Zeng (IAP, China), Jiayu Zhou (NOAA/NWS/Office of Science and Technology), and Pieter Hazenberg (The University of Arizona) are appreciated for their helpful discussions. Three anonymous reviewers are thanked for their insightful comments and suggestions. Michael Brunke at The University of Arizona is thanked for helping to download those reanalysis data. The ERA-40, ERA-Interim, and NCEP–NCAR reanalysis data were obtained from the High Performance Storage System at the NCAR Computational and Information Systems Laboratory (CISL). The MERRA data were obtained from the Goddard Earth Sciences (GES) Data and Information Services Center (DISC). The CRU TS3.10 data were obtained from online (at http://badc.nerc.ac.uk) as were the E-obs data (from http://www.ecad.eu).