Paul A. Dirmeyer Kaye L. Brubaker 04 / 15 / 2008

1. Characterization of the Global Hydrologic Cycle from a Back-Trajectory Analysis of Atmospheric Water Vapor Paul A. Dirmeyer Kaye L. Brubaker 04 / 15 / 2008

2. Recycling Ratio • Definition: 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. • The recycling ratio is a diagnostic measure of the potential for interactions between land surface hydrology and regional climate. • 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.

3. Bulk Methods • The bulk approach assumes that locally evaporated and externally advected moisture are well mixed in the air over the region of interest. • One major drawback: contain an atmospheric moisture flux term at the lateral boundaries defined as the product of two time-mean quantities—wind and humidity In actuality, perturbational expansion yields nonlinear term can be quite significant and has much of its signal on the time scale of synoptic waves.

4. Other Methods • Another drawback: must be calculated over predefined volumes using the wind and humidity information along the boundaries. Fine for calculating a single value over a large area, but difficult to produce a continuous map over a continent or the globe. • The most direct way of estimating recycling is to track the water vapor in the air from source (evapotranspiration) to sink (precipitation). (Isotopic Analysis) • Tracer modeling drawback: adds to the computational cost; any changes require a complete reintegration of the general circulation model; errors in the model climate contribute errors in the estimates of the hydrologic cycle.

5. Back-Trajectory Analysis Methodology • This approach uses a quasi-isentropic calculation of trajectories of water vapor backward in time (QIBT) from observed precipitation events, using atmospheric reanalysis to provide meteorological data for estimating the altitude, advection, and incremental contribution of evaporation to the water participating in each precipitation event. • It 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.

6. Chose an interval of 45 min to ensure statistical stability of results at minimum computational expense. • Trajectories are calculated first backward then forward and the average is taken to minimize the impact of interpolation errors in rapidly evolving or highly rotational flows. • Assume that the diabatic processes approximately balance out along the path between the highly diabatic surface evaporation and terminal precipitation events. • Assume that the water evaporated from the surface mixes uniformly through the atmospheric column within the period of the time step Fig 1. Schematic of (a) the division of precipitation over a pentad into increments of equal amount to be assigned to advected parcels; (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.

8. Fig. 3. The scaling regression curves from all test regions, and (bold) the curve through the arithmetic mean of the recycling ratios at each scale. Fig. 2. Estimated recycling ratios as a function of area from subregions over three of the test regions from Table 1, the average values for each scale (filled squares), and the best-fit regression line through the average values.

9. 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. • Relative minima in regions with strong advection from adjacent waters. • Recycling appears to be relatively high over much of South America south of the Amazon River all the way through the La Plata basin, etc.

10. Unshaded areas in seasonal maps occur over deserts where no precipitation is reported in the multiyear analysis. Recycling ratios are higher during the local warm or wet season, and lower in winter or the dry season. Robust recycling ratios at high northern latitudes are a spring and summer phenomenon.

11. 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.

12. At lower latitudes, high values in arid regions and low in the deep Tropics. Large mean and seasonal variability signals at high northern latitudes are not evident at interannual time scales. Strong signals mainly in the dry regions in the subtropics and midlatitudes that lie outside the rainbelts for a given season. 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.

13. A patchy distribution of weak but significant positive trends during boreal winter over Canada and the northern United States. 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.

14. 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 Saharain 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).

15. Conclusions • Overall, the 25-yr global average recycling ratio for the 105 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. • The overall patterns are similar, compared with those derived using a bulk method, in terms of the locations of minima and maxima, although there are differences in magnitude and detail. • Regions with strong interannual variability in recycling do not correspond directly to regions with strong intra-annual variability.