Characterization of the global hydrologic cycle from a back-trajectory analysis of atmospheric water vapor

Theeffect of grid size on the recycling fraction is removed using an empirical power-lawrelationship; this allows comparison among any land areas on a latitude/longitude grid.Recycling r

Characterization of the global hydrologic cycle from a back-trajectory analysis of atmospheric

water vapor

Paul A Dirmeyer1Kaye L Brubaker2

J Hydrometeorology Submitted:21 September 2005Revised: 6 May 2024

1Center for Ocean-Land-Atmosphere Studies, Calverton, Maryland

2 Dept Civil and Environmental Engineering, University of Maryland, College Park

1

Regional precipitation recycling may constitute a feedback mechanism affecting soil moisturememory and the persistence of anomalously dry or wet states Bulk methods, which estimaterecycling based on time-averaged variables, have been applied on a global basis, but thesemethods may underestimate recycling by neglecting the effects of correlated transients A back-trajectory method identifies the evaporative sources of vapor contributing to precipitation events

by tracing air motion backward in time through the analysis grid of a data-assimilating numericalmodel The back-trajectory method has been applied to several large regions; in this paper it isextended to all global land areas for 1979-2003 Meteorological information (wind vectors,humidity, surface pressure and evaporation) are taken from the NCEP/DOE reanalysis Aand ahybrid 3-hourly precipitation data set is produced to establish the termini of the trajectories Theeffect of grid size on the recycling fraction is removed using an empirical power-lawrelationship; this allows comparison among any land areas on a latitude/longitude grid.Recycling ratios are computed on a monthly basis for a 25 year period The annual and seasonalaverages are consistent with previous estimates in terms of spatial patterns, but the trajectorymethod generally gives higher estimates of recycling than a bulk method, using compatiblespatial scales High northern latitude regions show the largest amplitude in the annual cycle ofrecycling, with maxima in late spring/early summer Amplitudes in arid regions are small inabsolute terms, but large relative to their mean values Regions with strong interannualvariability in recycling do not correspond directly to regions with strong intra-annual variability.The average recycling ratio at a spatial scale of 105 km2 for all land areas of the globe is 4.5%; on

a global basis, recycling shows a weak positive trend over the 25 years, driven largely byincreases at high northern latitudes

1 Introduction

Understanding of the global hydrologic cycle is critical because all terrestrial life depends onlocal water resources, and the supply of these resources are shifting as a result of human-inducedland use and water use changes, and climate variations In order to maintain hydrologic balance,the water that flows into the oceans by the discharge of rivers must be matched by the advectionand convergence over land of water in the atmosphere All fresh water on or beneath the landsurface 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 singlewater molecule to work its way from the ocean to a given terrestrial location, with evaporationfrom the land surface or transpiration through the terrestrial biosphere occurring in theintermediate cycles Unlike over the oceans, evapotranspiration over land is usually limited to arate less than the maximum potential rate due to stresses such as those caused by low soilmoisture or sub-optimal conditions for photosynthesis in plants Therefore, changing landsurface conditions, whether caused directly by land use polices or as a response to fluctuations ortrends in climate, can impact the hydrologic circuit between land and atmosphere by changingevapotranspiration rates Certain regions of the globe appear to be particularly sensitive to suchfeedbacks (Koster et al 2004) This is an important topic of research with applications forimproving prediction (Trenberth et al 2003)

One of the principal yardsticks for quantifying the strength of the hydrologic cycle over specificterrestrial 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 fromthat 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 achange to evaporation over the area of concern has a direct and predictable impact on localprecipitation Of course, there are other feedbacks in the system, and in many parts of the

world they may dominate A change in regional evapotranspiration affects not only the supply ofwater carried by the circulation of the atmosphere, but can thermodynamically alter theatmosphere itself by changing the partitioning of surface heat fluxes, triggering changes to thecirculation patterns as well Nevertheless, the basic linear model behind many people’sconception 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 formulationswere 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 variousmethods that have been used The bulk approach makes several assumptions, such as that locallyevaporated 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 andhumidity:

V q V q F

V q V q V q V q F

′

′ +

=

′

′ +

′ +

′ +

=

(2)

1 Schultz and Tishler (2004) attribute the spread of this idea partly to the amateur scientist C.D

Wilber’s 1881 book, The Great Valleys and Prairies of Nebraska and the Northwest.

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

Another drawback of the bulk approach is that it must be calculated over pre-defined volumesusing the wind and humidity information along the boundaries That is fine for calculating asingle value for recycling ratio over a large area (large relative to the number of observationsalong the boundary or more typically, the number of grid boxes from a gridded data set) butmakes 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 localvariables 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 fromsource (evapotranspiration) to sink (precipitation) Isotopic analysis of precipitation candifferentiate between moisture that has evaporated from open water from that which has passedthrough the vascular systems of plants For example, Henderson-Sellers et al (2002) showedhow the isotopic ratios change as one moves upstream along the Amazon (showing theincreasing 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 analysiscannot pinpoint the location of the evaporation that contributed the moisture It can only providethe proportions of likely sources differentiated into broad categories

Tracer modeling provides a means to follow exactly the path of water within an atmosphericmodel Druyan and Koster (1989) were among the first to apply this Lagrangian approach towater vapor for the Sahel This method has been applied over the central United States inregional (Giorgi et al 1996) and global models (Bosilovich and Schubert 2001), and over

Eurasia (Numaguti 1999) Although more spatially precise than isotopic tracers, tracer modelinghas 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 hasproblems to be solved, such as reconciling the lack of conservation within a system where statevariables are assimilated (as is the case with all of today’s operational analysis and reanalysisefforts) with the need for a completely closed water budget within an analysis of the hydrologiccycle

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 basins of the Mississippi River basin, Sudradjat et al (2003) extended the study to interannualvariations, and Sudradjat (2002) applied the approach to the Amazon Basin The method hasalso been applied to examine moisture sources for specific extreme precipitation events over theMediterranean basin (Reale et al 2001, Turato et al 2004), and to validate isotopic analyses overRussia (Kurita et al 2004) Here we extend the analysis of Brubaker et al (2001) to all landareas of the globe The data sets used in the analysis are described in Section 2 Section 3explains the methodology, with an emphasis on changes to the original approach described inDirmeyer and Brubaker (1999) and the universality of scaling that allows us to comparerecycling over regions of differing areas The global climatology of recycling, includinganalyses of variability and trends, is given in Section 4 In Section 5 we compare this calculation

sub-to bulk estimates using the method of Trenberth (1999) Conclusions are presented in Section 6

2 Data Sets

All meteorological data except for observed precipitation come directly from the NationalCenters for Environmental Prediction (NCEP) / Department of Energy (DOE) reanalysis(Kanamitsu et al 2002) These data are on a 192x94 grid (1.875° longitude by approximately1.9° latitude) and span the period from 1979 to present (2004) We make use of the sigma-leveldiagnostics and surface flux fields at 6-hour intervals Specifically, the fields used are humidity,temperature, and wind (u and v components) all on the 16 lowest model sigma levels; as well assurface pressure, precipitation and total evaporation These data are used to calculateprecipitable water, potential temperature, and the advection of water vapor In order to avoidspurious excess convergence toward the poles, the meridional wind is scaled by the cosine oflatitude The land-sea mask from the reanalysis is also used to differentiate land grid boxes forthe calculation The data are linearly interpolated in time to the time step of the trajectorymethodology Trajectories are calculated both forward and backward following Merrill et al.(1986) to minimize the impact of interpolation errors in rapidly evolving or highly convergentflows

Several precipitation data sets are combined to produce a best estimate of precipitation sinks forthe back-trajectory calculation A hybrid 3-hourly precipitation data set is produced in thefollowing way

First, the reanalysis precipitation (6-hour forecast) is interpolated to a 3-houly amount Largeerrors are known to exist in the reanalysis estimates of precipitation – we use it primarily toestablish the position and movement of large-scale rainfall events, such as those associated withextratropical baroclinic systems

We then use the satellite-based CMORPH precipitation estimates (Joyce et al 2004) to correctthe 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 reanalysisgrid using simple bilinear interpolation A centered 31-day running mean is then calculated foreach 3-hour interval of the CMORPH data to establish the mean diurnal cycle of precipitationand its variation throughout the year At the time these analyses were performed, less than twoyears of CMORPH data were available Only data from March 2003 through April 2004 havebeen used For each day (delineated by 0000UTC) at low latitudes, the reanalysis precipitation isreplaced by the CMORPH mean diurnal cycle for that day, scaled to retain the total daily rainfallfrom the reanalysis The definition of “low latitude” for precipitation also varies withtimethroughout the year as the changing seasons bring different parts of the globe intosubtropical and mid-latitude weather regimes The CMORPH correction to the diurnal cycle isonly applied to a zonal band 60° wide, spanning 30° north and south of the latitude of solardeclination This limitation is meant to focus the correction on regions where precipitation ismost strongly diurnally forced (e.g., convection driven by solar heating) and not to alter theprecipitation where synoptic variations are predominant.

At this point in the process, each grid box of the globe contains what we deem to be the bestestimate of the local temporal distribution of precipitation within weather time scales The finalstep is to scale the precipitation fields one more time, using the observationally-based pentadestimates of Xie and Arkin (1997) The final scaling results in a hybrid model-observationalprecipitation product that retains the pentad mean values from Xie and Arkin (1997), but the sub-pentad 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 andatmospheric data sets are all on the reanalysis grid and span the period from January 1979through August 2004

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 providemeteorological data for estimating the altitude, advection, and incremental contribution ofevaporation 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) describehow the climatologies are calculated Here we give a qualitative description of the method, andrefer the reader to those previous papers for details.

The method relies on the use of high time resolution (daily or shorter) precipitation andmeteorological data to include the effects of transients on the transport of water vapor.Calculations are performed on the reanalysis grid, working backwards in time, starting withobserved precipitation at each grid box grouped into pentads (five-day intervals) This gives 73pentads per year During leap years a 6-day interval is used for the twelfth pentad, to include the

29th of February The method can run on a range of time steps – we chose an interval of 45minutes to ensure statistical stability of results at minimum computational expense At thespatial scale of the reanalysis data, we find that a time step of an hour orless produces stable results (i.e., the evaporative source regions do notchange 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 amass-conserving interpolation Trajectories are calculated first backward then forward and theaverage is taken following Merrill et al (1986) to minimize the impact of interpolation errors inrapidly evolving or highly rotational flows

The precipitation data are at a time resolution of three hours, so there are typically 40precipitation data intervals in each pentad across 1620 time steps If there is no precipitationover the grid box during the pentad, no calculations are made Otherwise, the five-dayprecipitation is divided into 100 equal parcelsincrements, and for each percent of precipitationthat occurs counting back through the 3-hour total, a back trajectory of its corresponding

atmospheric parcel is begun So for instance, if all of the precipitation occurs in the last 3-hourprecipitation interval of the pentad, then 25 parcels are launched in each of the first four timesteps counting backwards in the back-trajectory scheme Fig 1a illustrates schematically how atime series of precipitation is broken into a number of parcels of 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 withinthe grid box The altitude of the parcel is chosen randomly using the partial pressure of watervapor as a vertical coordinate, counting only the lowest 16 sigma layers This ensures that mostparcels are launched from relatively low altitudes, within the boundary layer This carries with itthe assumption that every molecule of water vapor within the tropospheric column is equallylikely to precipitate Since specific humidity drops rapidly with height, rarely are parcelslaunched above 600hPa

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 parcelsare advected on isentropic (theta) surfaces following the numerics of Merrill et al (1986) withthe exception that when a parcel is tracked back into the ground, its potential temperature isadjusted to the mean value of the boundary layer, to simulate the effect of surface sensible heatflux on the parcel This is a strong simplification – we assume that the diabaticprocesses (latent heat release and consumption from cloud formation anddissipation, PBL heating and radiational cooling) approximately balance outalong the path between the highly diabatic surface evaporation and terminalprecipitation events Given the limitations of the reanalysis data we stick tothe kinematic elements of the system Ideally for calculation of a recyclingclimatology 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 localevapotranspiration from the grid box over which the parcel lies (see Fig 1c) The method is notsensitive to random errors in evaporation, but systematic errors can affect the results of thecalculation (Sudradjat 2002) The fraction of the precipitaiton incrementarcel is set equal to thegrid box evapotranspiration (rate integrated over the time step) divided by the columnprecipitable water This mass is removed from the parcel before calculating the next advectioninterval, and added to the evaporative source from that grid box This approach invokes anotherassumption (probably the weakest in the method) that the water evaporated from the surfacemixes uniformly through the atmospheric column within the period of the time step This is not

an entirely bad assumption Strong vVertical mixing is proportional to the typically accompanieshigher evaporation rates, as both are mainly driven by the rate of surface radiative heating in thedaily growth of the PBL, as well as by mechanical processes in the event of strong low-levelwinds There may be synoptic situations leading to strong mixing without high evaporationrates, but generally not the reverse Thus the stronger the evaporation, the better will be theassumption The way the method is constructed, the water accounted for in each parcelassymtotically converges to zero, so some cutoff must be applied The parcel is traced backuntil at least 90% of its original mass precipitation increment is attributed to evapotranspiration,

or the 15-day period has been exceeded The evaporative source masses along the parcel’s pathare then adjusted scaled to account for the residual water, so that the total precipitation mass isaccounted for in the integral of all evaporative sources

This process is repeated for all parcels in the pentad to create a two-dimensional distribution ofevaporative 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 sourcedistributions 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 thebounds of the sink region.

Because of its definition, the recycling ratio  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 necessarilyreduces 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,  goes to one

(assuming an insignificant net gain or loss of water to space compared to the total precipitationflux)

This discrepancy would make it difficult to compare the recycling between two regions thatenclose different total areas Sudradjat (2002) showed a strong log-log relationship betweenrecycling ratio and area for the Mississippi Basin We have tested the scalability of recyclingover 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 8x8 grid boxarea is selected containing only land points The recycling ratio for a 25-year period iscalculated The region is then divided into two 4x8 sub-regions and the calculation is repeatedfor each sub-region This process is continued for four 4x4 sub-regions, and so on, down to 64individual grid boxes A scatter plot of recycling ratio as a function of area is produced for eachregion 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  and A for each set of subregions:

b A a

=

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

given, 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 gives a slightly lower curve (bold line in Fig 3) than the mean of thecoefficients (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

of the fine structure of the orography may also contribute to errors in moisture advection andprecipitation patterns in the analyses (e.g., Evans et al 2004), degradimpacting our estimates ofrecycling ratio in mountainous areas The other features are likely genuine, such as the relativeminima 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 Riverall 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 abroad swath of the high latitudes of the Northern Hemisphere, especially over eastern Siberia.Figure 5 separates the 25-year climatology by season Unshaded areas in seasonal maps mayoccur over deserts where no precipitation is reported in the multi-year analysis We see that therobust recycling ratios at high northern latitudes are a spring and summer phenomenon Ingeneral recycling ratios are higher during the local warm or wet season, and lower in winter orthe dry season Not all monsoon regions show a strong primary annual cycle of recycling Forinstance, there are peaks during MAM and SON over India and parts of Southeast Asia, andminima during the cores of the wet and dry season (and dry season for India) This contrastswith the monsoon regions of North America, northern Australia and the Sahel, where recyclingpeaks during the wet season Over South America south of the Amazon Basin, the regionexperiences more of an expansion and contraction of the area of high recycling, with theminimum attained during the dry season Recycling over the Amazon Basin reaches a peakduring SON, but the peak is during DJF over the Pampas and Pantanal regions Beyond theprevalent orographic recycling peaks, relatively high values are attained during JJA overAnatolia, the headwaters of the Ob and Yenisey rivers of central Asia, and the Mackenzie RiverBasin in northwestern Canada By this calculation, recycling rates over the northern Amazonbasin during the wet season are as low as over many desert regions, because of the strongadvection of maritime moisture from over the tropical Atlantic

Figure 6 shows the degree of seasonality in recycling ratio over the globe using several differentmetrics 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 strongannual 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

may beis an artifact of the rare sporadic rain events in the region leading to statistically unstableestimates, particularly when the observed and reanalysis precipitation (and thus reanalysisevaporation) are not synchronized The high values on the east coast of Greenland are alsocaused by large discrepancies between observed and reanalysis precipitation, making theevaporation (and thus the recycling ratio) very high More revealing are theregions with very low seasonal variations in recycling This includes much of the Amazon basinand adjacent Atlantic coastal regions of equatorial South America, the southern coast ofAustralia 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 thestandard deviation of the 12 monthly mean values of climatological recycling ratio (center panel)portrays a similar picture

The coefficient of variation (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 ahigh degree of seasonal variation, compared to their low mean values (see Fig 4) In addition toparts of northwestern North America and northeastern Asia, there are also regions of theSouthern Hemisphere with relatively high COV, including northwestern Australia, South Africaand South America south of 20°S The tropics as a whole are prominent as a region of lowCOV, with the lowest values over the southern Amazon basin and Matto Grosso, well south ofthe region of smallest absolute range There are also many interesting regional features, like thechain 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 relativemaximum in the North American monsoon region

The pattern of interannual variability, expressed as the COV of seasonal recycling ratios asnormalized by the 25-year seasonal means, is shown season by season in Fig 7 (unshaded areasare 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 andseasonal variability signals at high northern latitudes are not evident at interannual timescales.Instead we see strong signals mainly in the dry regions in the subtropics and mid-latitudes that lieoutside the rainbelts for a given season For example, during JJA the highest values ofinterannual COV lie over the dry-season monsoon regions of South America, southern Africaand northern Australia, as well as to the north of the Asian and Sahel monsoon regions and thesouthern Rockies Excluding the very high values over the Sahara, Arabia and Gobi deserts, theCOV 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 fromthe previous season’s rainfall

Trends in recycling ratio, expressed as percent per year over the 25-year span, are shown inFig 8 The trend is computed from the slope of the linear regression on the mean values fromeach season Significance of trends is calculated using the Cox-Stuart test with a confidencelevel of 95% There is a patchy distribution of weak but significant positive trends during borealwinter over Canada and the northern United States, but in boreal spring there is a broad region ofstrong increases in recycling over Canada, Alaska, Fennoscandia and the Arctic coast of easternSiberia, with sporadic small regions of positive and negative trends elsewhere The high-latitudepositive trends are consistent with the warming and extended growing season trends in theseareas (Serreze et al 2000, Tucker et al 2001) These trends carry over somewhat into JJA overNorth 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 thedeserts during SON in Fig 7 are also manifested as strong but statistically insignificant trendscause by sporadic infrequent rainfall events there There are also notable positive trends duringSON over large areas of South Asia and southern Africa (also present during DJF), and a kind ofdipole over South America with decreasing recycling in a band from Peru to southern Brazil, andpositive trends to the south Overall, there is a positive trend in the global mean annual mean

recycling ratio of 0.02% per year, with the main contribution coming from the trends at highnorthern latitudes The implication is a small intensification of the local hydrologic cycle inseveral areas

5 Comparison to Bulk Calculations

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

Differences between these studies could be due to the method or the data, or both Forcomparison to that study and to the QIBT recycling estimates obtained here, we have computedrecycling using Eq (4) and the data set assembled for this study This willshould pinpointdifferences in the data Differences could be due to the method or the data, or both

Trenberth (1999) obtained seasonal P from the Xie-Arkin product for 1979-1995, seasonal E from the NCEP/NCAR reanalyses (6-hour 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 monthlybasis, 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 thetwo different length scales are included (Figure 9b) for compareison directly to Trenberth’s

Figs 9 and 10 (we have even applied the same smoothing to T31) Figure 9a is analogous toTrenberth’s Fig 9 The results were are quite similar, with slightly lower recycling values in ourcase likely because of lower evaporation rates in the tropics and generally higher wind speedsover land in the NCEP/DOE reanalysis compared to the NCEP/NCAR reanalysis The two bulkestimates are particularly similar in pattern over the Americas and eastern Siberia, but there areimportant 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 hereand Trenberth’s (1999) bulk estimates are due only to the method, not to major differences in theinput data 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 alsocontributing to the dissimilarities

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

According to Trenberth’s (1999) perturbation analysis, we would expect recycling estimates toincrease when the estimation method captures transients in precipitation, evapotranspiration, andvapor transport In general, our results confirm this prediction For most of the globe, the QIBTrecycling exceeds the bulk recycling Over most mid-latitude regions, the difference is less than70% of the bulk value; however, in locations where the bulk recycling is quite low, such as theSahara 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 (allseasons) and equatorial Africa (DJF)