1. Introduction

Understanding of the global hydrologic cycle is critical because all terrestrial life depends on local water resources, and the supply of these resources is shifting as a result of human-induced land-use and water-use changes, and climate variations. To maintain hydrologic balance, the water that flows into the oceans by the discharge of rivers must be matched by the advection and convergence over land of water in the atmosphere. All freshwater on or beneath the land surface arrived as precipitation, and ultimately all of that water was evaporated from the oceans. However, it may have taken multiple “cycles” of precipitation and evaporation for any single water molecule to work its way from the ocean to a given terrestrial location, with evaporation from the land surface or transpiration through the terrestrial biosphere occurring in the intermediate cycles. Unlike over the oceans, evapotranspiration over land is usually limited to a rate less than the maximum potential rate due to stresses such as those caused by low soil moisture or suboptimal conditions for photosynthesis in plants. Therefore, changing land surface conditions, whether caused directly by land-use polices or as a response to fluctuations or trends in climate, can impact the hydrologic circuit between land and atmosphere by changing evapotranspiration rates. Certain regions of the globe appear to be particularly sensitive to such feedbacks (Koster et al. 2004). This is an important topic of research with applications for improving prediction (Trenberth et al. 2003).

One of the principal yardsticks for quantifying the strength of the hydrologic cycle over specific terrestrial regions is the recycling ratio. Definitions can vary slightly, but commonly it is taken to be the fraction of precipitation over a defined area that originated as evapotranspiration from that same area, with no intervening cycles of precipitation or surface evapotranspiration. Conceptually the recycling ratio has been appealing. In the simplest sense one imagines that a change to evaporation over the area of concern has a direct and predictable impact on local precipitation. Of course, there are other feedbacks in the system, and in many parts of the world they may dominate. We hypothesize that a strong control on atmospheric moisture supply manifest as a high recycling ratio may be a source of soil moisture memory, and this memory corresponds to an element of potential climate predictability that can be harvested. Thus, an important step to determining locations of enhanced predictability from the land surface will be to establish the global climatology of recycling ratio. This is particularly the case since soil moisture is so sparsely observed (Leese et al. 2001).

A change in regional evapotranspiration affects not only the supply of water carried by the circulation of the atmosphere, but can thermodynamically alter the atmosphere itself by changing the partitioning of surface heat fluxes, triggering changes to the circulation patterns as well. Nevertheless, the basic linear model behind many people’s conception of recycling has been hard to shake. It is the basis of legends such as the belief that “rain follows the plow.”¹

The first quantifications of recycling were made using bulk estimates. The first formulations were one-dimensional (Budyko 1974; Lettau et al. 1979) and later generalized to two-dimensional areas suitable to true budget studies (e.g., Brubaker et al. 1993; Eltahir and Bras 1994; Burde et al. 1996). Burde and Zangvil (2001) present a thorough overview of the various methods that have been used. The bulk approach makes several assumptions, such as that locally evaporated and externally advected moisture are well mixed in the air over the region of interest. One major drawback of bulk formulations is that they contain an atmospheric moisture flux term at the lateral boundaries defined as the product of two time-mean quantities—wind and humidity:

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Where the flux of moisture F is normal to a lateral boundary of the area, V is the component of the wind normal to that boundary, and q is the humidity. Typically these terms are vertically integrated to compute the total moisture flux across a boundary, but use monthly mean data. In many regions such fluxes occur when there are either strong moisture gradients or large temporal variability in humidity, so that changes in wind direction and speed are accompanied by very different values of humidity. In actuality, perturbational expansion yields

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The nonlinear term can be quite significant and has much of its signal on the time scale of synoptic waves.

Another drawback of the bulk approach is that it must be calculated over predefined volumes using the wind and humidity information along the boundaries. That is fine for calculating a single value for recycling ratio over a large area (large relative to the number of observations along the boundary or more typically, the number of grid boxes from a gridded dataset) but makes it difficult to produce a continuous map of recycling over a continent or the entire globe.

By assuming a length scale and calculating the mean moisture flux across that scale, Trenberth (1999) was able to use the bulk approach to formulate the recycling ratio based on local variables. His approach still suffered from the other drawbacks of the bulk formulations. However, the approach was able to produce global maps of estimates of the recycling ratio, including a characterization of the annual cycle of recycling.

The most direct way of estimating recycling would be to track the water vapor in the air from source (evapotranspiration) to sink (precipitation). Isotopic analysis of precipitation can differentiate between moisture that has evaporated from open water from that which has passed through the vascular systems of plants. For example, Henderson-Sellers et al. (2002) showed how the isotopic ratios change as one moves upstream along the Amazon (showing the increasing contribution due to transpiration) and the trends in isotopic ratios during the latter part of the twentieth century (suggesting changes in land-use practices). However, isotopic analysis cannot pinpoint the location of the evaporation that contributed the moisture. It can only provide the proportions of likely sources differentiated into broad categories.

Tracer modeling provides a means to follow exactly the path of water within an atmospheric model. Druyan and Koster (1989) were among the first to apply this Lagrangian approach to water vapor for the Sahel. This method has been applied over the central United States in regional (Giorgi et al. 1996) and global models (Bosilovich and Schubert 2001), and over Eurasia (Numaguti 1999). Although more spatially precise than isotopic tracers, tracer modeling has its drawbacks as well. Tracking tracers in a three-dimensional model of the atmosphere adds to the computational cost, especially in terms of storage, and requires choosing the source regions a priori. Any changes require a complete reintegration of the general circulation model. Also, errors in the model climate contribute errors in the estimates of the hydrologic cycle.

An ideal approach would be to incorporate tracers in an analysis model with data assimilation, which would constrain the model behavior with available observations. That approach still has problems to be solved, such as reconciling the lack of conservation within a system where state variables are assimilated (as is the case with all of today’s operational analysis and reanalysis efforts) with the need for a completely closed water budget within an analysis of the hydrologic cycle.

Until such a conserving data assimilation system becomes feasible, the best alternative might be to apply a back-trajectory analysis a posteriori to existing reanalysis fields. Brubaker et al. (2001) used such an approach to produce a climatology of the hydrologic cycle over the subbasins of the Mississippi River basin, Sudradjat et al. (2003) extended the study to interannual variations, and Sudradjat (2002) applied the approach to the Amazon basin. The method has also been applied to examine moisture sources for specific extreme precipitation events over the Mediterranean basin (Reale et al. 2001; Turato et al. 2004), and to validate isotopic analyses over Russia (Kurita et al. 2004). Here we extend the analysis of Brubaker et al. (2001) to all land areas of the globe. The datasets used in the analysis are described in section 2. Section 3 explains the methodology, with an emphasis on changes to the original approach described in Dirmeyer and Brubaker (1999) and the universality of scaling that allows us to compare recycling over regions of differing areas. The global climatology of recycling, including analyses of variability and trends, is given in section 4. In section 5 we compare this calculation to bulk estimates using the method of Trenberth (1999). Conclusions are presented in section 6.

2. Datasets

All meteorological data except for observed precipitation come directly from the National Centers for Environmental Prediction (NCEP)–Department of Energy (DOE) reanalysis (Kanamitsu et al. 2002). These data are on a 192 × 94 grid (1.875° longitude by approximately 1.9° latitude) and span the period from 1979 to the present (2004). We make use of the sigma-level diagnostics and surface flux fields at 6-h intervals. Specifically, the fields used are humidity, temperature, and wind (u and υ components), all on the 16 lowest model sigma levels, as well as surface pressure, precipitation, and total evaporation. These data are used to calculate precipitable water, potential temperature, and the advection of water vapor. To avoid spurious excess convergence toward the poles, the meridional wind is scaled by the cosine of latitude. The land–sea mask from the reanalysis is also used to differentiate land grid boxes for the calculation. Several precipitation datasets are combined to produce a best estimate of precipitation sinks for the back-trajectory calculation. A hybrid 3-hourly precipitation dataset is produced in the following way.

First, the reanalysis precipitation (6-h forecast) is interpolated to a 3-hourly amount. Large errors are known to exist in the reanalysis estimates of precipitation—we use it primarily to establish the position and movement of large-scale rainfall events, such as those associated with extratropical baroclinic systems.

We then use the satellite-based Climate Prediction Center (CPC) morphing technique (CMORPH) precipitation estimates (Joyce et al. 2004) to correct the diurnal cycle of reanalysis precipitation at low latitudes. This is accomplished as follows. The 3-hourly CMORPH data are scaled from their original 0.25° resolution onto the reanalysis grid using simple bilinear interpolation. A centered 31-day running mean is then calculated for each 3-h interval of the CMORPH data to establish the mean diurnal cycle of precipitation and its variation throughout the year. At the time these analyses were performed, less than two years of CMORPH data were available. Only data from March 2003 through April 2004 have been used. For each day (delineated by 0000 UTC) at low latitudes, the reanalysis precipitation is replaced by the CMORPH mean diurnal cycle for that day, scaled to retain the total daily rainfall from the reanalysis. The definition of “low latitude” for precipitation also varies throughout the year as the changing seasons bring different parts of the globe into subtropical and midlatitude weather regimes. The CMORPH correction to the diurnal cycle is only applied to a zonal band 60° wide, spanning 30° north and south of the latitude of solar declination. This limitation is meant to focus the correction on regions where precipitation is most strongly diurnally forced (e.g., convection driven by solar heating) and not to alter the precipitation where synoptic variations are predominant.

At this point in the process, each grid box of the globe contains what we deem to be the best estimate of the local temporal distribution of precipitation within weather time scales. The final step is to scale the precipitation fields one more time, using the observationally based pentad estimates of Xie and Arkin (1997). The final scaling results in a hybrid model–observational precipitation product that retains the pentad mean values from Xie and Arkin (1997), but the subpentad variability from CMORPH and the reanalysis. We use the hybrid precipitation estimates as the starting point for the quasi-isentropic back-trajectory analysis. The final surface and atmospheric datasets are all on the reanalysis grid and span the period from January 1979 through August 2004.

3. Methodology

Our approach uses a quasi-isentropic calculation of trajectories of water vapor backward in time (hereafter QIBT) from observed precipitation events, using atmospheric reanalyses to provide meteorological data for estimating the altitude, advection, and incremental contribution of evaporation to the water participating in each precipitation event. Dirmeyer and Brubaker (1999) provide the complete mathematical formalism of the method, and Brubaker et al. (2001) describe how the climatologies are calculated. Here we give a qualitative description of the method, and refer the reader to those previous papers for details.

The method relies on the use of high-time-resolution (daily or shorter) precipitation and meteorological data to include the effects of transients on the transport of water vapor. Calculations are performed on the reanalysis grid, working backward in time, starting with observed precipitation at each grid box grouped into pentads (5-day intervals). This gives 73 pentads per year. During leap years a 6-day interval is used for the 12th pentad, to include 29 February. The method can run on a range of time steps—we chose an interval of 45 min to ensure statistical stability of results at minimum computational expense. At the spatial scale of the reanalysis data, we find that a time step of an hour or less produces stable results (i.e., the evaporative source regions do not change as the time step is reduced further). The data are linearly interpolated in time to the time step of the trajectory methodology, with the exception of precipitation, which uses a mass-conserving interpolation. Trajectories are calculated first backward then forward and the average is taken following Merrill et al. (1986) to minimize the impact of interpolation errors in rapidly evolving or highly rotational flows.

The precipitation data are at a time resolution of 3 h, so there are typically 40 precipitation data intervals in each pentad across 160 time steps. If there is no precipitation over the grid box during the pentad, no calculations are made. Otherwise, the 5-day precipitation is divided into 100 equal increments, and for each percent of precipitation that occurs counting back through the 3-h total, a back trajectory of its corresponding atmospheric parcel is begun. So for instance, if all of the precipitation occurs in the last 3-h precipitation interval of the pentad, then 25 parcels are launched in each of the first four time steps counting backward in the back-trajectory scheme. Figure 1a illustrates schematically how a time series of precipitation is broken into a number of parcels containing equal water mass—some parcels may span more than one time step or rainfall event by this method of accounting.

An element of randomization is used to begin each parcel trajectory, as illustrated conceptually in Fig. 1b. First, the exact horizontal location is chosen randomly in latitude and longitude within the grid box. The altitude of the parcel is chosen randomly using the partial pressure of water vapor as a vertical coordinate, counting only the lowest 16 sigma layers. This ensures that most parcels are launched from relatively low altitudes, within the boundary layer. This carries with it the assumption that every molecule of water vapor within the tropospheric column is equally likely to precipitate. Since specific humidity drops rapidly with height, rarely are parcels launched above 600 hPa.

Trajectories are calculated going back no more than 15 days prior to the start of each pentad (i.e., at most 20 days of meteorological data are applied to each 5-day interval or rainfall). The parcels are advected on isentropic (theta) surfaces following the numerics of Merrill et al. (1986) with the exception that when a parcel is tracked back into the ground, its potential temperature is adjusted to the mean value of the boundary layer, to simulate the effect of surface sensible heat flux on the parcel. This is a strong simplification—we assume that the diabatic processes (latent heat release and consumption from cloud formation and dissipation, PBL heating, and radiational cooling) approximately balance out along the path between the highly diabatic surface evaporation and terminal precipitation events. Given the limitations of the reanalysis data we stick to the kinematic elements of the system. Ideally for calculation of a recycling climatology one would include Lagrangian tracers in the reanalysis model.

At each time step, a fraction of the precipitation increment in the parcel is attributed to local evapotranspiration from the grid box over which the parcel lies (see Fig. 1c). The method is not sensitive to random errors in evaporation and precipitation, but systematic errors can affect the results of the calculation (Brubaker et al. 2001; Sudradjat 2002). The fraction of the precipitation increment is set equal to the grid box evapotranspiration (rate integrated over the time step) divided by the column precipitable water. This mass is removed from the parcel before calculating the next advection interval, and added to the evaporative source from that grid box. This approach invokes another assumption (probably the weakest in the method) that the water evaporated from the surface mixes uniformly through the atmospheric column within the period of the time step. This is not an entirely bad assumption. Strong vertical mixing typically accompanies higher evaporation rates, as both are mainly driven by the rate of surface radiative heating in the daily growth of the PBL, as well as by mechanical processes in the event of strong low-level winds. There may be synoptic situations leading to strong mixing without high evaporation rates, but generally not the reverse. Thus the stronger the evaporation, the better the assumption. The way the method is constructed, the water accounted for in each parcel asymptotically converges to zero, so some cutoff must be applied. The parcel is traced back until at least 90% of its original precipitation increment is attributed to evapotranspiration, or the 15-day period has been exceeded. The evaporative source masses along the parcel’s path are then scaled to account for the residual water, so that the total precipitation mass is accounted for in the integral of all evaporative sources.

This process is repeated for all parcels in the pentad to create a two-dimensional distribution of evaporative sources for the precipitation sink over the grid box during that pentad. We aggregate up to monthly time intervals to further stabilize the statistics and reduce the size of the final dataset. The result is a global two-dimensional distribution for each individual land surface grid box (excluding Antarctica)—a total of 4257 based on the reanalysis grid. The evaporative source distributions may be added to provide the source for larger sink areas, such as major river basins. The fraction of the source that contributes to recycling is simply that portion that lies within the bounds of the sink region.

Because of its definition, the recycling ratio ρ is a function of the area A under consideration. A thought experiment illustrates this point. Consider the limit cases: as the sink area A is decreased to zero, the fraction of precipitation that originates as evaporation from that area necessarily reduces to zero as well, because the fetch remains largely unchanged while the target shrinks to nothing. At the other extreme, as A is increased to encompass the entire world, ρ goes to one (assuming an insignificant net gain or loss of water to space compared to the total precipitation flux).

This discrepancy would make it difficult to compare the recycling between two regions that enclose different total areas. Brubaker et al. (2001) showed a strong log–log relationship between recycling ratio and area for the Mississippi basin. We have tested the scalability of recycling over many regions of the globe. Table 1 lists 14 areas spanning all climate regimes from humid to dry and tropical to high latitude. The names of the areas indicate their approximate locations, and not the precise boundaries of river basins or continents. Over each region, an 8 × 8 grid box area is selected containing only land points. The recycling ratio for a 25-yr period is calculated. The region is then divided into two 4 × 8 subregions and the calculation is repeated for each subregion. This process is continued for four 4 × 4 subregions, and so on, down to 64 individual grid boxes. A scatterplot of recycling ratio as a function of area is produced for each region. Figure 2 shows examples for three of the regions. For every region there is an excellent power-law fit based on the average values of ρ and A for each set of subregions:

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Values of the best fit for coefficients a and b in each region are given in Table 1. The table also shows the values of the recycling ratio calculated based on this regression for areas of 10⁴, 10⁵, and 10⁶ km², which are plotted in Fig. 3. At the bottom of Table 1, the mean, standard deviation, and coefficient of variation (COV) for a and b are given as calculated among the 14 regions. The COV of b is 0.072, indicating that the standard deviation is about 1/14 the magnitude of the mean; the COV for b is an order of magnitude smaller than for a. Thus, we can posit a universal slope factor b to compare different regions. Then, the value of the intercept a can be estimated from the regression relationship for any location. The last line shows the values of a and b calculated as a best fit to the mean of the recycling ratios among the regions for the three areas, as well as the values of recycling ratio that result from a regression based on the best fit to compare to the actual mean of the recycling ratios given just above. The values of coefficients a and b calculated this way give a slightly lower curve than the mean of the coefficients (bold black line), but the slope is similar—different by about 0.15 standard deviations. In this paper, we choose a global value of 0.457 for b in order to scale the recycling ratios to a common area for plotting and comparison.

4. Climatology of recycling

With recycling scaled to a common area, we can produce a meaningful global gridded analysis of the recycling ratio. All figures in this section have been calculated for a reference area of 10⁵ km². Figure 4 shows the 25-yr mean value of recycling ratio, expressed as a percentage. Several features stand out. Areas of high terrain tend to stand out as having high recycling ratios. This may be an artifact of the combination of low precipitable water and high warm-season reanalysis evaporation rates over these regions, and may be spurious. The poor resolution of the fine structure of the orography may also contribute to errors in moisture advection and precipitation patterns in the analyses (e.g., Evans et al. 2004), affecting our estimates of recycling ratio in mountainous areas. The other features are likely genuine, such as the relative minima in regions with strong advection from adjacent waters (e.g., the northern Amazon basin, Mississippi basin, and coastal monsoon regions in South Asia and northwestern Mexico). Recycling appears to be relatively high over much of South America south of the Amazon River all the way through the La Plata basin, much of subtropical southern Africa, interior China, southern Europe including the regions surrounding the Black Sea, western North America, and a broad swath of the high latitudes of the Northern Hemisphere, especially over eastern Siberia.

Figure 5 separates the 25-yr climatology by season. Unshaded areas in seasonal maps may occur over deserts where no precipitation is reported in the multiyear analysis. In general, recycling ratios are higher during the local warm or wet season, and lower in winter or the dry season. We see that the robust recycling ratios at high northern latitudes are a spring and summer phenomenon. At these latitudes, water is unavailable for evapotranspiration during the winter season, when soil and water bodies are frozen; significant local sources of moisture are not possible until the spring thaw (Betts et al. 2001), when the low-elevation basins of Arctic rivers become vast wetlands fed by melting snow and thawing soil. The active season for high-latitude vegetation is limited to June–September (e.g., Harding and Lloyd 1998). Recent estimates based on remote sensing (Mialon et al. 2005) suggest a maximum summer open water extent of 22 × 10⁵ km² above 50°N (this estimate includes small lakes, inundated surfaces and wetlands, in Canada, Alaska, and Eurasia). The rate at which this open water and boreal vegetation supply evaporation, and whether that evaporation is recycled into local precipitation, depends on the available energy and mechanisms for storm formation. Serreze et al. (2002) estimated precipitation recycling as high as 25% for parts of northern Eurasia in July.

Not all monsoon regions show a strong primary annual cycle of recycling. For instance, there are peaks during March–May (MAM) and September–October (SON) over India and parts of Southeast Asia, and minima during the core of the wet season (and dry season for India). This contrasts with the monsoon regions of North America, northern Australia, and the Sahel, where recycling peaks during the wet season. Over South America south of the Amazon basin, the region experiences more of an expansion and contraction of the area of high recycling, with the minimum attained during the dry season. Recycling over the Amazon basin reaches a peak during SON, but the peak is during December–February (DJF) over the Pampas and Pantanal regions. Beyond the prevalent orographic recycling peaks, relatively high values are attained during June–August (JJA) over Anatolia, the headwaters of the Ob and Yenisey Rivers of central Asia, and the Mackenzie River basin in northwestern Canada. By this calculation, recycling rates over the northern Amazon basin during the wet season are as low as over many desert regions, because of the strong advection of maritime moisture from over the tropical Atlantic.

Figure 6 shows the degree of seasonality in recycling ratio over the globe using several different metrics. The magnitude of the climatological annual cycle of monthly recycling ratios, expressed as percentages, is shown in the top panel (maximum minus minimum). The high-latitude regions of the Northern Hemisphere, especially in the Pacific region, show a very strong annual cycle. Areas of elevated terrain also show large magnitudes of the annual cycle. There are also isolated extrema in the arid regions of northern Africa and southwestern Asia, which is an artifact of the rare sporadic rain events in the region leading to statistically unstable estimates, particularly when the observed and reanalysis precipitation (and thus reanalysis evaporation) are not synchronized. The high values on the east coast of Greenland are also caused by large discrepancies between observed and reanalysis precipitation, making the evaporation (and thus the recycling ratio) very high. More revealing are the regions with very low seasonal variations in recycling. This includes much of the Amazon basin and adjacent Atlantic coastal regions of equatorial South America, the southern coast of Australia along the Great Australian Bight, areas to the west and northwest of the Persian Gulf, and two regions of the Nile basin, including the delta and parts of Ethiopia. A plot of the standard deviation of the 12 monthly mean values of climatological recycling ratio (center panel) portrays a similar picture.

The COV (bottom panel) reveals the size of the seasonal cycle compared to the magnitude of the annual mean recycling ratio. Now the arid regions stand out as having a high degree of seasonal variation, compared to their low mean values (see Fig. 4). In addition to parts of northwestern North America and northeastern Asia, there are also regions of the Southern Hemisphere with relatively high COV, including northwestern Australia, South Africa, and South America south of 20°S. The Tropics as a whole are prominent as a region of low COV, with the lowest values over the southern Amazon basin and Mato Grosso, well south of the region of smallest absolute range. There are also many interesting regional features, like the chain of relative minimum COV that trails across the Amur, Yenisey, and Ob River basins, between Lake Balkhash and Kashmir, and over the Ustyurt Plateau, as well as the relative maximum in the North American monsoon region.

The pattern of interannual variability, expressed as the COV of seasonal recycling ratios as normalized by the 25-yr seasonal means, is shown season by season in Fig. 7 (unshaded areas are as in Fig. 5). At lower latitudes the maps share some characteristics with those for seasonal COV, with high values in arid regions and low in the deep Tropics. However, the large mean and seasonal variability signals at high northern latitudes are not evident at interannual time scales. Instead we see strong signals mainly in the dry regions in the subtropics and midlatitudes that lie outside the rainbelts for a given season. For example, during JJA the highest values of interannual COV lie over the dry-season monsoon regions of South America, southern Africa, and northern Australia, as well as to the north of the Asian and Sahel monsoon regions and the southern Rockies. Excluding the very high values over the Sahara, Arabia, and Gobi Deserts, the COV seems to be largest during the dry season in regimes of strong seasonal precipitation, consistent with an erratic evaporation response dependent on the availability of moisture from the previous season’s rainfall.

Trends in recycling ratio, expressed as percent per year over the 25-yr span, are shown in Fig. 8. The trend is computed from the slope of the linear regression on the mean values from each season. Significance of trends is calculated using the Cox–Stuart test (McCuen 2003) with a confidence level of 95%. There is a patchy distribution of weak but significant positive trends during boreal winter over Canada and the northern United States, but in boreal spring there is a broad region of strong increases in recycling over Canada, Alaska, Fennoscandia, and the Arctic coast of eastern Siberia, with sporadic small regions of positive and negative trends elsewhere. The high-latitude positive trends are consistent with the warming and extended growing season trends in these areas (Serreze et al. 2000; Tucker et al. 2001). These trends carry over somewhat into JJA over North America, with an expanding region of marginally significant reduced recycling over much of Siberia and western Europe. We can see that the strong interannual variations over the deserts during SON in Fig. 7 are also manifested as strong but statistically insignificant trends caused by sporadic infrequent rainfall events there. There are also notable positive trends during SON over large areas of South Asia and southern Africa (also present during DJF), and a kind of dipole over South America with decreasing recycling in a band from Peru to southern Brazil, and positive trends to the south. The implication is a small intensification of the local hydrologic cycle in several areas.

5. Comparison to bulk calculations

Trenberth (1999) computed recycling ratios on a global basis using a bulk formulation,

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where ρ is the recycling ratio, defined as the fraction of total precipitation (P) contributed by precipitation of local evaporative origin (P_m), E is evapotranspiration, and F the average atmospheric moisture transport over the region. In Eq. (4), L is an assigned length scale. Differences between Trenberth’s (1999) results and those reported here could be due to either the method or the data, or both. For comparison to that study and to the QIBT recycling estimates obtained here, we have computed recycling using Eq. (4) and the dataset assembled for this study. This should pinpoint differences in the data. Trenberth (1999) obtained seasonal P from the Xie–Arkin product for 1979–95, seasonal E from the NCEP–National Center for Atmospheric Research (NCAR) reanalyses (6-h model integrations), and F from the magnitude of the seasonal-mean vertically integrated water vapor transport vector from the NCEP–NCAR reanalysis. Our study uses the hybrid model-observation P described in section 2, E from the NCEP–DOE reananlysis (6 h, 1979–2004), and F as the magnitude of the vertically integrated vapor transport in the NCEP–DOE reanalysis. Recycling ratios are calculated on a monthly basis, and then averaged to seasonal values.

We calculated bulk recycling values using Eq. (4) and our dataset, with length scales of 1000 and 500 km, for comparison to Trenberth (1999). Annual average values of recycling based on the two different length scales are included. Figure 9b compares directly to Trenberth’s Fig. 10 (we have even applied the same smoothing to T31). Figure 9a is analogous to Trenberth’s Fig. 9. The results are quite similar, with slightly lower recycling values in our case likely because of lower evaporation rates in the Tropics and generally higher wind speeds over land in the NCEP–DOE reanalysis compared to the NCEP–NCAR reanalysis. The two bulk estimates are particularly similar in pattern over the Americas and eastern Siberia, but there are important regional differences in places such as Southeast Asia and much of Europe and Africa. Therefore, we cannot infer that differences between the QIBT recycling results presented here and Trenberth’s (1999) bulk estimates are due only to the method. However, differences in the relative magnitudes, and to a lesser extent the patterns, exist between Figs. 9 and 4 as well (as will become evident in Fig. 11). The method is also contributing to the dissimilarities.

To compare our QIBT recycling estimates to those derived from the bulk method, we must assign a compatible length scale for Eq. (4). A square region with area 10⁵ km² has a side length of 316 km; a circular region has diameter 357 km. As a compromise, we selected a length scale of 340 km. The bulk recycling results using Eq. (4) are shown in Fig. 10. Figure 11 shows the fractional difference between the QIBT estimates shown in Fig. 5 and the bulk estimates for the seasonal values.

According to Trenberth’s (1999) perturbation analysis, we would expect recycling estimates to increase when the estimation method captures transients in precipitation, evapotranspiration, and vapor transport. In general, our results confirm this prediction. For most of the globe, the QIBT recycling exceeds the bulk recycling. Over most midlatitude regions, the difference is less than 70% of the bulk value; however, in locations where the bulk recycling is quite low, such as the Sahara in SON, the QIBT estimate is more than double the bulk estimate. Notable exceptions, where the QIBT estimate is lower than the bulk estimate, are northern South America (all seasons) and equatorial Africa (DJF). Multivariate Taylor series expansion of Eq. (4) reveals both positive and negative terms proportional to the covariances among E, P, and F, as well as a positive term in P variance; therefore, it is difficult to make any quick inference about the sign and magnitude of the transient covariances in these cases. In addition to examining the temporal variance and covariance in E, P, and F, further perturbation analysis will require investigation into the effect of precipitation-free periods on recycling estimates (as discussed in Trenberth 1999) and the minimum time period over which the Budyko (1974) model should be applied. It is also possible that our method of adding moisture to the backward-advected air parcel underestimates the contribution of surface evapotranspiration to precipitation in regions and periods of deep convection.

6. Conclusions

Precipitation recycling ratios are estimated for land areas of the entire globe over a 25-yr period, using the quasi-isentropic back-trajectory (QIBT) method. The QIBT approach traces the air contributing to a precipitation event backward in time to map the most recent evaporative sources of the water vapor contributing to that event. Analysis is conducted on each land cell of a global 192 × 94 grid (1.875° longitude by approximately 1.9° latitude) on a pentad basis.

Precipitation recycling is a function of the analysis region’s total area, and cells defined by uniform intervals of latitude and longitude do not cover the same area on the earth’s surface. Recycling estimates for a variety of regions are found to scale approximately with the square root of area (area to the power 0.457). This allows us to compare recycling from different locations.

The result of the analysis is a time series of gridded recycling estimates for 4257 land grid cells, scaled to a common spatial extent (10⁵ km²), for 25 yr, from 1979 through 2003. Annual and seasonal averages are examined. In addition, the time series of 300 monthly values are subjected to standard time series analysis, including descriptive statistics, cycles, and trends.

Overall, the 25-yr global average recycling ratio for the10⁵ km² spatial extent is 4.5%. On both an annual and a seasonal basis, minima of recycling are observed in regions with strong advection from adjacent waters (e.g., the northern Amazon basin, Mississippi basin, and coastal monsoon regions in South Asia and northwestern Mexico). Recycling appears to be relatively high over much of South America south of the Amazon River through the La Plata basin, much of subtropical southern Africa, interior China, southern Europe (including the regions surrounding the Black Sea), western North America, and a broad swath of the high latitudes of the Northern Hemisphere, especially over eastern Siberia.

The global patterns of recycling on an annual and seasonal basis are compared with those derived using a bulk method based on time-averaged precipitation, evapotranspiration, and atmospheric water vapor transport (Trenberth 1999). The overall patterns are similar, in terms of the locations of minima and maxima, although there are differences in magnitude and detail. For compatible spatial scales, the QIBT method results in higher recycling estimates than the bulk method, as expected for a method that captures transient perturbations around the time-averaged values. A notable exception is northern South America, where the QIBT method gives lower recycling than the bulk method.

Monthly values are averaged across years to estimate an annual cycle of recycling. The high-latitude regions of the Northern Hemisphere, especially in the Pacific region, show a very strong annual cycle, as measured by the amplitude (maximum minus minimum). Regions with very low seasonal variations in recycling include much of the Amazon basin and adjacent Atlantic coastal regions of equatorial South America, the southern coast of Australia along the Great Australian Bight, areas to the west and northwest of the Persian Gulf, and two regions of the Nile basin, including the delta and parts of Ethiopia.

The coefficient of variation (COV) is computed for the 12 monthly values in the annual cycle. The COV allows us to identify locations where the annual cycle is significant related to the local mean, rather than in absolute terms. The arid regions stand out as having a high degree of seasonal variation, compared to their low mean values, whereas the Tropics are prominent as a region of low COV, with the lowest values over the southern Amazon basin and Mato Grosso, well south of the region of smallest absolute range.

Regions with strong interannual variability in recycling do not correspond directly to regions with strong intra-annual variability. The greatest interannual variability in recycling appears to occur during the dry season in regions with strongly seasonal precipitation regimes; this is consistent with erratic evapotranspiration supply following a variable rainy season.

Over the 25 yr of the study, high-latitude regions show positive trends in recycling during the boreal spring. There are also notable positive trends during SON over large areas of South Asia and southern Africa. Overall, there is a positive trend of 0.02% per year in the global mean annual recycling ratio, with the main contribution coming from the trends at high northern latitudes.

This work has produced a 25-yr time series of recycling on a monthly basis for all land areas excluding Antarctica. Model simplifications continue to hinder confidence in the results, most critically (a) the assumption that precipitation may be contributed by air parcels at any level in the atmosphere may instigate backtracking of air parcels that do not contribute precipitation at all in reality, and (b) the vertically well-mixed assumption in the treatment of evapotranspiration likely introduces spurious moisture supply into parcels traveling aloft. Further refinements, both in our method and in model representations of convection, will help to correct these issues. We intend to use this climatology as a baseline for validating a free-running GCM’s ability to simulate these patterns of recycling and source–sink patterns, and then to try to improve its water cycle simulation through systematic empirical correction of the GCM circulation and surface fluxes.

Differences between our approach and bulk methods (and other approaches for that matter) highlight the uncertainty that still exists in our understanding of the global atmospheric water cycle. The ideal way to construct such a climatology with current models and data is to have Lagrangian tracers of water explicitly within the reanalysis model. Then the trajectory and water budget calculations can be very precise yet be bounded by observations. However, accurate budgeting would require an approach to data assimilation different than that carried out by operational meteorological centers—one that adjusts fluxes rather than state variables so that water and energy balances are preserved. Such an approach could more accurately address the topic of climate change and its impact on the hydrologic cycle. In the meantime, these results will be useful in exploring associations between and among precipitation recycling, soil moisture memory, the persistence of anomalies, and climatic predictability. They also provide a new baseline for validating the ability of weather and climate models to simulate the global water cycle in the atmosphere and its variability.