Modelling the hydrological cycle in general circulation models (GCMs) of the atmosphere and numerical weather forecasting models is wrought with uncertainties. There is uncertainty in the estimation of precipitation rates associated with the representation of physical processes leading to droplet formation in clouds as well as in other components of the water balance – evaporation, transpiration and runoff. As a result water fluxes vary in magnitude among models . Yet, because of the crucial importance of water for society and the environment, it is important that the hydrological cycle is correctly represented.

In the present study three gridded precipitation data sets and three reanalysis precipitation and runoff products are tested. The precipitation data are the Climate Research Unit (CRU) time series (TS) version 3.21 data derived from gauge observations , the Global Precipitation Climatology Project (GPCP) version 2.2 data derived from a joint analysis of satellite data and gauge data and the Tropical Rainfall Monitoring Mission (TRMM) 3B43 and 3A12 monthly data. Full years of TRMM data were only available from 1998 onward. The three precipitation and runoff products tested are from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis , the European Centre for Medium-Range Weather Forecasts Interim Reanalysis (ERA Interim) and the NASA Global Modeling and Assimilation Office (GMAO) Modern Era Retrospective-analysis for Research and Applications (MERRA) Land reanalysis .

The precipitation and precipitation minus runoff fields are evaluated by first calculating annual potential water limited net primary productivity (NPP). NPP, the net amount of carbon absorbed by vegetation from the atmosphere through photosynthesis, is compared with satellite observed normalised difference vegetation index (NDVI) data to which it is closely linked . This approach has the advantage that precipitation fields are tested on independent data over large areas where precipitation data are sparse. Testing reanalyses on precipitation data may not be an independent test since precipitation data are frequently assimilated in reanalyses.

In the present study NPP, derived from both precipitation and precipitation minus runoff, is compared with NDVI for the period of 1982–2010. The comparisons are limited to the land surface between 45∘ S and 45∘ N, where correlations between precipitation and vegetation net primary productivity or vegetation index are high. Both spatial and temporal comparisons are made between water (precipitation or precipitation minus runoff) limited NPP and NDVI. Since precipitation fields have different spatial resolutions, comparisons are made for the spatial resolution at which the data are distributed as well as for the spatial resolution of the NCEP/NCAR reanalysis (1.875∘×1.875∘).

The paper is organised as follows: in Sect.  the vegetation index data, precipitation data and precipitation and runoff reanalyses are briefly discussed. In Sect.  the estimation of NPP from annual precipitation and annual precipitation minus runoff is described. The effects of errors in NPP of relevance for the present analysis are discussed. Section  provides the results of the spatial and temporal comparisons of NPP with NDVI and highlights examples where large deviations exist. The effect of scale on agreement between NDVI and NPP is investigated as well. Section  provides a discussion of the results.

Annual gridded precipitation data and annual precipitation reanalysis products (all six in mm y-1) are converted to annual potential net primary productivity (NPP in gCm-2yr-1), i.e. the net amount of carbon absorbed by land-surface vegetation from the atmosphere over a year limited by water availability only. Annual precipitation limited NPP is calculated using Lieth's model : NPPP=3000{1-exp⁡(-0.000664P)} with NPPP=annual precipitation limited NPPP=annual precipitation (mmyr-1). In a statistical sense Lieth's model can be seen as a data transformation where NPP increases linearly with precipitation at low values; at higher values the increase in NPP with precipitation becomes smaller until it reaches an upper limit near 5000 mmyr-1 (Fig. ). The spatial distributions of annual precipitation limited potential NPP for the six precipitation products analysed are shown in Fig. .

NPP is near-linearly linked to mean annual NDVI as follows : NPP=ϵfAPAR×PAR with ϵ=environment-dependent efficiency factorPAR=photosynthetically active radiationfAPAR=fraction of PAR absorbed by green parts of vegetation. Since the fAPAR is near-linearly related to NDVI , a near linear relationship is expected between NPP and NDVI .

The error in NPP (Eq. ) can be expressed as a sum of component errors: η=(ηP2+ηE2+ηQ2+ηG2+ηT2+ηI2+ηΔS+…)0.5, where η is the total error in NPP which consists of errors in the gridded precipitation data or reanalysis products (ηP). The investigation of the error ηP is the objective of the present study. Other error terms are related to ignoring components of the water budget in Eq. (). These are evaporation from soils and intercepted rainfall (ηE), runoff (ηQ), and infiltration to ground water (ηG). These components of the water budget are effectively “lost” to vegetation; i.e. these components are not taken up by plants and are transpired into the atmosphere. Errors associated with other factors not incorporated in Eq. () are limitations posed on vegetation by temperature (ηT), solar radiation ηI and changes in soil and groundwater storage ηΔS. The list of errors in Eq. () is not exhaustive and other errors (…), such as caused by ignoring differences in water use between C3 and C4 species, may affect the analysis. Under the assumption that errors are additive (Eq. ), a smaller error in ηP will lead to a smaller error in η since other errors are the same. Thus the key assumption here is that lower errors in ηP will lead to lower errors in NPP and improved statistics such as higher correlations between NDVI and NPP and a smaller root mean square error (ERMS s).

The analysis is limited to the land surface between 45∘ S and 45∘ N. At these latitudes water is limiting vegetation growth and the association among precipitation, NPP and NDVI is therefore high. As a result, the precipitation error term in Eq. (), ηP, is large compared to the other error terms. Exceptions are high-altitude areas where temperature is likely limiting plant growth, or areas where increased cloudiness and increased precipitation are linked with decreased solar radiation. In these areas lower or even negative correlations between precipitation and vegetation greenness may be expected.

Equation () shows that incorporation of more components in Eq. (), e.g. components of the water budget, should reduce, or at least not increase, the overall error in η. This provides a way to evaluate other components of the water budget such as runoff (Sect. ). If simulations of runoff are realistic, the NPP fields calculated from annual precipitation minus runoff ought to be closer to the observed NDVI values than the NPP fields calculated from annual precipitation. The evaluation of precipitation minus runoff is necessarily limited to the reanalyses since the CRU, TRMM and GPCP data do not contain runoff estimates. NPP from precipitation minus runoff is calculated using a modified form of Eq. (). NPPP-Q=3000×{1-exp⁡[-0.000664×(P-q)f]} with f=P-q̃/P̃P-q̃= median P-q for 1982–2010 and45∘S–45∘NP̃= medianPfor 1982–2010 and 45∘S–45∘N. The value for f varies between reanalysis products; fMERRA=0.95, fERA=0.89 and fNCEP=0.894. A value of f=0.892 is used, which is in the middle of the two closest median f values. Results for MERRA NPP calculations did not change when a value of f=0.95 was used.

The results are presented in two subsections. In Sect.  the analysis of precipitation data and reanalyses is presented. This includes the analysis of spatial correlations through time, the exploration of residual errors (biases and root mean square errors) and the analysis of gridded correlations between NPP and NDVI time series. Examples are highlighted of problems revealed by the spatial and temporal correlation analysis. In Sect.  the precipitation minus runoff reanalyses are analysed.

In the present study three land-surface precipitation data sets, three land-surface precipitation reanalyses and three precipitation minus runoff reanalyses were tested. Annual precipitation and precipitation minus runoff values were converted to NPP and compared with NDVI data for 1982–2010 at latitudes between 45∘ S and 45∘ N. At these latitudes correlations between precipitation derived NPP and NDVI are high because water limits vegetation growth.

The approach adopted in the present paper, testing gridded precipitation data and reanalyses with NDVI data, is different from the more common approach where precipitation reanalyses are directly compared with precipitation data. A disadvantage of the adopted approach is that two different parameters are compared, even though these parameters are closely linked for latitudes investigated. An advantage is that the NDVI data have continuous coverage for the entire land surface and their measurement is independent of that of the precipitation data. Furthermore, the adopted approach can be extended to incorporate other components of the hydrological cycle; the residual error is expected to decrease, or at least not increase, as more components of the hydrological budget are incorporated (Eq. ). As an example, the reanalysis precipitation minus runoff is compared with NDVI in the present study. Other components were not incorporated since runoff was the only parameter available for all reanalyses.

The NDVI data were obtained from two different satellite sensor systems; data from 1982 to 1999 were obtained from the broad-band AVHRR and data from 2001 to 2010 were obtained from the narrow-band MODIS. Different correction algorithms were applied to the two data sets; no solar zenith angle correction was applied to the MODIS data, which affects the seasonal NDVI cycle, but has a minimal effect on interannual variability. A less comprehensive correction for atmospheric effects was applied to the AVHRR data, which may lead to differences in areas where, e.g., variability in atmospheric water vapour or dust is large and is sustained for periods larger than 2 months.

Another limitation of the present study is that the NPP model does not take into account precipitation seasonality; thus, for the same annual precipitation amount, the same annual NPP is predicted for both areas with constant precipitation during the year and areas with extended dry and wet seasons.

Despite the three above limitations as well as the limitations mentioned in the discussion of Eq. (), precipitation limited NPP values correlate well with NDVI (Figs. and ); the spatial correlations between NDVI on the one hand and NPP derived from precipitation appeared consistent across the AVHRR and MODIS records (Fig. ). Spatial patterns and interannual variation in NDVI were reproduced to a large extent by the NPP calculated from precipitation data.

The consistency of spatial correlations over time (Fig. ) between NDVI and precipitation limited NPP is remarkable given that the number of stations used to obtain the CRU and GPCP data sets declines over time from more than 40 000 in 1982 to less than 10 000 in 2010. For the GPCP data the decline in the number of stations is in part compensated for by the incorporation of more accurate precipitation estimates from a newer generation of satellites , but this is not the case for the CRU data.

The decline in the number of stations available for the generation of global gridded data poses a problem for the spatial and temporal analysis in the present study. It is possible to analyse only those grid cells where a sufficiently large number of stations is available. However, this would lead to a decline over time in the number of grid cells incorporated in the analysis and would make both a comparison between years difficult as well as a comparison between observed fields and reanalysis fields. The advantage in analysing the full data set is that it provides an estimate of the accuracy of entire data sets. A side analysis of the CRU data (not included in the present study) showed that the spatial correlation decreased when cells were left out based on the number of stations contributing to the gridded estimate; for example, the spatial correlation between CRU NPP and FASIR NDVI for 1992 dropped from r=0.893 when all data were included to r=0.838 when cells were removed, with fewer than five stations contributing to the gridded estimate.

The precipitation data and reanalysis products fall into three groups in terms of their spatial consistency with the NDVI. The first group consists of the CRU and TRMM data. This group has the highest spatial correlations. The second group consists of the GPCP data and MERRA Land and ERA Interim reanalyses with somewhat lower spatial correlation and the third group consists of the NCEP/NCAR Interim precipitation with the lowest correlation. The reduced spatial correlation of the GPCP data can be attributed to the low spatial resolution since all precipitation data show similar correlations at the (low) resolution of the NCEP/NCAR reanalysis.

The positive bias shown in the GPCP data, CRU data and TRMM data in western Africa and the Indian sub-continent (Figs. 4 and 5) could be caused either by a deficiency in the NPP model or by deficiencies in the data. An error analysis by of the GPCP data based on a number of independent data sets indicates that GPCP precipitation is overestimated in these parts of the world, similar to the results of the present study (compare Fig. 4 with Fig. 7 in ). A study by comparing global gridded data with data from a dense rain gauge network in eastern Africa found that CRU data overestimated precipitation in mountainous regions as a result of an overcorrection for altitude. The biases in western Africa and the Indian sub-continent were even larger in the reanalysis fields than in the observed fields.

The temporal correlation analysis divides data sets into two groups: the first consists of the gridded CRU, TRMM and GPCP data sets, which have high temporal correlations in all semi-arid regions. As an aside, the GPCP data and CRU data differ only in terms of their spatial consistency and the GPCP data can therefore be improved by increasing the spatial resolution, e.g. by using the climatology of the CRU precipitation data. The second group with lower temporal correlations consists of the MERRA, ERA Interim and NCEP/NCAR reanalyses. Correlations were realistic for semi-arid regions; however, none of the reanalysis products showed realistic interannual variations in tropical northern Africa. Even the MERRA Land precipitation showed poor correlations despite assimilation of GPCP precipitation data into this product . Northern semi-arid Africa is thought to be sensitive to climate change and is likely an area where early indications of climate change are to be found. Nevertheless, modelling of temporal and spatial variability of precipitation in this area is poor and needs to be improved as a matter of urgency. In particular, the interannual variability in the ERA Interim precipitation, persisting for a number of years in a row, was much larger than observed.

Incorporation of runoff in the estimation of NPP, by calculating NPP from precipitation minus runoff, resulted in marginal improvements for the MERRA Land reanalysis. Results deteriorated by a small amount for the ERA Interim reanalysis and by a slightly larger amount for the NCEP/NCAR reanalysis. This lack of improvement likely indicates an overall weakness in the hydrological representation in land-surface models.

The CRU and TRMM precipitation data exhibit the most realistic spatial variations; the CRU, TRMM and GPCP precipitation data exhibit the most realistic temporal variations. The low spatial resolution of the GPCP data reduces realism of spatial variability.

Precipitation reanalyses exhibit realistic spatial and temporal variations for most parts of the world: the Americas, Australia, and Asia. However, spatial and temporal variations are not realistic for northern tropical Africa. Particular noteworthy problems are that extreme droughts (most notably the 1984 drought in the Sahel) are not simulated correctly. Furthermore, the interannual variability in the ERA Interim precipitation in the southern desert margin of the Sahara is too large.

ERA Interim precipitation appeared more realistic for the last 5–8 years of the record investigated.

The simulations of runoff in numerical weather forecasting models need to be improved. Only the MERRA Land reanalysis showed a modest improvement when runoff was incorporated in the calculation of NPP; other reanalysis products showed an increase in error when runoff was incorporated, indicating that errors in these simulations are large.

The proposed method, to test precipitation fields on NDVI data, can be extended to test other components of the water balance. NPP should match transpiration of water by plants most closely because of the link with carbon uptake through photosynthesis. This test was not applied since transpiration was only available for the MERRA Land reanalysis.