Global characterization of the hydrologic cycle from a quasi-isentropic back-trajectory analysis

of atmospheric water vapor

Paul A. Dirmeyer

Kaye L. Brubaker*

COLA Technical Report 196

* Dept. Civil and Environmental Engineering, University of Maryland, College Park.

Abstract:

Regional precipitation recycling may constitute a feedback mechanism affecting soil moisture memory and the persistence of anomalously dry or wet states. Bulk methods, which estimate recycling based on time-averaged variables, have been applied on a global basis, but these methods 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 numerical model. The back-trajectory method has been applied to several large regions; in this paper it is extended to all global land areas for 1979-2003. Meteorological information (wind vectors, humidity, surface pressure and evaporation) are taken from the NCEP/DOE reanalysis And a hybrid 3-hourly precipitation data set is produced to establish the termini of the trajectories. The effect of grid size on the recycling fraction is removed using an empirical power-law relationship; 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 seasonal averages are consistent with previous estimates in terms of spatial patterns, but the trajectory method generally gives higher estimates of recycling than a bulk method, using compatible spatial scales. High northern latitude regions show the largest amplitude in the annual cycle of recycling, with maxima in late spring/early summer. Amplitudes in arid regions are small in absolute terms, but large relative to their mean values. Regions with strong interannual variability 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 by increases at high northern latitudes.

2

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 are shifting as a result of human-induced

land 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 advection

and convergence over land of water in the atmosphere. All fresh water 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 sub-optimal 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. 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. A change in regional evapotranspiration affects not only the supply of water

3

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:

qVF ≡ (1)

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:

VqVqF

VqVqVqVqF′′+=

′′+′+′+= (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.

4

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 pre-defined 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 data set) 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

5

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 sub-

basins 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 data sets 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.

6

2. Data Sets

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). The data are on a 192x94 grid (1.875° longitude by approximately 1.9°

latitude) and span the period from 1979 to present (2004). We make use of the sigma-level

diagnostics 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 as

surface pressure, precipitation and total evaporation. These data are used to calculate

precipitable water, potential temperature, and the advection of water vapor. In order 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 data sets are combined to produce a best estimate of precipitation sinks for

the back-trajectory calculation. A hybrid 3-hourly precipitation data set is produced in the

following way.

First, the reanalysis precipitation (6-hour forecast) is interpolated to a 3-houly 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 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-hour interval of the CMORPH data to establish the mean diurnal cycle of precipitation

7

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 0000UTC) 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 with time. 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 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 and

atmospheric data sets are all on the reanalysis grid and span the period from January 1979

through August 2004.

3. Methodology

Our approach uses a quasi-isentropic back-trajectory (QIBT) calculation of water vapor

backward in time 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)

8

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 backwards in time, starting with

observed precipitation at each grid box grouped into pentads (five-day intervals). This gives 73

pentads 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 45

minutes. The precipitation data are at a time resolution of three hours, so there are typically 40

precipitation intervals in each pentad across 120 time steps. If there is no precipitation over the

grid box during the pentad, no calculations are made. Otherwise, the five-day precipitation is

divided into 100 equal parcels, and for each percent of precipitation that occurs counting back

through the 3-hour total, a back trajectory is begun. So for instance, if all of the precipitation

occurs in the last 3-hour precipitation interval, then 25 parcels are launched in each of the first

four time steps. Fig 1a illustrates how a time series of precipitation is broken into a number of

parcels of equal water mass.

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 600hPa.

9

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 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.

At each time step, a fraction of the parcel is attributed to local evapotranspiration from the grid

box over which the parcel lies (see Fig 1c). The fraction of the parcel 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. Vertical mixing is proportional to the evaporation rate, as both are mainly driven by

the rate of surface radiative heating. Thus the stronger the evaporation, the better the

assumption. The parcel is traced back until at least 90% of its original mass is attributed to

evapotranspiration, or the 15-day period has been exceeded. The evaporative source masses

along the parcel’s path are then adjusted 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 data

set. 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.

10

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. Sudradjat (2002) 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 8x8 grid box

area is selected containing only land points. The recycling ratio for a 25-year period is

calculated. The region is then divided into two 4x8 sub-regions and the calculation is repeated

for each sub-region. This process is continued for four 4x4 sub-regions, and so on, down to 64

individual grid boxes. A scatter plot 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:

bAa=ρ (3)

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,

11

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 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-year 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 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

12

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-year climatology by season. We see that the robust recycling ratios at

high northern latitudes are a spring and summer phenomenon. In general recycling ratios are

higher during the local warm or wet season, and lower in winter or the dry season. Not all

monsoon regions show a strong primary annual cycle of recycling. For instance, there are peaks

during MAM and SON over India, and minima during the cores of the wet and dry seasons.

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

may be an artifact of the sporadic rain events in the region leading to statistically unstable

estimates. 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 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 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

13

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 Matto 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-year seasonal means, is shown season by season in Fig 7. 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 timescales. Instead we see strong

signals mainly in the dry regions in the subtropics and mid-latitudes 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-year 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 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

14

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.

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. 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 high northern latitudes. The implication is a small

intensification of the local hydrologic cycle.

5. Comparison to Bulk Calculations

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

ρ = Pm

P= EL

PL + 2F (4)

where ρ is the recycling ratio, defined as the fraction of total precipitation (P) contributed by

precipitation of local evaporative origin (Pm), E is evapotranspiration, and F the average

atmospheric moisture transport over the region. In Eq. (4), L is an assigned length scale. For

comparison to that study and to the QIBT recycling estimates obtained here, we have computed

recycling using Eq. (4) and the data set assembled for this study. 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

15

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 (Fig. 9) for comparison to Trenberth’s Figs 9 and 10. The

results were 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. Therefore, we can infer that

differences between the QIBT recycling results presented here and Trenberth’s (1999) bulk

estimates are due to the method, not to major differences in the input data.

In order 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. We selected a length scale of 340 km.

The bulk recycling results using Eq. (4) are shown in Fig 10. Fig 11 shows the fractional

difference between the QIBT estimates shown in Fig. 5 and the bulk estimates.

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 mid-latitude 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).

16

6. Conclusions

Precipitation recycling ratios are estimated for land areas of the entire globe over a 25-year

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 192x94 grid (1.875° longitude by approximately 1.9° latitude), on a pentad basis. When

the evaporative sources of a precipitation are mapped, that pentad’s recycling is computed as the

ratio of within-cell source to total precipitation depth (or mass).

Precipitation recycling is a function of the analysis region’s area, and cells defined by uniform

intervals of latitude and longitude do not have 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 years, 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-year 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.

17

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 twelve 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 Matto 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.

18

Over the 25 years 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-year 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 back-tracking 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. 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.

Acknowledgements: This work was supported by NSF awards EAR 02-35575 (Brubaker) and

EAR 02-33320 (Dirmeyer).

19

References:

Bosilovich, M. G., and S. D. Schubert, 2001: Precipitation recycling over the central United States diagnosed from the GEOS-1 data assimilation system. J. Hydrometeor., 2, 26-35.

Brubaker, K. L., D. Entekhabi, and P. S. Eagleson, 1993: Estimation of continental precipitation recycling. J. Climate, 6, 1077-1089.

Brubaker, K. L., P. A. Dirmeyer, A. Sudradjat, B. S. Levy, and F. Bernal, 2001: A 36-year climatology of the evaporative sources of warm-season precipitation in the Mississippi river basin. J. Hydrometeor., 2, 537-557.

Budyko, M. I., 1974: . Climate and Life, Academic Press, New York, 508 pp.

Burde, G. I., A. Zangvil, and P. J. Lamb, 1996: Estimating the role of local evaporation in precipitation for a two-dimensional region. J. Climate, 9, 1328-1338 .

Burde, G. I., and A. Zangvil, 2001: The estimation of regional precipitation recycling. Part I: Review of recycling models. J. Climate, 14, 2497-2508.

Dirmeyer, P. A., and K. L. Brubaker, 1999: Contrasting evaporative moisture sources during the drought of 1988 and the flood of 1993. J. Geophys. Res., 104, 19383-19397.

Eltahir, E. A. B., and R. L. Bras, 1994: Precipitation recycling in the Amazon Basin. Quart. J. Roy. Meteor. Soc., 120, 861-880 .

Giorgi, F., L. O. Mearns, C. Shields, and L. Mayer, 1996: A regional model study of the importance of local versus remote controls of the 1988 drought and the 1993 flood over the central United States. J. Climate, 9, 1150-1162.

Henderson-Sellers, A., K. McGuffie, and H. Zhang, 2002: Stable isotopes as validation tools for global climate model predictions of the impact of Amazonian deforestation. J. Climate, 15, 2664-2677.

Joyce, R. J., J. E. Janowiak, P. A. Arkin, and P. Xie, 2004: CMORPH: A method that produces global precipitation estimates from passive microwave and infrared data at high spatial and temporal resolution. J. Hydrometeor., 5, 487-503.

Kanamitsu, M., W. Ebisuzaki, J. Woollen, S.-K. Yang, J. J. Hnilo, M. Fiorino, and G. L. Potter, 2002: NCEP-DOE AMIP-II reanalysis (R-2). Bull. Amer. Meteor. Soc., 83, 1631-1648.

Kurita, N., N. Yoshida, G. Inoue, and E. A. Chayanova, 2004: Modern isotope climatology of Russia: A first assessment . J. Geophys. Res., 109, D03102, doi:10.1029/2003JD003404.

Lettau, H., K. Lettau, and L. C. B. Molion, 1979: Amazonia's hydrologic cycle and the role of atmospheric recycling in assessing deforestation effects. Mon. Wea. Rev., 107, 227-238.

Merrill, J. T., R. Bleck, and D. Boudra, 1986: Techniques of Lagrangian trajectory analysis in isentropic coordinates. Mon. Wea. Rev., 114, 571-581.

Numaguti, A., 1999: Origin and recycling processes of precipitating water over the Eurasian continent: Experiments using an atmospheric general circulation model. J. Geophys. Res., 104, 1957-1972.

20

Reale, O., L. Feudale, and B. Turato, 2001: Evaporative moisture sources during a sequence of floods in the Mediterranean region. Geophys. Res. Let., 28, 2085-2088.

Schultz, S.K. and W.P. Tishler, 2004. “Which Old West and Whose?” in “American History 102: Civil War to the Present,” University of Wisconsin, http://us.history.wisc.edu/ hist102/ weblect/lec03/03_02.htm (accessed 6/2005).

Serreze, M. C., J. E. Walsh, F. S. Chapin III, T. Osterkamp, M. Dyurgerov, V. Romanovsky, W. C. Oechel, J. Morison, T. Zhang, and R. G. Barry, 2000: Observational Evidence of Recent Change in the Northern High-Latitude Environment. Climatic Change, 46, 159-207.

Sudradjat, A., 2002: Source-sink analysis of precipitation supply to large river basins. PhD Dissertation, [Available from University of Maryland, College Park, MD 20742, U.S.A.], 186 pp..

Sudradjat, A., K. L. Brubaker, and P. A. Dirmeyer, 2003: Interannual variability of surface evaporative moisture sources of warm-season precipitation in the Mississippi River Basin.. J. Geophys. Res., 108, doi: 10.1029/2002JD003061.

Trenberth, K. E., 1999: Atmospheric moisture recycling: Role of advection and local evaporation. J. Climate, 12, 1368-1381.

Trenberth, K. E., A. Dai, R. M. Rasmussen, and D. B. Parsons, 2003: The changing character of precipitation. Bull. Amer. Meteor. Soc., 84, 1205-1217.

Tucker, C. J., D. A. Slayback, J. E. Pinzon, S. O. Los, R. B. Myneni, M. G. Taylor, 2001: Higher northern latitude normalized difference vegetation index and growing season trends from 1982 to 1999. Int. J. Biometeor., 45, 184-190.

Turato, B., O. Reale, and F. Siccardi, 2004: Water vapor sources of the October 2000 Piedmont flood. J. Hydrometeor., 5, 693-712.

Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc., 78, 2539-2558.

21

Figure Captions: 1. Schematic of (a) the division of precipitation over a pentad into “parcels” of equal

amount; (b) the launching of parcels at random x-y locations and elevations of a

humidity-weighted vertical coordinate over a grid box (humidity indicated by the curve

labeled q); (c) the apportionment of water vapor in a parcel from a precipitation event to

evaporation during earlier time intervals along the isentropic back-trajectory path, and the

resulting depletion of water accounted for in the parcel.

2. Estimated recycling ratios as a function of area over three of the test regions from Table

1, the average values for each scale, and the best fit regression curve through the average

values.

3. The scaling regression curves from all test regions, and the curve through the arithmetic

mean of the recycling ratios at each scale.

4. The 25-year annual mean recycling ratio (%) at a representative spatial scale of 105km2.

5. As in Fig 4 for individual seasons.

6. The range of the 25-year mean climatological annual cycle (maximum minus minimum

monthly recycling ratios), the standard deviation among the 25-year mean for each

month, and the coefficient of variation (panel marked SD divided by Fig 4).

7. Interannual variation of seasonal mean recycling ratios expressed as coefficient of

variation (interannual standard deviations divided by Fig 5).

8. Trends in recycling ratio (% per year) during the 25-year period. Red and blue shading

show regions with significant trends at the 95% confidence limit; pale yellow and green

shading show trends that are not significant.

9. Bulk recycling ratio as computed using Trenberth’s (1999) formula, using representative

length scales of (a) 1000 km and (b) 500 km.

10. Bulk recycling ratio as computed using Trenberth’s (1999) formula, using a

representative length scale of 340 km, for comparison to Fig. 4.

11. Difference between QIBT (Fig. 4) and bulk (Fig. 10) recycling estimates, expressed as a

fraction of the bulk estimate.

22

ρρρρ = a A b Recycling Ratio ρρρρ for Area (km2)

Region SW corner a b 104 105 106

Mackenzie (131,77) 0.102 0.424 5.1% 13.4% 35.6%

Khatanga (54,80) 0.089 0.433 4.8% 13.0% 35.2%

E. Europe (14,73) 0.057 0.448 3.5% 9.8% 27.6%

LaPlata (158,31) 0.061 0.437 3.4% 9.4% 25.7%

Kalahari (10,33) 0.018 0.533 2.5% 8.6% 28.9%

Ob (33,73) 0.041 0.461 2.8% 8.2% 23.7%

China (56,60) 0.046 0.439 2.6% 7.2% 19.7%

Talimakan (44,65) 0.056 0.415 2.6% 6.7% 17.4%

Congo (8,44) 0.025 0.481 2.1% 6.4% 19.4%

Mississippi (139,65) 0.031 0.461 2.2% 6.2% 18.0%

Australia (71,31) 0.011 0.524 1.3% 4.4% 14.7%

Amazon (155,44) 0.016 0.470 1.2% 3.7% 10.8%

Persia (30,62) 0.014 0.462 1.0% 3.0% 8.6%

W. Sahara (189,56) 0.012 0.474 1.0% 2.9% 8.6%

Mean (a,b) 0.0414 0.462 2.9% 8.4% 24.3%

Std (a,b) 0.0278 0.033

COV (a,b) 0.671 0.072

Mean RR 0.0440 0.457 3.0% 8.5% 24.3% Table 1. The locations of test regions (8x8 grid boxes on the reanalysis grid) for determining the scaling of the recycling ratio, the coefficients of the power law relationship found by regression for each region, and the effective recycling ratio for three different reference region sizes in each location. Overall statistics are shown at the bottom of the table.

23

Fig 1. Schematic of (a) the division of precipitation over a pentad into “parcels” of equal amount; (b) the launching of parcels at random x-y locations and elevations of a humidity-weighted vertical coordinate over a grid box (humidity indicated by the curve labeled q); (c) the apportionment of water vapor in a parcel from a precipitation event to evaporation during earlier time intervals along the isentropic back-trajectory path, and the resulting depletion of water accounted for in the parcel.

a

b

c

24

Fig 2. Estimated recycling ratios as a function of area over three of the test regions from Table

1, the average values for each scale, and the best fit regression curve through the average values.

25

Fig 3. The scaling regression curves from all test regions, and the curve through the arithmetic

mean of the recycling ratios at each scale.

26

Fig 4. The 25-year annual mean recycling ratio (%) at a representative spatial scale of 105km2.

27

Figure 5. As in Fig 4 for individual seasons.

28

Figure 6. The range of the 25-year mean climatological annual cycle (maximum minus minimum monthly recycling ratios), the standard deviation among the 25-year mean for each month, and the coefficient of variation (panel marked SD divided by Fig 4).

29

Figure 7. Interannual variation of seasonal mean recycling ratios expressed as coefficient of

variation (interannual standard deviations divided by Fig 5).

30

Figure 8. Trends in recycling ratio (% per year) during the 25-year period. Red and blue shading show regions with significant trends at the 95% confidence limit; pale yellow and green shading show trends that are not significant.

31

Figure 9. Bulk recycling ratio as computed using Trenberth’s (1999) formula, using

representative length scales of (a) 1000 km and (b) 500 km.

32

Figure 10. Bulk recycling ratio as computed using Trenberth’s (1999) formula, using a

representative length scale of 340 km, for comparison to Fig. 4.

33

Figure 11. Difference between QIBT (Fig. 4) and bulk (Fig. 10) recycling estimates, expressed

as a fraction of the bulk estimate.