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    Land–sea mask used for computing the spatial averages over North America, South America, Europe, Africa, Asia, and Australia. The table shows the areas of the regions considered within each continent.

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    Relative difference between CFSR evaporation (over the oceans) and evapotranspiration (over the continents), with and without considering changes in the near-surface temperature. The impact is generally higher over the continents, while over the oceans, the amplitude of the intra-annual variations is larger.

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    Number of monitoring stations per 0.5° × 0.5° grid cell in (a),(c),(e) January 1989 and (b),(d),(f) December 2006 for the (a),(b) GPCC v4.0; (c),(d) GPCC v5.0; and (e),(f) CPC datasets. A good spatial coverage with observation stations can be observed over North America (GPCC v5.0 and CPC) and Europe (GPCC v4.0 and v5.0), while the number of gauges over North America is significantly reduced in GPCC v4.0. Over most of the tropical regions like the Congo or Amazon basin, high-latitude regions, and large parts of Asia, the three datasets use a maximum of 1–2 gauges per grid cell, whereas some areas are completely ungauged.

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    (a)–(f) Mean annual number of gauges used in the precipitation observations from GPCC v4.0, GPCC v5.0, and CPC. Version 4.0 shows a significant drop in the number of gauges between 2000 and 2001 over North America and Australia, while version 5.0 of the GPCC product is based on a nearly constant number of observation stations during the complete time series. Over South America, Europe, and Africa, the update from v4.0 to v5.0 results in little improvement only, as both versions show a nearly constant decline over time. Over Asia, GPCC v5.0 is using about 1000 gauges more than version 4.0 until 2000. The CPC product is based on about 1000 gauges over Europe and 500 gauges over the whole of Africa, while more than 14 000 gauges are used to generate the gridded precipitation observations over North America between 1991 and 2003.

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    Long-term mean annual precipitation between 1989 and 2006 (mm day−1). The three observation datasets (a) GPCC, (b) CRU, and (c) CPC are in good agreement over most of the regions, even if CPC assumes less rainfall over central Africa. The precipitation estimates from the three reanalyses (d) Interim, (e) MERRA, and (f) CFSR show similar large-scale patterns, while significant differences exist in the spatial distribution and the amount of rainfall on smaller scales.

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    Absolute differences of the mean annual precipitation (mm day−1) from 1989 to 2006 between GPCC and (a) CRU, (b) CPC, (c) Interim, (d) MERRA, and (e) CFSR. CRU shows a good agreement with GPCC. CPC is drier over the Congo basin, the Himalayas, and the northern part of the Andes. The largest differences between GPCC and the three reanalyses can be observed over the tropics and the mountain ranges. CFSR also has a wet bias over mid- to high northern latitudes, while MERRA shows a dry pattern that extends over large parts of South America.

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    (a),(c) Variability of rainfall P (mm day−1) and (b),(d) range of temperature T2 (°C) of (a),(b) the ensemble of gridded observations and (c),(d) the ensemble of reanalyses. The ensemble of rainfall observations is generated from GPCC, GPCP, DEL, CRU, and CPC, while the temperature range is based on DEL and CRU. The reanalysis ensemble consists of Interim, MERRA, and CFSR for both precipitation and temperature. The reanalyses generally produce a larger variability especially over the tropics and the whole of South America. Over the Congo basin, however, the precipitation variability of the observation ensemble reaches values of up to 3 mm day−1. The temperature range from the three reanalyses shows the largest values over South America, the Congo basin, the Sahara, and Greenland, where differences of more than 5°C can be observed.

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    (a)–(j) Area-averaged spatial correlations in mean annual precipitation of GPCP, CRU, CPC, Interim, MERRA, and CFSR in relation to GPCC for the various regions. Values close to 1 indicate that the precipitation patterns from the respective dataset are in good agreement with the spatial distribution of rainfall from GPCC. In most of the regions, all datasets reproduce the spatial rainfall patterns from GPCC with a correlation coefficient >0.7 between 1989 and 2006. The largest deviations can be observed over South America, where especially MERRA shows correlation coefficients <0.6 (until 1998) and ~0.6 (from 1998). Compared to the reanalyses, the agreement between GPCC and the observation datasets is generally better. Over most of the regions, Interim shows the highest correlation coefficients in relation to GPCC.

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    Same as Fig. 8 but for area-averaged differences in the mean annual precipitation (mm day−1). On a global scale, MERRA agrees best with GPCC, but shows significant deviations especially over the Southern Hemisphere (likely due to the large differences over South America). Good agreement between GPCC and MERRA can also be observed over North America, while over Europe, Interim performs best. Over Australia, MERRA and CFSR are of comparable agreement with the observations, but the differences between GPCC and Interim increase toward the end of the time series. In general, the observations from CPC show large deviations from GPCC over South America and Africa due to CPC’s drier conditions in these regions. GPCP has a slight wet bias especially over the northern hemispheric regions (North America, Europe, and Asia), which might be due to corrections for the gauge undercatch error.

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    Same as Fig. 8 but for long-term (17 yr) averaged differences of monthly precipitation (mm day−1). Over most of the regions, the differences between CFSR and GPCC show an intra-annual cycle that is obvious in South America and to a lesser extent over North America, Europe, and Asia. Both Interim and MERRA show a good agreement with GPCC over North America, Europe, and Asia, while over South America, Interim and MERRA assume too-moist and too-dry conditions, respectively, during an intra-annual cycle. A significant dry bias between GPCC and Interim can be observed over Australia during the period from January to March, whereas the other datasets are in good agreement with GPCC during the same period.

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    Same as Fig. 8 but for area-averaged spatial correlations of the long-term (17 yr) mean monthly rainfall. Values close to 1 indicate that the respective dataset is in good agreement with the spatial distribution of rainfall from the GPCC product. Globally, the three reanalyses and observations reproduce the variations in the intra-annual rainfall patterns with a correlation coefficient >0.7 and >0.8, respectively. A significant intra-annual cycle can be observed over North America and Europe, which has its lowest values during the period from July to August (North America). Over South America, MERRA shows correlation coefficients <0.5 during September–February. A similar intra-annual cycle, but less pronounced, can be observed for Interim and CFSR with its minimum between October and November. Over Australia, a significant drop in the spatial correlations can be observed in April and the period from October to November. As this drop is evident in both the reanalyses and the observations, there might be some shortcomings in the GPCC precipitation patterns during these months.

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    Taylor plots of spatial statistics of the mean monthly precipitation in January and July for GPCP, CRU, CPC, Interim, MERRA, and CFSR with respect to GPCC; each data point in a plot displays the correlation as the angle between the x axis and the data point, the standard deviation (normalized) as the y coordinate, and the root-mean-square difference (normalized) as the radial distance of one month of a specific year with respect to GPCC.

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    Differences in the annual mean temperatures (°C) at 2 m between (a) Interim, (b) MERRA, and (c) CFSR and CRU. The largest differences between MERRA and CRU can be observed over South America, where MERRA shows a warm bias >4°C. The deviation pattern agrees well with the differences in the long-term mean precipitation estimates, where MERRA revealed a dry bias in these regions. This is also true for Interim, which assumes too-cold and too-wet conditions over the Congo basin. All three reanalyses show a warm bias over Siberia, while large parts of Greenland and the mountain ranges are generally too cold.

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    Vertically integrated moisture fluxes and moisture flux convergences (mm day−1) from (a) Interim, (b) MERRA, and (c) CFSR. Positive values depict areas with a surplus of precipitation (i.e., P > E), while evaporation and evapotranspiration, respectively, are larger than precipitation over regions with negative values. In general, negative PE values over the continents should only be expected in regions containing large lakes or inland seas. The direction and the amount of moisture transported are represented by the vector field. Large differences of the reanalyses can be observed along the ITCZ over the oceans, where CFSR shows larger moisture flux convergences than Interim and MERRA. There is also a positive pattern east of Brazil, which is absent in the other reanalyses. This results in a generally increased depletion of water in the CFSR over the oceans.

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    (a) Global, (b) continental, and (c) oceanic annual water balance (1015 kg yr−1). Here PE budgets are plotted as black lines, while the atmospheric budgets are represented by the dotted gray lines. On annual time scales, the difference between PE and the moisture flux divergences is an estimate of the atmospheric water forcing increment in the reanalysis models. The closure of the combined atmospheric–terrestrial water budget would require both PE and − · Q to be equal. MERRA and CFSR show an unrealistic increase of oceanic PE from 1998, which is likely due to changes in the assimilated observations. Over the continents, the PE budgets from Interim and MERRA are in better agreement with the moisture fluxes, leading to a nearly closed continental atmospheric–terrestrial water budget. CFSR overestimates continental PE as well, which causes an imbalanced residual of about 30 × 1015 kg yr−1.

  • View in gallery

    (a) Global, (b) continental, and (c) oceanic intra-annual water balance (1014 kg month−1). Here PE budgets are plotted as black lines, while the atmospheric budgets are represented by the dotted gray lines. For the monthly budgets, changes in the atmospheric water vapor content dW/dt were considered as well. Interim and MERRA show a good closure of the global atmospheric–terrestrial intra-annual budgets. Over the continents, there is a clear cycle with its minimum (maximum) in June (January) in both PE and the atmospheric moisture budgets, which might be explained by the decrease (increase) of evapotranspiration (precipitation) during the boreal winter (summer) over the large continental areas of Northern Hemisphere. The CFSR PE estimates show a bias both over the oceans and the continents, causing a significant imbalance of the global intra-annual atmospheric–terrestrial moisture budget.

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    (a) Global, (b) continental, and (c) oceanic precipitable water estimates (mm) from the three reanalyses. Globally, Interim shows higher values until 1995. Between 1992 and early 1998, the three reanalyses are in very good agreement, which is likely due to the assimilation of similar observations during that period. After 1998, the MERRA and CFSR estimates are higher when compared to Interim. This also holds for the time evolution of the atmospheric water vapor over the oceans. Again, it is presumed that the increase in 1998 is due to changes in the assimilated observations in both MERRA and CFSR but not in Interim. When compared to other components of the large-scale water cycle, the water vapor estimates are in much better agreement, which is likely due to the forcing of the estimates toward observations in all three reanalyses.

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    Precipitable water (mm) from the reanalyses and the HOAPS dataset over the ice-free ocean. Between 1992 and 1998, the three reanalyses are in good agreement with the HOAPS observations. It is obvious that the increase in 1998 of both MERRA and CFSR causes an overestimation of precipitable water when compared to HOAPS. Interim shows an overestimation before 1992, but reveals a good agreement with HOAPS for the rest of the time period.

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The Hydrological Cycle in Three State-of-the-Art Reanalyses: Intercomparison and Performance Analysis

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  • 1 Karlsruhe Institute of Technology, Institute of Meteorology and Climate Research, Department of Atmospheric Environmental Research (IMK-IFU), Garmisch-Partenkirchen, Germany
  • 2 Karlsruhe Institute of Technology, Institute of Meteorology and Climate Research, Department of Atmospheric Environmental Research (IMK-IFU), Garmisch-Partenkirchen, and Institute of Geography, Regional Climate and Hydrology, University of Augsburg, Germany
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Abstract

The three state-of-the-art global atmospheric reanalysis models—namely, ECMWF Interim Re-Analysis (ERA-Interim), Modern-Era Retrospective Analysis for Research and Applications (MERRA; NASA), and Climate Forecast System Reanalysis (CFSR; NCEP)—are analyzed and compared with independent observations in the period between 1989 and 2006. Comparison of precipitation and temperature estimates from the three models with gridded observations reveals large differences between the reanalyses and also of the observation datasets. A major source of uncertainty in the observations is the spatial distribution and change of the number of gauges over time. In South America, active measuring stations were reduced from 4267 to 390. The quality of precipitation estimates from the reanalyses strongly depends on the geographic location, as there are significant differences especially in tropical regions. The closure of the water cycle in the three reanalyses is analyzed by estimating long-term mean values for precipitation, evapotranspiration, surface runoff, and moisture flux divergence. Major shortcomings in the moisture budgets of the datasets are mainly due to inconsistencies of the net precipitation minus evaporation and evapotranspiration, respectively, (PE) estimates over the oceans and landmasses. This imbalance largely originates from the assimilation of radiance sounding data from the NOAA-15 satellite, which results in an unrealistic increase of oceanic PE in the MERRA and CFSR budgets. Overall, ERA-Interim shows both a comparatively reasonable closure of the terrestrial and atmospheric water balance and a reasonable agreement with the observation datasets. The limited performance of the three state-of-the-art reanalyses in reproducing the hydrological cycle, however, puts the use of these models for climate trend analyses and long-term water budget studies into question.

Corresponding author address: Christof Lorenz, Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Kreuzeckbahnstraße 19, 82467 Garmisch-Partenkirchen, Germany. E-mail: christof.lorenz@kit.edu

Abstract

The three state-of-the-art global atmospheric reanalysis models—namely, ECMWF Interim Re-Analysis (ERA-Interim), Modern-Era Retrospective Analysis for Research and Applications (MERRA; NASA), and Climate Forecast System Reanalysis (CFSR; NCEP)—are analyzed and compared with independent observations in the period between 1989 and 2006. Comparison of precipitation and temperature estimates from the three models with gridded observations reveals large differences between the reanalyses and also of the observation datasets. A major source of uncertainty in the observations is the spatial distribution and change of the number of gauges over time. In South America, active measuring stations were reduced from 4267 to 390. The quality of precipitation estimates from the reanalyses strongly depends on the geographic location, as there are significant differences especially in tropical regions. The closure of the water cycle in the three reanalyses is analyzed by estimating long-term mean values for precipitation, evapotranspiration, surface runoff, and moisture flux divergence. Major shortcomings in the moisture budgets of the datasets are mainly due to inconsistencies of the net precipitation minus evaporation and evapotranspiration, respectively, (PE) estimates over the oceans and landmasses. This imbalance largely originates from the assimilation of radiance sounding data from the NOAA-15 satellite, which results in an unrealistic increase of oceanic PE in the MERRA and CFSR budgets. Overall, ERA-Interim shows both a comparatively reasonable closure of the terrestrial and atmospheric water balance and a reasonable agreement with the observation datasets. The limited performance of the three state-of-the-art reanalyses in reproducing the hydrological cycle, however, puts the use of these models for climate trend analyses and long-term water budget studies into question.

Corresponding author address: Christof Lorenz, Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Kreuzeckbahnstraße 19, 82467 Garmisch-Partenkirchen, Germany. E-mail: christof.lorenz@kit.edu

1. Introduction

Global and regional atmospheric retrospective analysis models (reanalyses) play a crucial role in today’s hydrological and hydrometeorological research. These global atmospheric reanalyses aim at assimilating a large amount of historical observation data to provide a physically consistent basis for the most important hydrological, hydrometeorological, and atmospheric quantities. To bring these various observations into a consistent scheme, computation of the reanalysis models is performed via state-of-the-art data assimilation methods like three- or four-dimensional variational data assimilation (3DVAR or 4DVAR) that constrain the observations with physically reasonable time evolution and budget equations. These reanalyses can be used to analyze the global climate system, atmosphere, and land surface processes on large to continental scales and to understand exchange processes between these different regimes. Global atmospheric reanalyses also are often used as forcing data for regional hydrological or hydrometeorological simulations, such as numerical weather predictions and regional climate simulations. Three of the most widely used reanalyses are the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim), the Modern-Era Retrospective Analysis for Research and Applications (MERRA) from the National Aeronautics and Space Administration (NASA), and the Climate Forecast System Reanalysis (CFSR) from the National Centers for Environmental Prediction (NCEP).

Reanalyses represent an approximation of the real world. Because of the changing amount of assimilated observational data, different data assimilation methods, and different model equations and assumptions, results of reanalysis models deviate significantly, even if they should be similar in principle. Therefore, it is necessary to validate these global atmospheric models with observational datasets.

Such comparisons were made by, for example, Janowiak et al. (1997), Poccard et al. (2000), or Higgins et al. (2010), with rainfall estimates from the CFSR and its predecessor, the NCEP– National Center for Atmospheric Research (NCAR) reanalysis, being validated against precipitation observations. Bosilovich et al. (2008) compared precipitation from the 40-yr ECMWF Re-Analysis (ERA-40), the two older NCEP reanalyses (which are often referred to as NR1 and NR2), and the Japanese 25-yr Reanalysis (JRA-25) with data from the Global Precipitation Climatology Project (GPCP) and the widely used Climate Prediction Center Merged Analysis of Precipitation (CMAP) on both the continents and the oceans. In Hagemann et al. (2005), different quantities contributing to the global hydrological cycle of ERA-Interim’s predecessor ERA-40 were analyzed in detail, while Chido and Haimberger (2009) or Mueller et al. (2010) investigated the closure of water and energy budgets in the ERA-Interim reanalysis. A more detailed comparison is given in, for example, Trenberth et al. (2007), where estimates of the most important quantities of the global water cycle are presented. On regional scales, Yeh and Famiglietti (2008) concentrated on the estimation of evapotranspiration. Considerations relating to the hydrological cycle over the United States were presented by Roads et al. (1994). Seneviratne et al. (2004) analyzed the water budget closure over the Mississippi basin and presented estimates of monthly water storage variations based on water vapor flux convergence, atmospheric water vapor content, and river runoff. Similar work was performed by Betts et al. (1999, 2003, 2005, 2009), who analyzed energy and mass budgets of ERA-40 and ERA-Interim over several river basins (especially in North America). An assessment of the applicability of the ERA-40 model for the detection of climate trends was made by Bengtsson et al. (2004).

In this study, the three state-of-the-art reanalyses ERA-Interim, MERRA, and CFSR are compared. The reanalyses are evaluated by comparing quantities—such as precipitation, temperature, and atmospheric water vapor—with observational datasets from the Global Precipitation Climatology Centre (GPCC), the GPCP, the Climate Prediction Center (CPC), the Climate Research Unit (CRU), the University of Delaware (DEL), and the Hamburg Ocean Atmosphere Parameters and Fluxes from Satellite Data (HOAPS). Differences in the total amount, spatial variability, and distribution of gauges of the gridded rainfall observations are analyzed in order to estimate the uncertainties incorporated in these datasets. Special emphasis is devoted to the comparison of precipitation estimates from the reanalyses because of their importance in the hydrological cycle.

In addition, the closure of the water budgets in the three reanalyses are analyzed and it will be estimated how well the transport processes between the oceans and the continents as well as moisture exchange between the land surface and the atmosphere are balanced. For this purpose, long-term mean values of precipitation, evapotranspiration, surface runoff, and atmospheric moisture flux divergences are computed. As evapotranspiration and surface runoff are the dominating quantities of moisture transport from the surface back into the atmosphere and oceans, respectively, the estimates from the reanalyses are used to investigate how well the water budgets in the models are closed.

2. Data and methods

a. Reanalysis data

For comparison, three different global atmospheric retrospective analyses are used—namely, ERA-Interim from ECMWF (Simmons et al. 2006; Berrisford et al. 2009), MERRA from the NASA Goddard Space Flight Center (GSFC) [National Oceanic and Atmospheric Administration (NOAA)] (Rienecker et al. 2011), and CFSR (Saha et al. 2010) from NOAA/NCEP. The two latter reanalyses cover the satellite period from 1979 to the present, while ERA-Interim was intended to cover the period from 1989 to the present to provide a bridge between ECMWF’s previous reanalysis ERA-40 (Uppala et al. 2005) and a forthcoming next-generation reanalysis. Recently, the ERA-Interim archive was extended to cover the years between 1979 and 1989 as well. The CFSR dataset succeeds the widely used NCEP–NCAR reanalysis (Kalnay et al. 1996). The novelties of this reanalysis are the coupling to the ocean during the generation of the 6-h guess field, an interactive sea ice model, and the assimilation of satellite radiances for the entire period (Saha et al. 2010). Furthermore, the analysis system used in CFSR for the atmosphere, the Gridpoint Statistical Interpolation (GSI) scheme, is nearly the same as the one used by MERRA at NASA GSFC. The MERRA atmosphere-only reanalysis is being conducted over the same years with nearly the same input data (Saha et al. 2010). However, observation processing, model equations, and the main scope of the reanalyses differ significantly. The resulting differences in modeled variables thus reveal uncertainty ranges of present-day reanalysis models (see Table 1 for further details of these datasets).

Table 1.

Summary of the three reanalyses.

Table 1.

According to Kalnay et al. (1996) or Kistler et al. (2001), gridded variables from reanalyses can be separated into three classes, which vary by the influence of assimilated observations on the variable. The type A variables (e.g., upper-air temperatures or horizontal winds) are strongly influenced by the observations, and are thus assumed to be the most reliable variables. Type B variables (e.g., surface and 2-m temperatures) are influenced by both the observations and the model while type C variables (e.g., precipitation or surface runoff) are derived solely from the model.

b. Gridded observation data

To validate the three different reanalyses, we compare precipitation and temperature estimates from the reanalyses with gridded observations from GPCC (Rudolf and Schneider 2005), GPCP (Adler et al. 2003), CRU (Mitchell and Jones 2005), the Unified Gauge-based Analysis of Global Daily Precipitation from the CPC (Chen et al. 2008), and DEL (Matsuura and Willmott 2009). For validation of the atmospheric water vapor over the oceans, data from the HOAPS product (Andersson et al. 2010) are used, which is based on satellite observations from the Special Sensor Microwave Imager (SSM/I) on satellites of the Defense Meteorological Satellites Program and provides reliable estimates of oceanic precipitation, evaporation, and other atmospheric variables.

The continental precipitation and temperature datasets contain at least daily (CPC) or monthly (GPCC, CRU, and DEL) means at a spatial resolution of 0.5° × 0.5° for the whole world (see Table 2 for further details of the gridded observation products).

Table 2.

Summary of the observation datasets containing precipitation P, near-surface temperature T2, and the atmospheric water vapor content W.

Table 2.

In principle, the different datasets should provide similar precipitation and temperature values. Differences of global fields must be considered as uncertainty ranges, which can be expected when using such datasets for validation purposes. To generate gridded observations from in situ measurements, the different data centers apply similar interpolation algorithms and may therefore exhibit similar biases (particularly in areas with complex terrain).

Two main error sources lead to uncertainties in precipitation observations. The sampling error, which is due to the irregular distribution of gauges, has a magnitude of about ±7%–40% of the true area-mean precipitation (Schneider et al. 2008). Rudolf and Rubel (2005) report that sampling errors between 15% and 100% can be expected for sparsely gauged regions (less than 3 gauges per 2.5° × 2.5° grid cell). The second error is due to the undercatch of precipitation gauges, which results from wind-field deformation above the gauge orifice, losses from wetting on internal walls of the collector and in the container, and losses due to evaporation from the container (Rudolf and Rubel 2005). The gauge undercatch error might be large especially during winter in the high-latitude regions or over mountain ranges, as there will be a high amount of solid precipitation. This leads to an underestimation of the true precipitation of up to 50%. Since 2007, GPCC has been providing event-based correction factors (Fuchs et al. 2001; Schneider et al. 2008) to account for the systematic gauge undercatch error. Before 2007, the corrections consisted of monthly climatologies as proposed in Legates and Willmott (1990), which are still applied to the GPCP precipitation product. The original GPCC full data product used for this study does not include such corrections (A. Becker 2011, personal communication).

In the course of this study, the GPCC precipitation product was updated from version 4.0 to 5.0. Even though the new dataset is based on a denser station network, the differences of area-averaged values or long-term mean fields are not significant (not shown here). Therefore, the GPCC v4.0 product was used for reference observations in this study, but the differences in the distribution and total number of gauges between version 4.0 and 5.0 are discussed briefly (see section 3a).

c. Area averaging of gridded data

For the validation of the reanalyses’ rainfall estimates with the observation datasets, all fields were remapped to the resolution of the GPCC dataset (i.e., 0.5° × 0.5°) using a first-order conservative interpolation (Jones 1999). From these fields, area-weighted averages were computed over different regions using the continental mask shown in Fig. 1. As GPCC only contains gauge-based observations, the oceans or the poles were not considered for comparison of the precipitation fields. Consequently, the global and hemispheric averages do only represent the rainfall over land. For investigating the water budget closure, a correct differentiation between the processes over land and the oceans is crucial. We did not perform any additional interpolation for this analysis, but used the fields in the models’ native resolutions. The area-averaged values over the continents and oceans were calculated using the land–sea masks from the three reanalyses. For the evaluation of the oceanic water cycle components, we used a dynamic land–sea mask, as the satellite observations from HOAPS are available over ice-free ocean only.

Fig. 1.
Fig. 1.

Land–sea mask used for computing the spatial averages over North America, South America, Europe, Africa, Asia, and Australia. The table shows the areas of the regions considered within each continent.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

d. The global water balance

The terrestrial large-scale water balance (mm month−1) can be written as
e1
where dS/dt is the change in the terrestrial water storage, P is precipitation, E is evapotranspiration, and R is total runoff—that is, the sum of surface runoff and subsurface runoff (Willmott et al. 1985; Peixoto and Oort 1992). According to Yeh and Famiglietti (2008), the change in the total terrestrial water storage depends on its surface component, the soil moisture, and the groundwater components. The total soil water depends largely on the characteristics of the land surface model in the reanalyses. Interim and CFSR provide soil moisture values divided into multiple levels. MERRA does not consider a multilevel soil model for computing the interaction between the land surface and the atmosphere. The water storage term dS/dt can thus be computed as a residual term like in, for example, Roads et al. (1994). When analyzing water budgets in atmospheric reanalysis models, it is convenient to further consider a term for the analysis increment—that is, the increment that is due to the forcing of the models toward the observations. The terrestrial water balance equation is then modified to
e2
where is accounting for surface residual water forcing. As further proposed in Roads et al. (2002) and Szeto et al. (2008), the water storage tendency term is combined with residual forcing—that is, . According to Kleidon and Schymanski (2008) or Seneviratne et al. (2004), it can be assumed that for climatic time scales the total soil water content remains constant and its tendency can be neglected. This assumption results in the simplified terrestrial water balance equation of
e3
where overbars indicate averaging over a climatic time scale. The imbalance of this equation provides information on the magnitude of the disturbances of the water budgets introduced by surface water forcing .
Apart from the continental water budget, exchange of water between the continents and oceans is balanced as well. Over multiyear averages, the global water budget should be closed—that is, the convergence (PE) of moisture over land should equal the divergence (EP) of moisture over the ocean (Hagemann et al. 2005); that is,
e4
In general, this value must be positive over the continents because of a surplus of precipitation, while there is more evaporation over the oceans.
These terrestrial budgets can be linked to the atmosphere by the atmospheric water balance equation
e5
where E and P are actual gridpoint evapotranspiration (or evaporation over the oceans) and precipitation at the surface (Roads et al. 1994). Here W denotes the total column water content in the atmosphere and · Q is the net balance of moisture flux (i.e., moisture flux divergence), which is defined as
e6
with air pressure p (Pa), the gravitational acceleration g (m s−2), the horizontal wind vector vh (m s−1), and the specific humidity q (kg kg−1). When computed from reanalyses, moisture flux divergences are based on type A and type B variables only, precipitation, evaporation, and evapotranspiration are type C variables. Again, it is convenient to add a term accounting for the analysis increment to the atmospheric water balance equation:
e7
The atmospheric tendency term dW/dt can be combined with the residual forcing; that is, (Roads et al. 2002; Szeto et al. 2008). On annual or longer time scales, the variations of the atmospheric water storage W are often assumed to be negligible (Peixoto and Oort 1992). For monthly time scales, this assumption does not hold, however. The vertically integrated moisture flux divergences are directly linked to the vertical exchange terms of the terrestrial water balance:
e8
As in case of the surface water balance, misclosure of the equation when using long-term averages is an estimate of the magnitude of the analysis increment of the atmospheric water forcing . Equation (1) can be combined with Eq. (5) to obtain another linked balance equation:
e9
As the atmospheric and terrestrial tendency terms can be assumed to be negligible over longer time scales, the atmospheric net input of moisture in a certain area must be balanced by a terrestrial net outflow at the surface; that is, (Roads et al. 1994). The imbalance of this equation is a rough estimate of the total atmospheric and surface water analysis increments.

e. Computation of spatial correlations

To analyze the agreement of spatial patterns between two datasets, spatial correlations are computed for further analysis. This yields information about the extent to which certain events (e.g., large-scale rainfall) agree in terms of location, dimension, and magnitude when using various datasets. We compute the spatial correlations between two datasets x and y according to
e10
where n is the number of grid points of a given area χ, xi,t and yi,t are the actual gridpoint values at the time t, the overbar denotes the spatial mean value of the area, and σx,t and σy,t are the standard deviations of the two datasets x and y of the area χ at the time t. Here T is the number of time steps contributing to a temporal subset like, for example, all Januaries of the considered time series or all months of a specific year.

Apart from time series of spatial correlations, we use the Taylor diagrams (Taylor 2001) to analyze the level of agreement of rainfall patterns from different data sources. In this case, the standard deviation (the radial distance of a data point from the origin) is a measure of the intensity and variability of the patterns, while the correlations (the angle between the x axis and a data point) reflect how well the analyzed datasets reproduce the rainfall patterns from a reference dataset. The root-mean-square difference (radial distance between the reference data point and another data point) is a measure of the average pixelwise differences between two datasets and computed from the standard deviations and the correlations.

f. Computation of CFSR evapotranspiration

In contrast to Interim and MERRA, CFSR does not provide fields of total evapotranspiration. Therefore, these fields are computed from latent heat flux, which is given in energy flux form (i.e., in units of W m−2). The transformation into units of mm (i.e., mass flux form) was performed via
e11
where E is evapotranspiration (mm), λE is the latent heat flux (W m−2), and Le is the latent heat of evaporation (J kg−1), which can be approximated through
e12
with Tc being the near-surface temperature in degrees Celsius (e.g., Jacobson 2007). The latent heat flux fields from CFSR include both evaporative flux from liquid and snow sublimation from snow surface. Equation (11) must consequently be corrected for sublimation:
e13
where λS is sublimation and Ls is the latent heat of sublimation, which is the sum of the latent heats of evaporation and melting (e.g., Jacobson 2007):
e14
According to CFSR, the influence of the temperature can be neglected (R. Yang 2011, personal communication). Our computations support this assumption. On monthly time scales, the temperature causes an increase of the continental evapotranspiration of about 2.1% with a maximum during the summer months (Fig. 2). Over the oceans, the impact is smaller (about 1.7%), but has a strong semiannual signal with its maxima in the summer and winter months. By considering the magnitudes of other major water cycle components, the functional dependencies of Le and Lc on temperatures are found to exert little impact on the calculations of evaporation and evapotranspiration, respectively, from latent heat flux. Thus, the corrections for temperature can be neglected on these spatial and temporal scales. For small-scale studies and especially during summer months, however, the influence might be significant and should be taken into account.
Fig. 2.
Fig. 2.

Relative difference between CFSR evaporation (over the oceans) and evapotranspiration (over the continents), with and without considering changes in the near-surface temperature. The impact is generally higher over the continents, while over the oceans, the amplitude of the intra-annual variations is larger.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

3. Results

a. Distribution of gauges in the observation datasets

To validate the global atmospheric reanalyses, rainfall observations, interpolated to a regular grid as described in, for example, Chen et al. (2008) and Rudolf and Schneider (2005), are used. As a matter of fact, the quality of these gridded precipitation fields depends primarily on the number of active gauges and their spatial distribution. The interpretation of interpolated gridded observations in regions with a few gauges only or a disadvantageous spatial distribution of such observation stations remains open.

Figure 3 shows the number of gauges per grid cell at the beginning and the end of the considered time series for GPCC v4.0, GPCC v5.0, and CPC. In 1989 (Figs. 3a,c,e), a dense network of observation stations existed over North America, central Europe, coastal regions of Australia, and the eastern part of Brazil. The GPCC products also exhibit a good spatial coverage of South Africa, while only few gauges are located in the rain-laden regions of tropical Africa, South America, and Southeast Asia and large parts of the subtropics, Eurasia, and high-latitude regions. Depending on the geographic location of these ungauged regions, an interpolation might introduce large uncertainties. This is particularly true if the complex cycle of tropical precipitation or the high spatial variability of rainfall over mountain ranges is considered. Figures 3b,d,f shows the amount of gauges per grid cell in December 2006. Spatial coverage with observation stations has changed drastically, especially for the GPCC v4.0 data in North America, South America, and Africa. Large parts of the tropics and deserts remain completely ungauged over hundreds of kilometers in both GPCC and CPC datasets. The update from version 4.0 to 5.0 of the GPCC product significantly improved spatial coverage of North America and Australia, while there is only little improvement over South America, central Africa, or large parts of Eurasia. As is obvious from Fig. 4, the number of gauges decreased significantly for all three observation datasets over most of the regions. At the end of the period studied, only 1314 (CPC), 390 (GPCC v4.0), and 555 (GPCC v5.0) gauges remain, which are used to compute the precipitation fields over South America. Although the decrease in active gauges is not that significant over the Asian continent, comparison of the numbers of gauges over Europe and Asia again illustrates the very sparse distribution of gauges in the latter regions. In contrast to this, the CPC dataset is based on about 10 000 gauges over North America in the beginning and the end of the time period, while in between, the number of gauges increases up to ~17 000 in 2003. This shows that there are certain regions where the gridded GPCC and CPC products are based on a dense network of gauges and, hence, provide a scientifically sound basis to validate modeled precipitation fields. On the other hand, the reliability of the observation datasets remains questionable especially over the tropics, deserts, mountain ranges, and large parts of the Asian continent because of the decreasing number of active gauges and their sparse spatial distribution.

Fig. 3.
Fig. 3.

Number of monitoring stations per 0.5° × 0.5° grid cell in (a),(c),(e) January 1989 and (b),(d),(f) December 2006 for the (a),(b) GPCC v4.0; (c),(d) GPCC v5.0; and (e),(f) CPC datasets. A good spatial coverage with observation stations can be observed over North America (GPCC v5.0 and CPC) and Europe (GPCC v4.0 and v5.0), while the number of gauges over North America is significantly reduced in GPCC v4.0. Over most of the tropical regions like the Congo or Amazon basin, high-latitude regions, and large parts of Asia, the three datasets use a maximum of 1–2 gauges per grid cell, whereas some areas are completely ungauged.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Fig. 4.
Fig. 4.

(a)–(f) Mean annual number of gauges used in the precipitation observations from GPCC v4.0, GPCC v5.0, and CPC. Version 4.0 shows a significant drop in the number of gauges between 2000 and 2001 over North America and Australia, while version 5.0 of the GPCC product is based on a nearly constant number of observation stations during the complete time series. Over South America, Europe, and Africa, the update from v4.0 to v5.0 results in little improvement only, as both versions show a nearly constant decline over time. Over Asia, GPCC v5.0 is using about 1000 gauges more than version 4.0 until 2000. The CPC product is based on about 1000 gauges over Europe and 500 gauges over the whole of Africa, while more than 14 000 gauges are used to generate the gridded precipitation observations over North America between 1991 and 2003.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

b. Precipitation

1) Long-term mean annual precipitation

The long-term mean annual rainfalls (Fig. 5) obtained from the different reanalyses are in general agreement with the observational references when looking at the spatial precipitation patterns. The large-scale rain-laden regions of the tropics in South and Central America, central Africa, and Southeast Asia show precipitation rates of up to 11 mm day−1 in all products. These moist regions are clearly separated from the large subtropic desert regions with very limited precipitation. In addition, good agreement in the precipitation patterns can be found, for example, in Australia and over the moist regions in the southeastern part of North America and the drier Great Plains. Large mountain ranges, especially the Andes, the Alps, and the Himalayas, can be identified because of their wet conditions compared to the surrounding regions. Except for MERRA, all datasets show a maximum in annual precipitation at the headwaters of the Amazon River, which extends along the course of the river down to the Atlantic. In the MERRA dataset, this maximum is shifted eastward. In the regions between southern Brazil and the southern foothills of the Andes, GPCC, CRU, CPC, Interim, and CFSR show a mean precipitation rate of about 4–5 mm day−1, contrary to a distinguished dry region with less than 2 mm day−1 predicted by MERRA.

Fig. 5.
Fig. 5.

Long-term mean annual precipitation between 1989 and 2006 (mm day−1). The three observation datasets (a) GPCC, (b) CRU, and (c) CPC are in good agreement over most of the regions, even if CPC assumes less rainfall over central Africa. The precipitation estimates from the three reanalyses (d) Interim, (e) MERRA, and (f) CFSR show similar large-scale patterns, while significant differences exist in the spatial distribution and the amount of rainfall on smaller scales.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

In general, the highest differences in spatial variability and the amount of rainfall can be found over tropical South America, central Africa, Southeast Asia, and the large mountain ranges of the Andes and the Himalayas. These differences cause large-scale deviation patterns, which can reach magnitudes of up to ±4 mm day−1 (Fig. 6). Even when focusing on the ensemble of the observation datasets GPCC, GPCP, CRU, DEL, and CPC, differences of up to 3 mm day−1 result in central Africa (Fig. 7a), which are likely introduced by uncertainties in the observations due to the sparse distribution of gauges in these regions. In the three reanalyses, the differences in spatial variability and the amount of precipitation are even larger compared to the observations. The mid- to high-latitude rainfall estimates by CFSR appear to be significantly biased, as there are deviations of up to 2 mm day−1 (Fig. 6e). Higgins et al. (2010) investigated the reliability of CFSR precipitation over North America and concluded that parts of this bias can be explained by an overactive diurnal cycle in the atmospheric component of CFSR. The observation datasets are based on a dense network of gauges and show only small deviations in these regions. It can thus be assumed that there are some inaccuracies in the CFSR estimates.

Fig. 6.
Fig. 6.

Absolute differences of the mean annual precipitation (mm day−1) from 1989 to 2006 between GPCC and (a) CRU, (b) CPC, (c) Interim, (d) MERRA, and (e) CFSR. CRU shows a good agreement with GPCC. CPC is drier over the Congo basin, the Himalayas, and the northern part of the Andes. The largest differences between GPCC and the three reanalyses can be observed over the tropics and the mountain ranges. CFSR also has a wet bias over mid- to high northern latitudes, while MERRA shows a dry pattern that extends over large parts of South America.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Fig. 7.
Fig. 7.

(a),(c) Variability of rainfall P (mm day−1) and (b),(d) range of temperature T2 (°C) of (a),(b) the ensemble of gridded observations and (c),(d) the ensemble of reanalyses. The ensemble of rainfall observations is generated from GPCC, GPCP, DEL, CRU, and CPC, while the temperature range is based on DEL and CRU. The reanalysis ensemble consists of Interim, MERRA, and CFSR for both precipitation and temperature. The reanalyses generally produce a larger variability especially over the tropics and the whole of South America. Over the Congo basin, however, the precipitation variability of the observation ensemble reaches values of up to 3 mm day−1. The temperature range from the three reanalyses shows the largest values over South America, the Congo basin, the Sahara, and Greenland, where differences of more than 5°C can be observed.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

A significant discrepancy exists between the precipitation patterns from GPCC, Interim, and MERRA in South America and central Africa (Figs. 6c,d). These differences were also noted in Trenberth et al. (2011). Interim overestimates rainfall over the Andes and central Africa up to 2.5 mm day−1, while MERRA shows a large-scale underestimation in central South America and central Africa and an overestimation over coastal regions. It is well known that tropical precipitation in the MERRA reanalysis over South America has its shortcomings. Therefore, a corrected dataset for land hydrology will be released in the near future (Reichle et al. 2011). CFSR indicates conditions that are too moist in the center and underestimates rainfall east of the Congo basin along the course of the Nile (Fig. 6e). Poccard et al. (2000) and Sylla et al. (2010) discuss that rainfall simulations in these regions is a very complex task and might lead to large discrepancies. As the largest part of precipitable water in central Africa arises from evapotranspirating water in the tropical rain forests (Van der Ent et al. 2010), these deviations might be due to shortcomings in the models’ land–atmosphere interactions in this complex environment. On the other hand, the number of active gauges (Fig. 3d) shows that their spatial density decreased significantly during the period considered. This means that uncertainty is up to ±3 mm day−1 in these regions because of the variability of the ensemble of observations (Fig. 7a). Only the Interim precipitation exceeds the uncertainty given by the observations over a large area. The other two reanalyses are within the bounds given by the observations and are therefore assumed to be more realistic.

Precipitation over the Andes is generally overestimated in the reanalyses, while all datasets show less rainfall over the Himalayas than to GPCC. This might be due to the impact of orography on convective events caused by the differences in resolution and the description of the underlying terrain model. On the other hand, the high spatial variability of precipitation in mountain ranges aggravates reliable areawide observations. Because of the sparse distribution of gauges and the errors caused by the undercatch of solid precipitation, the quality of interpolated rainfall values from GPCC, CPC, and CRU remains questionable in these regions.

2) Time evolution of global, hemispheric, and tropic precipitation

The global and Northern Hemispheric correlations and differences (Figs. 8a,b and 9a,b) of the four observation datasets and the Interim and MERRA reanalyses are relatively constant over time. Although the number of gauges used for generating the observation datasets and the amount of observations assimilated in the reanalyses changed significantly between 1989 and 2006, there is only a minor impact on the agreement with GPCC on these scales. Over the Southern Hemisphere and the tropics, the spatial correlations (Figs. 8c,d) exhibit a wider range between the datasets. It is difficult to determine, however, whether this range is due to the reduction of gauges or changes in the assimilated observations.

Fig. 8.
Fig. 8.

(a)–(j) Area-averaged spatial correlations in mean annual precipitation of GPCP, CRU, CPC, Interim, MERRA, and CFSR in relation to GPCC for the various regions. Values close to 1 indicate that the precipitation patterns from the respective dataset are in good agreement with the spatial distribution of rainfall from GPCC. In most of the regions, all datasets reproduce the spatial rainfall patterns from GPCC with a correlation coefficient >0.7 between 1989 and 2006. The largest deviations can be observed over South America, where especially MERRA shows correlation coefficients <0.6 (until 1998) and ~0.6 (from 1998). Compared to the reanalyses, the agreement between GPCC and the observation datasets is generally better. Over most of the regions, Interim shows the highest correlation coefficients in relation to GPCC.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Fig. 9.
Fig. 9.

Same as Fig. 8 but for area-averaged differences in the mean annual precipitation (mm day−1). On a global scale, MERRA agrees best with GPCC, but shows significant deviations especially over the Southern Hemisphere (likely due to the large differences over South America). Good agreement between GPCC and MERRA can also be observed over North America, while over Europe, Interim performs best. Over Australia, MERRA and CFSR are of comparable agreement with the observations, but the differences between GPCC and Interim increase toward the end of the time series. In general, the observations from CPC show large deviations from GPCC over South America and Africa due to CPC’s drier conditions in these regions. GPCP has a slight wet bias especially over the northern hemispheric regions (North America, Europe, and Asia), which might be due to corrections for the gauge undercatch error.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

The CFSR series show a general wet bias over the Northern Hemisphere and a drop in the global continental rainfall toward GPCC from 1998 (Figs. 9a,b). Interestingly, the differences between CFSR and GPCC increase again after 2000 over both the tropical regions between 15°N and 15°S and the Southern Hemisphere (Figs. 9c,d), while the bias over the Northern Hemisphere is slightly reduced. The decline between 1998 and 2000 is also evident from the Interim rainfall over the tropics and the Southern Hemisphere but not in MERRA. During these years, all three reanalyses and the CRU observations show a sudden increase in the near-surface temperature (not shown), which might be related to the gaps in the precipitation estimates.

The CPC observations show a dry bias of about −0.3 mm day−1 over the Northern and −0.4 mm day−1 over the Southern Hemisphere in relation to GPCC (Figs. 9b,d). In general, precipitation over the Southern Hemisphere and the tropics has a higher variability in spatial correlations and deviations relating to GPCC. In contrast to the reanalyses, the observation datasets are in good agreement, even if the deviations from GPCC are larger because of the higher precipitation rates in these regions. Spatial variability of rainfall observations over the Southern Hemisphere correlates with a correlation coefficient of at least 0.8 and, hence, is a reliable basis for validating the reanalyses on large spatial scales. It can also be noticed that the reanalyses’ spatial correlations over the Southern Hemisphere are dominated by the variations between 15°N and 15°S. Especially after 1995, the MERRA dataset depicts a quasi-periodic signal in the spatial correlations over the Southern Hemisphere and the tropics (Figs. 8c,d).

The global intra-annual differences between the CFSR rainfall estimates and the GPCC observations have an annual cycle with maximal deviations in the period from March to June (Fig. 10a). Interim tends to slightly overestimate the GPCC rainfall over the Northern Hemisphere with largest deviations of about 0.3 mm day−1 occurring from March to May. The tropical and Southern Hemispheric Interim precipitation rates are higher throughout the year with a distinct peak during the period from September to December where deviations from GPCC of up to 0.75 mm day−1 can be observed. Thus, on the global scale, Interim assumes slightly higher precipitation rates than GPCC, with the largest differences occurring in the periods from March to May and from September to December—that is, in the Northern and Southern Hemispheric spring months (Figs. 10a–d). MERRA does not exhibit a clear annual cycle over the Northern or Southern Hemisphere; deviations in the tropics are maximal during the period from November to April. The intra-annual spatial correlations between MERRA and GPCC show a clear annual cycle especially over the Southern Hemisphere, which is mainly dominated by variations between 15°N and 15°S (Figs. 11c,d). CFSR and Interim show a similar annual cycle with a generally higher correlation except for the period from September to November over the Southern Hemisphere, where Interim agrees better with GPCC than CFSR. Over the Northern Hemisphere, the reanalyses are in good agreement with an average correlation coefficient of about 0.8 (Fig. 11b).

Fig. 10.
Fig. 10.

Same as Fig. 8 but for long-term (17 yr) averaged differences of monthly precipitation (mm day−1). Over most of the regions, the differences between CFSR and GPCC show an intra-annual cycle that is obvious in South America and to a lesser extent over North America, Europe, and Asia. Both Interim and MERRA show a good agreement with GPCC over North America, Europe, and Asia, while over South America, Interim and MERRA assume too-moist and too-dry conditions, respectively, during an intra-annual cycle. A significant dry bias between GPCC and Interim can be observed over Australia during the period from January to March, whereas the other datasets are in good agreement with GPCC during the same period.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Fig. 11.
Fig. 11.

Same as Fig. 8 but for area-averaged spatial correlations of the long-term (17 yr) mean monthly rainfall. Values close to 1 indicate that the respective dataset is in good agreement with the spatial distribution of rainfall from the GPCC product. Globally, the three reanalyses and observations reproduce the variations in the intra-annual rainfall patterns with a correlation coefficient >0.7 and >0.8, respectively. A significant intra-annual cycle can be observed over North America and Europe, which has its lowest values during the period from July to August (North America). Over South America, MERRA shows correlation coefficients <0.5 during September–February. A similar intra-annual cycle, but less pronounced, can be observed for Interim and CFSR with its minimum between October and November. Over Australia, a significant drop in the spatial correlations can be observed in April and the period from October to November. As this drop is evident in both the reanalyses and the observations, there might be some shortcomings in the GPCC precipitation patterns during these months.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

The Taylor diagrams in Fig. 12 show that on a global scale, all three reanalyses and the observations reproduce the spatial rainfall patterns from GPCC with a correlation coefficient of >0.7. The statistics over the Northern or Southern Hemisphere and the tropics indicate that the level of agreement between GPCC and the other datasets decreases when the area of interest is reduced. It is also evident that CFSR predicts a too-high spatial variability compared to GPCC during the summer months of the Northern and Southern Hemisphere, which is indicated by higher RMSD values. MERRA agrees best with GPCC during the boreal summer. Over the Southern Hemisphere and the tropics, MERRA shows the lowest correlation coefficients (<0.6 for some years) of the three reanalyses. The performance of the models in reproducing the GPCC rainfall patterns changes significantly depending on the region and time (month) but even from year to year. This is also true for the observation datasets although the other gridded rainfall observations on these scales agree better with GPCC than the reanalyses.

Fig. 12.
Fig. 12.

Taylor plots of spatial statistics of the mean monthly precipitation in January and July for GPCP, CRU, CPC, Interim, MERRA, and CFSR with respect to GPCC; each data point in a plot displays the correlation as the angle between the x axis and the data point, the standard deviation (normalized) as the y coordinate, and the root-mean-square difference (normalized) as the radial distance of one month of a specific year with respect to GPCC.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

3) Time evolution of continental-scale precipitation

Over South America, the correlations of Interim and CFSR are in good agreement with an average correlation coefficient of about 0.7, while MERRA predicts completely different rainfall patterns, resulting in a low spatial correlation coefficient of ~0.5 (Fig. 8h). As regards the intra-annual spatial variability (Fig. 11h), the lowest correlations of MERRA are found between October and January. On the other hand, the differences in total precipitation between MERRA and GPCC (Fig. 10h) show a reduced annual cycle compared to the correlations. This indicates that intra-annual variations in the amount of precipitation are in good agreement with the observations, while there are major differences in spatial variability. The Taylor diagrams (Fig. 12) confirm the problems of the MERRA dataset in this respect, which cannot be explained by outliers exclusively. MERRA’s annual mean correlations and deviations (Figs. 8h and 9h) converge toward GPCC and the other datasets over South America, leading to better precipitation estimates at the end of the time series. The time when the MERRA precipitation estimates improve coincides with the assimilation of observations from the Advanced Microwave Sounding Unit (AMSU) on the NOAA-15 satellite. This assimilation is performed only over the oceans, but Bosilovich et al. (2011) note that such satellite epoch changes might indirectly affect the MERRA water balances over land through altered moisture.

Over North America, Europe, and Asia, significant wet biases in the mean annual and intra-annual CFSR precipitation are found (Figs. 9e,f,g and 10e,f,g). While spatial correlations decrease during the period from May to August over North America, they are in good agreement with the other reanalyses (Figs. 8e,f,g and 11e,f,g). Over Europe, the Interim reanalysis matches well with the GPCC observations with an average spatial correlation coefficient >0.8 and a deviation of less than 0.1 mm day−1 on interannual and intra-annual time scales. The Taylor diagrams representing July over North America and Europe reveal that some data points predict a correlation coefficient <0.7, which is likely due to an increase of convective precipitation. This is confirmed by the reanalyses’ intra-annual spatial correlations, with the lowest correlation coefficients occurring in May (Europe; Fig. 11f) and from July to August (North America; Fig. 11e).

Over Asia, South America, and Africa, the differences between CFSR and GPCC decrease significantly, which might be explained by the assimilation of AMSU data (Figs. 9g,h,i). After 1998, the wet bias of CFSR over Asia is constantly reduced to 0.6 mm day−1 while bias reduction over the other continents is only temporary, as the differences between CFSR and GPCC increase toward the end of the time period.

Over North America, the MERRA precipitation estimates show the smallest deviations from the GPCC observations on both interannual and intra-annual time scales even though the slightly biased Interim estimates tend to display higher spatial correlations (Figs. 8e and 11e). Over Europe, the precipitation estimates from Interim are superior to the other two reanalyses (Figs. 8f, 9f, 10f, and 11f), while Interim has a wet bias over Africa because of the overestimation of precipitation in the Congo basin (Fig. 6c). A general dry bias of the CPC observations can be noticed over all regions except for North America and Australia. It is mentioned in the dataset description that especially over large parts of Africa and South America the observations should be treated carefully, as there is a very sparse distribution of gauges, even if the spatial correlations are in good agreement with the other datasets.

Over Australia, it can be seen that the three reanalyses and the observations from CRU show similar spatial correlations, which differ from GPCC especially in April and November (Fig. 11j). These drops are also evident for GPCP and CPC, but to a smaller extent. As CRU and CPC are based solely on gauge observations, the Australian rainfall patterns from GPCC have to differ from the other datasets. However, this difference had not yet been detected.

c. 2-m temperature

The mean annual differences of the reference temperatures given by the CRU dataset and the three reanalyses are shown in Fig. 13. The patterns of larger temperature differences are closely related to the differences in the precipitation fields (Fig. 6). The MERRA temperature estimates (Fig. 13b) seem to have a warm bias especially in South America, where the difference between MERRA and CRU reaches values of up to 6°C. This warm bias may cause an increased saturation deficit of the air, which might explain the underestimation of South American precipitation in the MERRA dataset. A similar effect can be noticed over central Africa, where MERRA predicts too-warm conditions and too-little rainfall. The Interim field (Fig. 13a) shows a cold bias in central Africa and South America and, thus, a decreased saturation deficit, which results in larger rainfall compared to the other datasets. The relation between the temperature and precipitation biases might also be explained by the reduced clouds and precipitation in these regions, leading to excess solar radiation reaching the surface, which results in an increased temperature.

Fig. 13.
Fig. 13.

Differences in the annual mean temperatures (°C) at 2 m between (a) Interim, (b) MERRA, and (c) CFSR and CRU. The largest differences between MERRA and CRU can be observed over South America, where MERRA shows a warm bias >4°C. The deviation pattern agrees well with the differences in the long-term mean precipitation estimates, where MERRA revealed a dry bias in these regions. This is also true for Interim, which assumes too-cold and too-wet conditions over the Congo basin. All three reanalyses show a warm bias over Siberia, while large parts of Greenland and the mountain ranges are generally too cold.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

In general, it can be concluded that the temperature range (Fig. 7d) of the three reanalyses is similar to that of the precipitation fields (Fig. 7c). The widest range of temperature observations (Fig. 7b) can be detected over the large mountain ranges. This might be due to an elevation correction performed in the DEL dataset, but not in CRU. Over the largest parts of the continents, a general uncertainty of about 1°C can be expected. When considering this value as an uncertainty bound, the large-scale deviations of MERRA and Interim over South America or the Congo basin and the general cold bias in the CFSR dataset over the whole Sahara indicate significant inaccuracies in the reanalyses. On the other hand, only slight deviations are encountered over North America, Europe, and Australia. Overall, Interim shows the best agreement with CRU.

d. Closure of the water budgets

1) Surface water budget

Table 3 summarizes the computed long-term mean values of the different quantities contributing to the global and continental-scale water budgets. The estimates from Trenberth et al. (2007) and Oki and Shinjiro (2006) are presented here as well for reference. In the long-term mean, Interim and MERRA show a reasonable closure of the global surface water balance, as PE over land equals the divergence of moisture EP over the oceans. Interim generally predicts more oceanic precipitation and evaporation. Both datasets achieve a closure of the combined continental–oceanic water budget [Eq. (4)] with a remaining residual of about 1% (Interim) and 5% (MERRA) of the continental PE moisture budget. Similar values for Interim and MERRA were also reported by Trenberth et al. (2011). Jung et al. (2010) estimated a mean total land surface evapotranspiration of 65 ± 3 × 1015 kg yr−1 between 1982 and 2008, which agrees with the estimates from Oki and Shinjiro (2006). It should be noted that small deviations of the estimates may be due to differences in the used land–sea mask or, when compared to the estimates from, for example, Bosilovich et al. (2011), a different time period.

Table 3.

Mean global water cycle components over land and ocean between 1989 and 2006 (1015 kg yr−5); the values in the rightmost columns are the long-term estimates from Trenberth et al. (2007; TB) and Oki and Shinjiro (2006; OKI) and are printed here as a reference.

Table 3.

On the other hand, CFSR leaves an imbalance of about 80% of the continental surface water budget due to an overestimation and underestimation of continental and oceanic PE values, respectively. It can be assumed that the too-small oceanic PE value of CFSR mainly arises from an overestimation of rainfall, as both Interim and MERRA assume an evaporation surplus of about 8% with respect to the water that precipitates over the oceans, while CFSR predicts only 2%. This is confirmed by the evaluation with the HOAPS dataset (Table 4), as CFSR predicts significantly more rainfall than the other datasets. This might be due to the high moisture convergence in the oceanic domain of the intertropical convergence zone (ITCZ) (Fig. 14c). There are also patterns of large positive PE values south east and west of South America, which are absent in Interim and MERRA, assuming a significantly larger depletion of water over the oceans.

Table 4.

Mean oceanic precipitation, evaporation, and PE between 1989 and 2006 from Interim, MERRA, CFSR, and satellite observations from the HOAPS dataset (mm day−1). The numbers in the brackets denote the standard deviations.

Table 4.
Fig. 14.
Fig. 14.

Vertically integrated moisture fluxes and moisture flux convergences (mm day−1) from (a) Interim, (b) MERRA, and (c) CFSR. Positive values depict areas with a surplus of precipitation (i.e., P > E), while evaporation and evapotranspiration, respectively, are larger than precipitation over regions with negative values. In general, negative PE values over the continents should only be expected in regions containing large lakes or inland seas. The direction and the amount of moisture transported are represented by the vector field. Large differences of the reanalyses can be observed along the ITCZ over the oceans, where CFSR shows larger moisture flux convergences than Interim and MERRA. There is also a positive pattern east of Brazil, which is absent in the other reanalyses. This results in a generally increased depletion of water in the CFSR over the oceans.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

According to Fig. 15a, there is a shift in the global PE moisture budgets of CFSR and MERRA in 1998. Both depict a significant increase of oceanic PE (Fig. 15c), with CFSR reaching values of about 20 × 1015 kg yr−1 in 2001. In both cases, this is caused by an increase in oceanic rainfall, while Interim predicts a decrease (not shown). The increase in MERRA and CFSR is likely due to the assimilation of sounding radiances from AMSU-A on the NOAA-15 satellite from 1998 (Nicolas and Bromwich 2011; Bosilovich et al. 2011). Robertson et al. (2011) detected that the assimilation of AMSU-A data has a significant impact on the MERRA water vapor increments, leading to an increased amount of moisture in the model. This agrees with the time evolution of the total atmospheric water vapor content (Figs. 17a,c), which shows a sudden increase of both MERRA and CFSR in 1998. Robertson et al. (2011) further concluded that the additional moisture causes an increase of precipitation especially over the tropic oceans. If so, there should also be an increase in oceanic evaporation for compensating the shift in oceanic rainfall, which cannot be detected in MERRA and CFSR. The significant changes of many CFSR variables in 1998 are discussed by Wang et al. (2010) and Xue et al. (2010).

Fig. 15.
Fig. 15.

(a) Global, (b) continental, and (c) oceanic annual water balance (1015 kg yr−1). Here PE budgets are plotted as black lines, while the atmospheric budgets are represented by the dotted gray lines. On annual time scales, the difference between PE and the moisture flux divergences is an estimate of the atmospheric water forcing increment in the reanalysis models. The closure of the combined atmospheric–terrestrial water budget would require both PE and − · Q to be equal. MERRA and CFSR show an unrealistic increase of oceanic PE from 1998, which is likely due to changes in the assimilated observations. Over the continents, the PE budgets from Interim and MERRA are in better agreement with the moisture fluxes, leading to a nearly closed continental atmospheric–terrestrial water budget. CFSR overestimates continental PE as well, which causes an imbalanced residual of about 30 × 1015 kg yr−1.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

The continental PE estimates (Fig. 15b) are in much better agreement than the oceanic moisture budgets. In 1998, however, changes are significant, as MERRA predicts an increase of 6 × 1015 kg yr−1. The CFSR budgets decrease by about 12 × 1015 kg yr−1 between 1998 and 2000. The gap in the continental PE budgets is less distinct and becomes smaller toward the end of the time series. The differences and spatial correlations of precipitation estimates from MERRA and GPCC show a sudden change in 1998 over South America only (Figs. 8h, 9h). CFSR precipitation deviations from GPCC, however, exhibit significant gaps over Asia, South America, and Africa (Fig. 9g,h,i). The reason has not yet been revealed, but if the assimilation of AMSU data causes these changes in the precipitation estimates, the impact of assimilation would differ significantly for both MERRA and CFSR.

As a result of the oceanic PE increase, the annual budgets between the oceans and the continents are highly distorted in MERRA and CFSR. CFSR shows a positive oceanic PE average of 8.6 × 1015 kg yr−1 between 1999 and 2006, which obviously is not reasonable. The MERRA PE oceanic moisture budgets exhibit a change in sign after 2005. According to Rienecker et al. (2011), Interim does not use these observations and, thus, shows no shift in 1998. Interim’s oceanic PE moisture budgets reveal a permanent downward trend until 1998, after which the budgets fluctuate around −45 × 1015 kg yr−1, which agrees with the reference values in Table 3.

Another significant shift in both MERRA and CFSR is assumed to occur in 2001 when data from the NOAA-16 satellite are introduced. Indeed, there is a distinct increase in the oceanic PE estimates of MERRA between 2000 and 2001. In the CFSR dataset, there also is an upward shift of oceanic PE estimates between 1999 and 2001, but the effect seems to weaken at the end of the time series.

When analyzing the continental surface water balance [Eq. (3)], MERRA shows the best performance in closing the long-term water balance. The surplus of evaporation over the continents is balanced by reduced runoff compared to the other reanalyses and the reference estimates. This leads to a significantly smaller surface water forcing residual in the terrestrial water storage of 2.6 × 1015 kg yr−1. As the time evolution of both the annual PE moisture budgets and the total annual runoff (not shown) are not constant over time, however, RESs changes as well. For water budget studies on shorter time scales, this changing imbalance should not be neglected. As reported by Roads et al. (2002), the storage change dS/dt may be significant during shorter periods and, hence, a large part of RESs might be due to natural processes rather than artificial forcing increments. CFSR and Interim have larger residuals of 19.0 × 1015 kg yr−1 and 9 × 1015 kg yr−1, respectively, between runoff and continental PE even if the runoff estimates seem to be more realistic compared to MERRA.

The global intra-annual water budgets (Fig. 16a) show a clear annual cycle with the minimum PE in June due to the increased evaporation and reduced precipitation during the Northern Hemispheric summer months. Compared to the annual PE moisture budgets, the intra-annual variations of MERRA and Interim are in much better agreement. Even if CFSR reproduces a similar annual cycle, there is a significant deviation of about 30 × 1014 kg month−1 from the other reanalyses, which causes a remaining imbalance during an intra-annual cycle of the global PE moisture budgets.

Fig. 16.
Fig. 16.

(a) Global, (b) continental, and (c) oceanic intra-annual water balance (1014 kg month−1). Here PE budgets are plotted as black lines, while the atmospheric budgets are represented by the dotted gray lines. For the monthly budgets, changes in the atmospheric water vapor content dW/dt were considered as well. Interim and MERRA show a good closure of the global atmospheric–terrestrial intra-annual budgets. Over the continents, there is a clear cycle with its minimum (maximum) in June (January) in both PE and the atmospheric moisture budgets, which might be explained by the decrease (increase) of evapotranspiration (precipitation) during the boreal winter (summer) over the large continental areas of Northern Hemisphere. The CFSR PE estimates show a bias both over the oceans and the continents, causing a significant imbalance of the global intra-annual atmospheric–terrestrial moisture budget.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

2) Atmospheric and combined atmospheric–terrestrial water balance

The global atmospheric water budgets · Q (Fig. 15a) are nearly constant during the analyzed period. Consequently, the atmospheric moisture exchange between the oceans and the continents is a fully closed cycle in the three reanalyses. As the time series of moisture flux divergences obtained by the three reanalyses are in good agreement, it is concluded that using the atmospheric budgets for quantifying the exchange of moisture between the oceans and landmasses is more reliable than the modeled PE moisture budgets. The closure of the global combined atmospheric–terrestrial water balance [Eq. (8)] reveals some shortcomings: Interim predicts too-high (too low) PE estimates until 1996 (from 1996). CFSR has a significant moist bias (i.e., too-high global PE values) over the whole time series with a sudden increase likely due to the assimilation of AMSU data in 1998, while MERRA shows the same gap with too-dry (too wet) conditions until 1999 (from 1999). Over the continents (15b), both the atmospheric and terrestrial budgets are in good agreement, leading to the closure of the combined atmospheric–terrestrial water balance. Hence, the largest part of the global imbalance comes from the large gaps between the PE moisture budgets and the moisture flux divergences over the oceans (Fig. 15c). As the changes in the tendency terms of atmospheric and terrestrial water storage can be neglected on annual time scales, the differences between the moisture flux divergences and the PE budgets are an estimate of the atmospheric water forcing due to the assimilation of observations. Hence, the impact on MERRA and Interim is less pronounced over the continents than over the oceans.

As regards long-term monthly moisture budgets, the global, continental, and oceanic Interim and MERRA PE values and atmospheric moisture fluxes are in very good agreement (Fig. 16). We assume that even if the annual variations of the water cycle show significant shortcomings, the modeled processes are balanced well on a monthly time scale. The CFSR budgets show a significant overestimation of PE over both the continents and the oceans, resulting in a significant imbalance that has its maximum between September and October, where the global water budget leaves a monthly imbalance of up to 48 × 1014 kg month−1 (i.e., the intra-annual water cycle is not closed in CFSR). It should be noted, however, that CFSR does not provide fields of evapotranspiration. The imbalance might be affected largely by the approximation of E from fields of latent heat flux and sublimation [Eq. (13)]. As the long-term average of continental evapotranspiration agrees with the model estimates from Trenberth et al. (2007), however, it is likely that the too-high PE values arise from the CFSR precipitation.

3) Atmospheric water vapor

Figure 17 shows the monthly mean of total precipitable water over the complete time series. Globally, Interim predicts more atmospheric vapor before 1998 and less vapor after 1998 compared to MERRA and CFSR (Fig. 17a). The main differences between the datasets result from deviations over the oceans (Fig. 17c) that can be divided clearly into three periods. Before 1992, the Interim water vapor exceeds the estimates from CFSR and MERRA. Between 1992 and 1998, the three reanalyses are in good agreement, as the models use similar observational data in this period. After 1998, CFSR and MERRA show an increase of the precipitable water over the oceans, which has already been discussed in section 1. Compared to the differences in the reanalyses’ water budgets, the time series of precipitable water are in good agreement. This is emphasized by Fig. 18 where also satellite observations from the HOAPS dataset representing the total atmospheric water vapor over the ice-free ocean are shown. Especially during the period between 1992 and 1998, the reanalyses successfully reproduce the annual cycle of water vapor over the oceans. After 1998, MERRA and CFSR overestimate the amount of precipitable water, while Interim still shows a good agreement with HOAPS. On the other hand, Interim clearly overestimates atmospheric water vapor before 1992, while MERRA and CFSR agree well with HOAPS. This changing level of agreement is likely due to the assimilation of different data sources, as all three reanalyses use similar observations between 1992 and 1998 only.

Fig. 17.
Fig. 17.

(a) Global, (b) continental, and (c) oceanic precipitable water estimates (mm) from the three reanalyses. Globally, Interim shows higher values until 1995. Between 1992 and early 1998, the three reanalyses are in very good agreement, which is likely due to the assimilation of similar observations during that period. After 1998, the MERRA and CFSR estimates are higher when compared to Interim. This also holds for the time evolution of the atmospheric water vapor over the oceans. Again, it is presumed that the increase in 1998 is due to changes in the assimilated observations in both MERRA and CFSR but not in Interim. When compared to other components of the large-scale water cycle, the water vapor estimates are in much better agreement, which is likely due to the forcing of the estimates toward observations in all three reanalyses.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Fig. 18.
Fig. 18.

Precipitable water (mm) from the reanalyses and the HOAPS dataset over the ice-free ocean. Between 1992 and 1998, the three reanalyses are in good agreement with the HOAPS observations. It is obvious that the increase in 1998 of both MERRA and CFSR causes an overestimation of precipitable water when compared to HOAPS. Interim shows an overestimation before 1992, but reveals a good agreement with HOAPS for the rest of the time period.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-088.1

Changes in the atmospheric water vapor content dW/dt were considered when computing the monthly water budgets. There is a strong annual cycle especially over the continents, leading to maximal values of dW/dt in spring and autumn. This agrees with, for example, Rasmusson (1968) and is also considered in Seneviratne et al. (2004). However, changes in the vertically integrated water vapor usually are smaller by several orders of magnitude compared to other quantities of the hydrological cycle and do not vary on annual time scales, as the intra-annual cycle of dW/dt is closed with sufficient accuracy in all three reanalyses (not shown). It is therefore proposed to neglect dW/dt for large-scale and long-term water budget studies.

4) Evaluation of hydrological variables over the oceans

Mean estimates of modeled precipitation, evaporation, and PE over the ice-free oceans are presented and compared with satellite observations from HOAPS in Table 4. As another reference, the GPCP dataset predicts a mean precipitation rate of about 3.0 mm day−1. CFSR shows an overestimation of oceanic rainfall of 0.6 mm day−1. As evaporation from CFSR is only about 0.3 mm day−1 higher compared to HOAPS, the mean PE moisture budget is positive, showing an overestimation of 0.7 mm day−1. All three reanalyses overestimate the PE moisture budget, but in Interim, this is due to an overestimation of precipitation and evaporation, while MERRA underestimates evaporation. Hence, it is impossible to make a general statement about the origins of the too-large oceanic PE moisture budgets in the analyzed reanalyses.

4. Summary and conclusions

The present study demonstrated major differences of differences between the three reanalyses ERA-Interim from ECMWF, MERRA from NASA, and CFSR from NCEP. Precipitation is one of the most important quantities of the water cycle. Its estimates are highly uncertain in terms of spatial variability and total amount. The largest discrepancies occur in the summer months of the respective hemisphere, because convective effects still are a large source of uncertainty. However, a validation of, for example, tropical or mountainous rainfall also remains difficult because of the large differences of the observation datasets in these areas. This can be attributed to the irregular distribution of gauges especially in such complex and highly variable regions. Hence, there are large parts of South America and Africa that are completely ungauged. For regions with a dense network of gauges like North America, Australia, or Europe, it may be concluded that Interim still provides the most reliable rainfall estimates. The largest problem in these areas is the decrease of active gauges during the period considered. The quality of an interpolated product over a continuously changing network of observations remains questionable. On the other hand, validation of the coarsely resolved GPCC and reanalysis precipitation estimates with in situ rainfall observations is not yet meaningful because of the precipitation’s high spatial variability and dependence on surrounding terrain.

In data-sparse regions, the general tendency of the datasets considered can be regarded examined only. It may be concluded that major shortcomings exist in the spatial patterns of South American rainfall in MERRA and in the total amount of mid- to high-latitude precipitation in CFSR where a significant bias was detected. In the case of the MERRA reanalysis, these shortcomings are well known. Thus, NASA is currently performing a land-only rerun of the MERRA reanalysis in which observational data from GPCP and other independent global data products are used to correct and evaluate MERRA’s land surface hydrology (Rienecker et al. 2011). The corrected precipitation estimates are already available and will replace the original MERRA products in the near future (Reichle et al. 2011).

The differences in the amount and spatial patterns of continental rainfall between GPCC and the other datasets remain more or less constant during the whole period (except for South American precipitation in the MERRA dataset). This is important, as the assimilation of observations, which became available during the period considered, does not seem to significantly affect the precipitation estimates over the landmasses. The situation is clearly different for oceanic precipitation that exhibits a significant shift in late 1998 when sounding radiances from AMSU were assimilated into both MERRA and CFSR. Atmospheric reanalysis models are still sensitive to the introduction of observational data. Similar findings were also presented in Bengtsson et al. (2004) for the ERA-40 reanalysis.

The uncertainties in the precipitation estimates of the three reanalyses are highly correlated with the variability in the temperature fields. An obvious connection was found between the large-scale underestimation of South American precipitation from MERRA and a general warm bias in these regions. To make statements about the validity of an atmospheric reanalysis, it is not sufficient to consider one quantity like, for example, precipitation only, but also other variables must be taken into account. This is crucial to the closure of the water budgets of these datasets. When introducing new observations, CFSR and MERRA became significantly imbalanced after 1998. Oceanic precipitation increased because of the assimilation of sounding radiances from AMSU. In both CFSR and MERRA, the increase in total water is not balanced by an increase in oceanic evaporation or a decrease of continental PE estimates, leaving a large gap in the global water balance. The atmospheric budgets do not show such a sudden shift, but tend to increase during the time series considered. Furthermore, the differences of the PE estimates are much larger than those of their atmospheric counterpart. It may therefore be concluded that they are still more reliable than the terrestrial PE values.

Because of the limitations presented, the performance of all three reanalyses in reproducing the hydrological cycle still causes doubts in the use of such models for climate trend analyses and long-term water budget studies.

Acknowledgments

We thank the European Centre for Medium-Range Weather Forecast, the Global Modeling and Assimilation Office, the Goddard Earth Sciences Data and Information Services Center, the National Centers for Environmental Prediction, and the National Center for Atmospheric Research for creating and providing the reanalysis data. GPCC data were obtained from http://gpcc.dwd.de. GPCP rainfall observations are developed and computed by the NASA Goddard Space Flight Center’s Laboratory for Atmospheres as a contribution to the GEWEX Global Precipitation Climatology Project (http://precip.gsfc.nasa.gov/). The CRU high-resolution precipitation and temperature data were downloaded from the British Atmospheric Data Centre (http://badc.nerc.ac.uk/view/badc.nerc.ac.uk__ATOM__dataent_1256223773328276). The daily rainfall observations from the Climate Prediction Center are provided at ftp.cpc.ncep.noaa.gov/precip/CPC_UNI_PRCP/GAUGE_GLB/. Precipitation and temperature observations from the University of Delaware were created at the Center for Climatic Research at the Department of Geography (http://climate.geog.udel.edu/~climate/). We would also like to thank Prof. Dr. Tonie van Dam (University of Luxemburg), Dr. Patrick Laux (Karlsruhe Institute of Technology), and Balaji Devaraju (University of Stuttgart), who improved this paper with their comments and corrections. This work is part of the Direct Waterbalance subproject of the DFG priority programme 1257 Mass Transport and Mass Distribution in the System Earth (http://www.massentransporte.de).

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