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

1 Characterization of the global hydrologic cycle from a back-trajectory analysis of atmospheric water vapor 10 11 12 13 14 15 16 17 Paul A Dirmeyer1 18 19 20 Kaye L Brubaker2 21 22 23 24 25 26 27 28 J Hydrometeorology 29 Submitted:21 September 2005 30 Revised: 20 October 2022 311Center for Ocean-Land-Atmosphere Studies, Calverton, Maryland 12 Dept Civil and Environmental Engineering, University of Maryland, College Park 1Abstract: 2Regional precipitation recycling may constitute a feedback mechanism affecting soil moisture 3memory and the persistence of anomalously dry or wet states Bulk methods, which estimate 4recycling based on time-averaged variables, have been applied on a global basis, but these 5methods may underestimate recycling by neglecting the effects of correlated transients A back- 6trajectory 7by method identifies the evaporative sources of vapor contributing to precipitation events tracing air motion backward in time through the analysis grid of a data-assimilating numerical 8model The back-trajectory method has been applied to several large regions; in this paper it is 9extended to all global land areas for 1979-2003 Meteorological information (wind vectors, 10humidity, surface pressure and evaporation) are taken from the NCEP/DOE reanalysis Aand a 11hybrid 3-hourly precipitation data set is produced to establish the termini of the trajectories The 12effect of grid size on the recycling fraction is removed using an empirical power-law 13relationship; 14Recycling 15averages 16method 17spatial generally gives higher estimates of recycling than a bulk method, using compatible scales High northern latitude regions show the largest amplitude in the annual cycle of 19absolute in recycling not correspond directly to regions with strong intra-annual variability average recycling ratio at a spatial scale of 10 km2 for all land areas of the globe is 4.5%; on global basis, recycling shows a weak positive trend over the 25 years, driven largely by 23increases with maxima in late spring/early summer Amplitudes in arid regions are small in terms, but large relative to their mean values Regions with strong interannual 20variability 22a ratios are computed on a monthly basis for a 25 year period The annual and seasonal are consistent with previous estimates in terms of spatial patterns, but the trajectory 18recycling, 21The this allows comparison among any land areas on a latitude/longitude grid at high northern latitudes 11 Introduction 2Understanding of the global hydrologic cycle is critical because all terrestrial life depends on 3local water resources, and the supply of these resources are shifting as a result of human-induced 4land use and water use changes, and climate variations In order to maintain hydrologic balance, 5the water that flows into the oceans by the discharge of rivers must be matched by the advection 6and convergence over land of water in the atmosphere All fresh water on or beneath the land 7surface arrived as precipitation, and ultimately all of that water was evaporated from the oceans 8However, 9water 10from it may have taken multiple “cycles” of precipitation and evaporation for any single molecule to work its way from the ocean to a given terrestrial location, with evaporation the land surface or transpiration through the terrestrial biosphere occurring in the 11intermediate 12rate cycles Unlike over the oceans, evapotranspiration over land is usually limited to a less than the maximum potential rate due to stresses such as those caused by low soil 13moisture 14surface 15trends or sub-optimal conditions for photosynthesis in plants conditions, whether caused directly by land use polices or as a response to fluctuations or in climate, can impact the hydrologic circuit between land and atmosphere by changing 16evapotranspiration 17feedbacks rates Certain regions of the globe appear to be particularly sensitive to such (Koster et al 2004) 18improving prediction (Trenberth 19One et al 2003) regions is the recycling ratio Definitions can vary slightly, but commonly it is taken be the fraction of precipitation over a defined area that originated as evapotranspiration from 22that same area, with no intervening cycles of precipitation or surface evapotranspiration 23Conceptually 24change the recycling ratio has been appealing In the simplest sense one imagines that a to evaporation over the area of concern has a direct and predictable impact on local 25precipitation This is an important topic of research with applications for of the principal yardsticks for quantifying the strength of the hydrologic cycle over specific 20terrestrial 21to Therefore, changing land Of course, there are other feedbacks in the system, and in many parts of the 1world they may dominate A change in regional evapotranspiration affects not only the supply of 2water carried by the circulation of the atmosphere, but can thermodynamically alter the 3atmosphere itself by changing the partitioning of surface heat fluxes, triggering changes to the 4circulation patterns as well 5conception of recycling has been hard to shake It is the basis of legends such as the belief that 6“rain 7The follows the plow”1 first quantifications of recycling were made using bulk estimates The first formulations 8were one-dimensional (Budyko 1974, Lettau et al; 1979) and later generalized to two- 9dimensional 101994, that have been used The bulk approach makes several assumptions, such as that locally 12evaporated 13One areas suitable to true budget studies (e.g., Brubaker et al 1993, Eltahir and Bras Burde et al 1996) Burde and Zangvil (2001) present a thorough overview of the various 11methods 14at Nevertheless, the basic linear model behind many people’s and externally advected moisture are well mixed in the air over the region of interest major drawback of bulk formulations is that they contain an atmospheric moisture flux term the lateral boundaries defined as the product of two time-mean quantities – wind and 15humidity: F  qV 16 17Where 18the the flux of moisture F is normal to a lateral boundary of the area, V is the component of wind normal to that boundary, and q is the humidity Typically these terms are vertically 19integrated 20many to compute the total moisture flux across a boundary, but use monthly-mean data In regions such fluxes occur when there are either strong moisture gradients or large temporal 21variability in humidity, so that changes in wind direction and speed are accompanied by very 22different values 23 of humidity In actuality, perturbational expansion yields: F  q V  q V   q V  q V  F  q V  q V  11 Schultz and Tishler (2004) attribute the spread of this idea partly to the amateur scientist 2Wilber’s 1881 book, The Great Valleys and Prairies of Nebraska and the Northwest (1) (2) C.D 1The nonlinear term can be quite significant and has much of its signal on the time scale of 2synoptic waves 3Another drawback of the bulk approach is that it must be calculated over pre-defined volumes 4using the wind and humidity information along the boundaries That is fine for calculating a 5single value for recycling ratio over a large area (large relative to the number of observations 6along the boundary or more typically, the number of grid boxes from a gridded data set) but 7makes it difficult to produce a continuous map of recycling over a continent or the entire globe 8By assuming a length scale and calculating the mean moisture flux across that scale, Trenberth 9(1999) was able to use the bulk approach to formulate the recycling ratio based on local 10variables His approach still suffered from the other drawbacks of the bulk formulations 11However, the approach was able to produce global maps of estimates of the recycling ratio, 12including a 13The characterization of the annual cycle of recycling most direct way of estimating recycling would be to track the water vapor in the air from 14source (evapotranspiration) to sink (precipitation) 15differentiate 16through 17how between moisture that has evaporated from open water from that which has passed the vascular systems of plants For example, Henderson-Sellers et al (2002) showed the isotopic ratios change as one moves upstream along the Amazon (showing the 18increasing 19of Isotopic analysis of precipitation can contribution due to transpiration) and the trends in isotopic ratios during the latter part the twentieth century (suggesting changes in land use practices) However, isotopic analysis 20cannot pinpoint the 21the location of the evaporation that contributed the moisture It can only provide proportions of likely sources differentiated into broad categories 22Tracer modeling provides a means to follow exactly the path of water within an atmospheric 23model Druyan and Koster (1989) were among the first to apply this Lagrangian approach to 24water vapor for the Sahel This method has been applied over the central United States in 25regional (Giorgi et al 1996) and global models (Bosilovich and Schubert 2001), and over 1Eurasia 2has 3to (Numaguti 1999) Although more spatially precise than isotopic tracers, tracer modeling its drawbacks as well Tracking tracers in a three-dimensional model of the atmosphere adds the computational cost, especially in terms of storage, and requires choosing the source 4regions 5Also, 6An a priori 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 ideal approach would be to incorporate tracers in an analysis model with data assimilation, 7which would constrain the model behavior with available observations That approach still has 8problems to be solved, such as reconciling the lack of conservation within a system where state 9variables are assimilated (as is the case with all of today’s operational analysis and reanalysis 10efforts) with the need for a completely closed water budget within an analysis of the hydrologic 11cycle 12Until 13to such a conserving data assimilation system becomes feasible, the best alternative might be apply a back-trajectory analysis a posteriori to existing reanalysis fields Brubaker et al 14(2001) used such an approach to produce a climatology of the hydrologic cycle over the sub- 15basins of the Mississippi River basin, Sudradjat et al (2003) extended the study to interannual 16variations, 17also and Sudradjat (2002) applied the approach to the Amazon Basin The method has been applied to examine moisture sources for specific extreme precipitation events over the 18Mediterranean 19Russia 20areas basin (Reale et al 2001, Turato et al 2004), and to validate isotopic analyses over (Kurita et al 2004) Here we extend the analysis of Brubaker et al (2001) to all land of the globe The data sets used in the analysis are described in Section Section 21explains the methodology, with an emphasis on changes to the original approach described in 22Dirmeyer and Brubaker (1999) and the universality of scaling that allows us to compare 23recycling over regions of differing areas 24analyses 25to The global climatology of recycling, including of variability and trends, is given in Section In Section we compare this calculation bulk estimates using the method of Trenberth (1999) Conclusions are presented in Section 22 Data Sets 3All meteorological data except for observed precipitation come directly from the National 4Centers for Environmental Prediction (NCEP) / Department of Energy (DOE) reanalysis 5(Kanamitsu 61.9° et al 2002) These data are on a 192x94 grid (1.875° longitude by approximately latitude) and span the period from 1979 to present (2004) We make use of the sigma-level 7diagnostics and surface flux fields at 6-hour intervals Specifically, the fields used are humidity, 8temperature, 9surface and wind (u and v components) all on the 16 lowest model sigma levels; as well as pressure, precipitation and total evaporation 10precipitable These data are used to calculate water, potential temperature, and the advection of water vapor In order to avoid 11spurious excess convergence toward the poles, the meridional wind is scaled by the cosine of 12latitude The land-sea mask from the reanalysis is also used to differentiate land grid boxes for 13the calculation 14methodology 15(1986) The data are linearly interpolated in time to the time step of the trajectory Trajectories are calculated both forward and backward following Merrill et al to minimize the impact of interpolation errors in rapidly evolving or highly convergent 16flows 17Several 18the precipitation data sets are combined to produce a best estimate of precipitation sinks for back-trajectory calculation A hybrid 3-hourly precipitation data set is produced in the 19following way 20First, the reanalysis precipitation (6-hour forecast) is interpolated to a 3-houly amount Large 21errors are known to exist in the reanalysis estimates of precipitation – we use it primarily to 22establish the position and movement of large-scale rainfall events, such as those associated with 23extratropical baroclinic systems 24We then use the satellite-based CMORPH precipitation estimates (Joyce et al 2004) to correct 25the diurnal cycle of reanalysis precipitation at low latitudes This is accomplished as follows 1The 3-hourly CMORPH data are scaled from their original 0.25° resolution onto the reanalysis 2grid using simple bilinear interpolation A centered 31-day running mean is then calculated for 3each 3-hour interval of the CMORPH data to establish the mean diurnal cycle of precipitation 4and its variation throughout the year At the time these analyses were performed, less than two 5years of CMORPH data were available Only data from March 2003 through April 2004 have 6been used For each day (delineated by 0000UTC) at low latitudes, the reanalysis precipitation is 7replaced 8from by the CMORPH mean diurnal cycle for that day, scaled to retain the total daily rainfall the reanalysis 9timethroughout 10subtropical 11only applied to a zonal band 60° wide, spanning 30° north and south of the latitude of solar where synoptic variations are predominant this point in the process, each grid box of the globe contains what we deem to be the best 16estimate 17step of the local temporal distribution of precipitation within weather time scales The final is to scale the precipitation fields one more time, using the observationally-based pentad 18estimates of Xie and Arkin (1997) The final scaling results in a hybrid model-observational 19precipitation 20pentad 21as This limitation is meant to focus the correction on regions where precipitation is strongly diurnally forced (e.g., convection driven by solar heating) and not to alter the 14precipitation 15At the year as the changing seasons bring different parts of the globe into and mid-latitude weather regimes The CMORPH correction to the diurnal cycle is 12declination 13most The definition of “low latitude” for precipitation also varies with product that retains the pentad mean values from Xie and Arkin (1997), but the sub- variability from CMORPH and the reanalysis We use the hybrid precipitation estimates the starting point for the quasi-isentropic back-trajectory analysis The final surface and 22atmospheric data sets are all on the reanalysis grid and span the period from January 1979 23through August 2004 24 253 Methodology 1Our approach uses a quasi-isentropic calculation of trajectories of water vapor backward in time 2(hereafter QIBT) from observed precipitation events, using atmospheric reanalyses to provide 3meteorological 4evaporation 5provide data for estimating the altitude, advection, and incremental contribution of to the water participating in each precipitation event Dirmeyer and Brubaker (1999) the complete mathematical formalism of the method, and Brubaker et al (2001) describe 6how the climatologies are calculated Here we give a qualitative description of the method, and 7refer the reader to those previous papers for details 8The method relies on the use of high time resolution (daily or shorter) precipitation and 9meteorological 10Calculations 11observed 12pentads 1329th data to include the effects of transients on the transport of water vapor are performed on the reanalysis grid, working backwards in time, starting with precipitation at each grid box grouped into pentads (five-day intervals) This gives 73 per year During leap years a 6-day interval is used for the twelfth pentad, to include the of February The method can run on a range of time steps – we chose an interval of 45 14minutes to ensure statistical stability of results at minimum computational expense At the 15spatial scale of the reanalysis data, we find that a time step of an hour or 16less produces stable results (i.e., the evaporative source regions not 17change 18to as the time step is reduced further) The data are linearly interpolated in time the time step of the trajectory methodology, with the exception of precipitation, which uses a 19mass-conserving 20average 21rapidly 22 is taken following Merrill et al (1986) to minimize the impact of interpolation errors in evolving or highly rotational flows The precipitation data are at a time resolution of three hours, so there are typically 40 23precipitation 24over 26that data intervals in each pentad across 1620 time steps If there is no precipitation the grid box during the pentad, no calculations are made 25precipitation interpolation Trajectories are calculated first backward then forward and the Otherwise, the five-day is divided into 100 equal parcelsincrements, and for each percent of precipitation occurs counting back through the 3-hour total, a back trajectory of its corresponding 1Sudradjat, A., 2002: Source-sink analysis of precipitation supply to large river basins PhD Dissertation, [Available from University of Maryland, College Park, MD U.S.A.], 186 pp 4Sudradjat, 20742, 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 7Trenberth, K E., 1999: Atmospheric moisture recycling: Role of advection and local evaporation J Climate, 12, 1368-1381 9Trenberth, K E., A Dai, R M Rasmussen, and D B Parsons, 2003: The changing character of precipitation Bull Amer Meteor Soc., 84, 1205-1217 10 11Tucker, C J., D A Slayback, J E Pinzon, S O Los, R B Myneni, M G Taylor, 2001: Higher 12 northern latitude normalized difference vegetation index and growing season trends from 13 1982 to 1999 Int J Biometeor., 45, 184-190 14Turato, B., O Reale, and F Siccardi, 2004: Water vapor sources of the October 2000 Piedmont 15 flood J Hydrometeor., 5, 693-712 16Xie, P., and P A Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge 17 observations, satellite estimates, and numerical model outputs Bull Amer Meteor Soc., 18 78, 2539-2558 23 1Figure Captions: Schematic of (a) the division of precipitation over a pentad into “parcels”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., and the resulting depletion of water accounted for in the parcel See text for details Estimated recycling ratios as a function of area from subregions over three of the test 10 regions from Table 1, the average values for each scale (filled squares), and the best fit 11 regression curve line through the average values 12 13 The scaling regression curves from all test regions, and (bold) the curve through the arithmetic mean of the recycling ratios at each scale 14 The 25-year annual mean recycling ratio (%) at a representative spatial scale of 105km2 15 As in Fig for individual seasons 16 The range of the 25-year mean climatological annual cycle (maximum minus minimum 17 monthly recycling ratios), the standard deviation among the 25-year mean for each 18 month, and the coefficient of variation (panel marked SD divided by Fig 4) 19 20 Interannual variation of seasonal mean recycling ratios expressed as coefficient of variation (interannual standard deviations divided by Fig 5) 21 Trends in recycling ratio (% per year) during the 25-year period Red and blue shading 22 show regions with significant trends at the 95% confidence limit; pale yellow and green 23 shading show trends that are not significant 24 25 26 27 Bulk recycling ratio as computed using Trenberth’s (1999) formula, using representative length scales of (a) 51000 km and (b) 10500 km 10 Bulk recycling ratio as computed using Trenberth’s (1999) formula, using a representative length scale of 340 km, for comparison to Fig 54 24 11 Difference between QIBT (Fig 54) and bulk (Fig 10) recycling estimates, expressed as a fraction of the bulk estimate a 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 b c 38 Fig Schematic of (a) the division of precipitation over a pentad into increments “parcels” 39 of equal amount to be assigned to advected parcels; (b) the launching of parcels at random x- 40 y locations and elevations of a humidity-weighted vertical coordinate over a grid box 41 (humidity indicated by the curve labeled q); (c) the apportionment of water vapor in a parcel 25 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 See text for details 26 1Fig Estimated recycling ratios as a function of area from subregions over three of the test 2regions from Table 1, the average values for each scale (filled squares), and the best fit 3regression curve line through the average values 27 2Fig The scaling regression curves from all test regions, and (bold) the curve through the 3arithmetic mean of the recycling ratios at each scale 28 2Fig The 25-year annual mean recycling ratio (%) at a representative spatial scale of 105km2 29 2Fig As in Fig for individual seasons 30 2Fig The range of the 25-year mean climatological annual cycle (maximum minus minimum 3monthly 4the recycling ratios), the standard deviation among the 25-year mean for each month, and coefficient of variation (panel marked SD divided by Fig 4) 31 2Fig Interannual variation of seasonal mean recycling ratios expressed as coefficient of 3variation (interannual standard deviations divided by Fig 5) 32 1Fig Trends in recycling ratio (% per year) during the 25-year period Red and blue shading 2show regions with significant trends at the 95% confidence limit; pale yellow and green shading 3show trends that are not significant 33 3Fig Bulk recycling ratio as computed using Trenberth’s (1999) formula, using representative 4length scales of (a) 51000 km and (b) 10500 km 34 2Fig 10 Bulk recycling ratio as computed using Trenberth’s (1999) formula, using a 3representative length scale of 340 km, for comparison to Fig 54 35 2Fig 11 Difference between QIBT (Fig 54) and bulk (Fig 10) recycling estimates, expressed as a 3fraction of the bulk estimate 36  = a Ab 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% La Plata (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% Region 2Table The locations of test regions (8x8 grid boxes on the reanalysis grid) for determining the 3scaling 4for of the recycling ratio, the coefficients of the power law relationship found by regression each region, and the effective recycling ratio for three different reference region sizes in each 5location Recycling Ratio  for Area (km2) Overall statistics are shown at the bottom of the table 37 ... much of the Amazon basin adjacent Atlantic coastal regions of equatorial South America, the southern coast of Australia 10along the Great Australian Bight, areas to the west and northwest of the. .. adjacent Atlantic coastal of equatorial South America, the southern coast of Australia along the Great Australian areas to the west and northwest of the Persian Gulf, and two regions of the Nile Basin... beneath the land 7surface arrived as precipitation, and ultimately all of that water was evaporated from the oceans 8However, 9water 1 0from it may have taken multiple “cycles” of precipitation and