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  • View in gallery

    (top) Total seasonal source evaporation (kg m−2) for all precipitation over ice-free land based on MERRA atmospheric data with MERRA-Land evaporation and precipitation estimates. (bottom) Difference when only data from MERRA are used.

  • View in gallery

    The 27-yr mean distribution of evaporative sources for precipitation over the outlined areas: (top) the West and East Coasts, (middle) the Great Plains, and (bottom) the Mississippi River basin east of the Great Plains. Amounts are expressed as the portion of total precipitation originating as evaporation from each MERRA grid box in parts per million, normalized so the global sum for each area equals 1.

  • View in gallery

    Fraction of precipitation originating as evaporation over land by season. Regions with climatological rainfall rates less than 0.1 mm day−1 and permanent ice points are masked in white.

  • View in gallery

    As in Fig. 3, but for distance to the center of mass of the mean evaporative source distribution for each land grid point (km).

  • View in gallery

    The average relative entropy at each point (dimensionless) calculated between the climatological evaporative moisture source and the source for each of the 27 yr by season. Large values indicate greater interannual variability in the source of moisture supplying local precipitation. Regions with climatological rainfall rates less than 0.1 mm day−1 or where the RE calculation failed because of divisions by zero are masked in white.

  • View in gallery

    Relative entropy (dimensionless) between the climatological evaporative source distribution and the evaporative source distribution for the three driest years calculated for each ice-free land grid point using monthly data and then averaged for each season. Regions with climatological rainfall rates less than 0.1 mm day−1 are masked in white. Areas where the relative entropy is not significant at the 90% confidence level are shaded dark gray.

  • View in gallery

    As in Fig. 6, but for the wettest three years.

  • View in gallery

    As in Fig. 7, but calculated using pentad instead of monthly data. No significance screening has been applied.

  • View in gallery

    As in Fig. 6, but for the natural logarithm of the ratio of the relative entropy calculated with pentad data (rather than calculated with monthly data).

  • View in gallery

    Difference (three wettest minus three driest years) in the average distance between precipitation at each land point and the evaporative source supplying that precipitation, expressed as a percentage of the climatological average distance. Positive values indicate dry conditions have closer moisture sources than wet.

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Comparing Evaporative Sources of Terrestrial Precipitation and Their Extremes in MERRA Using Relative Entropy

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  • 1 Department of Atmospheric, Oceanic and Earth Sciences, George Mason University, Fairfax, Virginia, and Center for Ocean–Land–Atmosphere Studies, Institute of Global Environment and Society, Calverton, Maryland
  • | 2 Jackson School of Geosciences, University of Texas at Austin, Austin, Texas
  • | 3 Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | 4 Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, and SAIC, Greenbelt, Maryland
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Abstract

A quasi-isentropic, back-trajectory scheme is applied to output from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and a land-only replay with corrected precipitation to estimate surface evaporative sources of moisture supplying precipitation over every ice-free land location for the period 1979–2005. The evaporative source patterns for any location and time period are effectively two-dimensional probability distributions. As such, the evaporative sources for extreme situations like droughts or wet intervals can be compared to the corresponding climatological distributions using the method of relative entropy. Significant differences are found to be common and widespread for droughts, but not wet periods, when monthly data are examined. At pentad temporal resolution, which is more able to isolate floods and situations of atmospheric rivers, values of relative entropy over North America are typically 50%–400% larger than at monthly time scales. Significant differences suggest that moisture transport may be a key factor in precipitation extremes. Where evaporative sources do not change significantly, it implies other local causes may underlie the extreme events.

Corresponding author address: Paul Dirmeyer, George Mason University, Dept. of Atmospheric, Oceanic and Earth Sciences, 4400 University Dr., Mail Stop 2B3, Fairfax, VA 22030. E-mail: dirmeyer@cola.iges.org

This article is included in the Advancing Drought Monitoring and Prediction Special Collection.

Abstract

A quasi-isentropic, back-trajectory scheme is applied to output from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and a land-only replay with corrected precipitation to estimate surface evaporative sources of moisture supplying precipitation over every ice-free land location for the period 1979–2005. The evaporative source patterns for any location and time period are effectively two-dimensional probability distributions. As such, the evaporative sources for extreme situations like droughts or wet intervals can be compared to the corresponding climatological distributions using the method of relative entropy. Significant differences are found to be common and widespread for droughts, but not wet periods, when monthly data are examined. At pentad temporal resolution, which is more able to isolate floods and situations of atmospheric rivers, values of relative entropy over North America are typically 50%–400% larger than at monthly time scales. Significant differences suggest that moisture transport may be a key factor in precipitation extremes. Where evaporative sources do not change significantly, it implies other local causes may underlie the extreme events.

Corresponding author address: Paul Dirmeyer, George Mason University, Dept. of Atmospheric, Oceanic and Earth Sciences, 4400 University Dr., Mail Stop 2B3, Fairfax, VA 22030. E-mail: dirmeyer@cola.iges.org

This article is included in the Advancing Drought Monitoring and Prediction Special Collection.

1. Introduction

Rain or snow falling over any particular location is composed of condensed water vapor that entered the atmosphere as surface evaporation from a range of upstream locations. Surface and atmospheric conditions along the paths of moisture advection determine the ultimate sources of evaporative moisture, which generally have a combination of oceanic and terrestrial origins. Knowledge of the sources of moisture supplying precipitation over a particular location could be used to understand how upstream surface changes may affect local hydrology and to potentially aid prediction (e.g., Dirmeyer and Kinter 2010; Bagley et al. 2012; Spracklen et al. 2012).

There are three basic approaches to estimating the connection between surface evaporation from specific locations and subsequent precipitation of that water. The simplest, but most limited in capabilities, is the bulk method, which relies on regional atmospheric moisture budgets at relatively long time scales, typically 1 month (Brubaker et al. 1993). This approach is most often used to estimate precipitation recycling as derived by Budyko (1974)—the portion of precipitation over a given area that originated as evaporation within the same area (e.g., Eltahir and Bras 1994; Gong and Eltahir 1996; Trenberth 1999). Burde et al. (1996) showed that this method has an implicit assumption of one-dimensionality that causes errors, which can be accounted for in a two-dimensional derivation, further refined by Burde and Zangvil (2001). These approaches typically use global atmospheric reanalyses as the source of the necessary meteorological fields. Dominguez et al. (2006) recognized that the lack of water budget closure in reanalyses could affect the bulk estimates but decided the impact was small over the United States. Bisselink and Dolman (2008) came to the same conclusion for Europe. This approach has been extended to differentiate solely between terrestrial and oceanic moisture sources (e.g., Gimeno et al. 2012; Goessling and Reick 2011). Van der Ent (2010) developed a backtracking model based on the vertically integrated moisture transport and the constraints of atmospheric water balance, but still in the Eulerian framework. Keys et al. (2012) developed an interesting variant on that approach to estimate the “precipitation sheds” of regions to assess their potential vulnerability to changing evapotranspiration with land use changes.

Another approach is to include water vapor tracers directly within a three-dimensional model of the atmosphere. This approach typically accomplishes the tracing in a Lagrangian framework, providing a highly accurate set of trajectories for water vapor parcels. Druyan and Koster (1989) tagged water vapor evaporation from specific regions in a global model to compare moisture sources during wet and dry conditions over the Sahel. Numaguti (1999) performed a continental-scale tracer analysis over Eurasia, while Bosilovich and Schubert (2002) performed a global study of evaporative sources of precipitation using tracers in a global atmospheric model. Stohl and James (2004) used a dispersion model driven by reanalyses to examine a case study of moisture transport over Europe and a 1-yr global assessment. Stohl and James (2005) applied the method to diagnose oceanic moisture sources to major river basins. A variation on the tracer approach is to use stable water isotopes as the markers, a method that has been applied in both observational and modeling studies (e.g., Salati et al. 1979; Tian et al. 2001; Henderson-Sellers et al. 2004; Kurita et al. 2004; Yoshimura et al. 2004).

The bulk approaches mentioned above suffer several shortcomings, including errors introduced by the coarse temporal and vertical resolution of the methodology and data, lack of water budget closure in reanalysis datasets, and neglect of nonlinear processes and asymmetrical moisture advection. Tracers embedded within atmospheric models can have “perfect” tracking of water vapor at the full spatial and temporal resolution. However, they tend to add great expense to the simulations, especially in terms of computer memory use and data storage, as each additional evaporative source requires another full three-dimensional state variable to be carried in the model and integrated forward in time. Also, calculations from these methods are subject to all the systematic errors of the model, which can often be substantial for quantities like precipitation and evaporation (Kanamitsu et al. 2002). Models can be constrained by data assimilation, but the assimilation of humidity violates conservation and closure of the water budget, which cannot be handled elegantly by tracers.

A compromise is to calculate the tracers a posteriori from atmospheric analyses at a high spatial and temporal resolution that resolves the synoptic-scale fluctuations in water vapor, and even the diurnal cycle, as well as the vertical structure of moisture in the atmosphere, but may not use data from every time step of the atmospheric model producing the analysis. When using reanalyses as the source of the meteorological forcing data, the issue of lack of closure of the water budget still arises but is less severe, particularly when observed precipitation data are used to constrain the model simulations. This method has been used to independently validate other methods of estimating precipitation recycling and its variability (Brubaker et al. 2001; Sudradjat et al. 2003; Dirmeyer and Brubaker 2007), define regional links between tropical moisture and midlatitude floods (Dirmeyer and Brubaker 1999; Reale et al. 2001; Sudradjat 2002; Turato et al. 2004; Dirmeyer and Kinter 2009, 2010; Wei et al. 2012), quantify links between nations through the atmospheric branch of the hydrologic cycle (Dirmeyer et al. 2009), estimate remote impacts of tropical land use change (Bagley et al. 2012), and study the fate of evaporated irrigation water (Tuinenburg et al. 2012; Wei et al. 2013).

In this paper, we present results of this type of approach, the quasi-isentropic, back-trajectory scheme of Dirmeyer and Brubaker (2007) applied globally at a higher spatial resolution than it has been previously, using National Aeronautics and Space Administration (NASA) reanalysis products. In addition to determining sources of evaporated moisture supplying precipitation and estimating recycling ratios, differences in the distribution of sources during droughts and wet intervals are quantified. The goal of this analysis is to determine when and where extreme precipitation events can be attributed to changes in the sources of moisture supplying the precipitation.

Section 2 describes the datasets used, the back-trajectory technique that estimates the distribution of evaporative sources for moisture supplying precipitation over any location, and a robust statistical method to compare distributions of evaporative sources. The basic distributions of moisture sources are presented in section 3. Section 4 investigates how source regions vary in the cases of precipitation extremes. Discussion is presented in section 5.

2. Data and methods

The global meteorological analysis used for this study is the Modern-Era Retrospective Analysis for Research and Applications (MERRA; Rienecker et al. 2011). MERRA uses version 5 of the Goddard Earth Observing System (GEOS-5) atmospheric model and data assimilation system at a resolution of ⅔° longitude by ½° latitude, overlying the Catchment Land Surface Model (Koster et al. 2000; Ducharne et al. 2000). MERRA placed an emphasis on improved simulation of the global hydrologic cycle, assimilating instantaneous precipitation rates (Decker et al. 2012), and some aspects of the hydrologic cycle appear to have improved relative to other reanalyses (Trenberth et al. 2011). Nevertheless, model biases and discontinuities from changing satellite platforms introduce precipitation errors (Robertson et al. 2011; Trenberth et al. 2011), which affect the surface water budget, and there is evidence that interannual precipitation variance may be weak in key areas (Bosilovich 2013).

Jiménez et al. (2011) compared many reanalyses and other global estimates of surface heat fluxes and found MERRA to be in line with other products, but it had some vagaries associated with precipitation and canopy interception biases, especially over South America. Reichle et al. (2011) performed a land-only replay of the land model component to produce an analysis called MERRA-Land, where precipitation from the observationally based Global Precipitation Climatology Project (GPCP; Huffman et al. 2009; Xie et al. 2003) is used to correct MERRA precipitation. This results in estimates of evaporation and other surface quantities that are more consistent with observations. The period of overlap for these datasets is 1979–2005, so all analysis is performed for those 27 yr. Dirmeyer (2011) showed that MERRA-Land surface flux data produce estimates of land–atmosphere coupling that are much more consistent with a wide range of other datasets than MERRA.

These data are used to drive the quasi-isentropic, back-trajectory scheme that estimates the distribution of surface evaporation that supplies precipitation as a function of space and time (Brubaker et al. 2001; Dirmeyer and Brubaker 2007). It is a Lagrangian method that traces the advection of moisture back in time from precipitation events and uses upstream evaporation and precipitable water estimates to determine the probabilistic distribution of surface evaporation supplying the precipitated water vapor to the atmosphere. We use observed precipitation data, disaggregated in time using the reanalysis precipitation, because atmospheric models struggle to reproduce observed precipitation amounts. Data are aggregated in time over 5-day (pentad) and monthly intervals, with a spatial distribution for every land surface grid point. As long as there is any precipitation during a pentad, the algorithm traces the same number of parcels backward in time. The water mass represented by each parcel will be the same within any pentad, but may vary greatly between pentads, in proportion to the precipitation during the pentad. On a high-resolution global grid such as MERRA, this generates a very large set of two-dimensional source fields. The source fields for a set of grid boxes, delineating a river basin, nation, or any arbitrary land area, can be easily calculated by aggregation from the resolution grid.

The spatial pattern of surface evaporative sources is effectively a two-dimensional probability distribution in latitude and longitude. There exist objective quantitative methods to determine the degree of similarity between two probability distributions. Relative entropy, which also goes by other names such as information divergence and Kullback–Leibler divergence, is such a quantification (see DelSole and Tippett 2007). The relative entropy (RE) between two parametric distributions p and q on a discrete spatial grid is defined as (Kleeman 2002)
eq1
where i is the index of the grid points (in our case it is two dimensional in latitude and longitude but it applies over any number of dimensions), q(i) is the climatological distribution evaporative source, and each of the distributions are defined as having a sum total of unity. Thus, we normalize the spatial distributions before applying this method. The global integral of the evaporative source for any grid point is, by definition, equal to the total water precipitated over the grid point. The normalization sets this total to unity (i.e., we divide by the total water precipitated), as the relative entropy method requires that the distribution be probabilistic and unitless.

For two identical distributions, RE = 0. Any deviations will increase the value of RE. The value of REp,q ≠ REq,p, but the ranking is preserved with either choice of p and q, and RE is invariant to linear and nonlinear transforms. The calculation is performed on the lower-resolution GPCP data grid, and only differences significant at the 90% confidence level are shown.

What is not straightforward, however, is quantification of a statistical significance in the difference between two distributions when they do not share identical or well-described low-order moments (DelSole and Tippett 2007). For example, the significance in the shift between two normal distributions can be quantified, but if one or both distributions are nonnormal or otherwise do not share basic shape parameters, significance can only be determined by Monte Carlo bootstrap techniques. The mean evaporative source and that for each of the 27 individual years, for each season, are used to calculate relative entropies, and the mean and standard deviation of the 27 values are calculated at each point. This is then compared to the same calculations made for each combination of 3 yr, a sample size of 2925, but only for a subsample of 100 points and seasons (computational expense is otherwise prohibitive). Assuming that the variability of relative entropy is normally distributed and that a linear transform can be used for the means and standard deviations between the combinations of 27 taken 3 at a time and combinations of 27 taken 1 at a time, we scale the significance thresholds.

3. Evaporative sources

Figure 1 shows the total evaporative source supplying precipitation over land (Antarctica and other ice-covered points excluded) aggregated from monthly data for each season. Two sets of estimates are used: one based on MERRA with precipitation corrected by GPCP and MERRA-Land estimates of evaporation (top panels) and one based solely on the original MERRA output. The bottom panels show the difference between evaporative source estimates with MERRA alone minus the estimates where MERRA-Land is used for terrestrial evaporation and precipitation estimates. Looking first at the top panels, there is a clear seasonality to both the terrestrial and oceanic sources of evaporation supplying precipitation over land. The strongest sources tend to be in low latitudes over land and adjacent open oceans, although a number of areas in the northern midlatitudes become prominent in June–August (JJA). The strength of oceanic sources correlates strongly to the distance to shore, but there are exceptions (e.g., the closed 30 kg m−2 contour in the North Pacific during JJA).

Fig. 1.
Fig. 1.

(top) Total seasonal source evaporation (kg m−2) for all precipitation over ice-free land based on MERRA atmospheric data with MERRA-Land evaporation and precipitation estimates. (bottom) Difference when only data from MERRA are used.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

The bottom panels of Fig. 1 show that MERRA evaporation (and precipitation) over land is generally much higher than GPCP observations suggest should be the case. Yet, MERRA has a very strong cross-equatorial gradient in terrestrial precipitation, with erroneously dry conditions over much of South America and Africa. These systematic errors greatly impact the estimates of evaporative sources, motivating our use of MERRA-Land for our calculations. The percentage of evaporated moisture feeding precipitation over the land areas in the top panels is 52%, 62%, 50%, and 45% during March–May (MAM), JJA, September–November (SON), and December–February (DJF), respectively. When the MERRA output with its precipitation biases is used to estimate evaporative sources, the terrestrial percentages increase to 55%, 64%, 52%, and 46%.

Figure 2 gives a notion of how regional evaporative sources appear, using the example of the conterminous United States. The mean surface evaporative sources supplying precipitation to four regions are presented, normalized to indicate the percentage of the total supplied from each MERRA grid box. The grouping of states is meant to approximate the Great Plains (middle panel), the Mississippi River basin east of the Great Plains (bottom panel), and the remaining territory on the West and East Coasts (top panel). This and all future figures are based on the estimates using the corrected precipitation and MERRA-Land evaporation. The source into the western United States is seen to have a long fetch stretching from the subtropical North Pacific, indicative of the “atmospheric rivers” that supply much of the moisture for winter rain and snow (e.g., Dettinger et al. 2011). There is also a great deal of moisture supplied from terrestrial evapotranspiration over northern California, Oregon, and Washington, according to this analysis.

Fig. 2.
Fig. 2.

The 27-yr mean distribution of evaporative sources for precipitation over the outlined areas: (top) the West and East Coasts, (middle) the Great Plains, and (bottom) the Mississippi River basin east of the Great Plains. Amounts are expressed as the portion of total precipitation originating as evaporation from each MERRA grid box in parts per million, normalized so the global sum for each area equals 1.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

The Great Plains and eastern Rockies have an evaporative source that mainly comes from the western Gulf of Mexico, as well as terrestrial areas in the southern part of the region, and sporadic moister localities across the Intermountain West. The region of the Pacific off the coast of Baja California is also a moisture source prior to the onset of the North American monsoon (see Brubaker et al. 2001).

Figure 2 (bottom) shows the evaporative source supplying precipitation over the states of the Mississippi basin mainly east of the Great Plains. This area also shows a major oceanic source from the Gulf of Mexico, but with more extent into the northern Caribbean Sea (see Dirmeyer and Kinter 2010) and little moisture coming from the west. There is again a substantial terrestrial source over the southern and central portions of the area.

Figure 2 (top) also shows the evaporative source for the East Coast, which shows much more of a source from the open Atlantic than does the Mississippi basin area. Again, little moisture supplying precipitation comes from the west—most comes from the south. Recycling over each area, defined as the fraction or percentage of the total evaporative moisture source that lies within the boundaries of the region, are 12%, 22%, 19%, and 14% for the West Coast, Great Plains, Mississippi valley, and East Coast, respectively. For the same regions, oceanic moisture sources account for 81%, 48%, 46%, and 53% of precipitation.

Figure 3 shows for each season the fraction of precipitation at each grid point that originated from evaporation over land. The pattern of mean low-level flow is evident in the patterns. In midlatitudes, where winds are predominantly from the west, the west coasts predominantly receive moisture of oceanic origin, and the eastern sides of continents have much more moisture of terrestrial origin. The pattern is reversed at low latitudes. The global mean percentages of terrestrial sources of moisture supplying terrestrial precipitation are 46%, 50%, 40%, and 38% during boreal spring, summer, fall, and winter, respectively.

Fig. 3.
Fig. 3.

Fraction of precipitation originating as evaporation over land by season. Regions with climatological rainfall rates less than 0.1 mm day−1 and permanent ice points are masked in white.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

There are also some pronounced regional seasonal cycles. Large areas of central Asia into Siberia receive more than 90% of their precipitation from land evaporation during spring and summer. The region around Ethiopia and Sudan has a large oscillation between oceanic sources in the winter and spring and terrestrial sources during summer into fall. Much of southern Africa has a similar variation, but 6 months out of phase. The general east–west gradient over North America is maintained throughout the year but fluctuates from a predominance of marine sources in winter to a much larger portion of continental sources in summer. Most of Eurasia also shows the same annual cycle as North America.

Very strong gradients are evident across the steep terrain of the Himalayas, with large terrestrial proportions over the Tibetan Plateau and predominant oceanic sources to the south. This gradient extends northeastward across China. There are also fairly strong gradients along the Rift Valley of Africa, but curiously, there is little apparent signature of the Rocky Mountains or Andes except in the immediate vicinity of the Altiplano.

The distance from each terrestrial grid point to the central moment of the climatological evaporative source is shown in Fig. 4. This gives an indication of the average distance water vapor travels in the air before falling as rain or snow at that location. Arid regions far from open ocean typically have the largest values, with substantial areas of the Sahara (all seasons) and south-central Asia (all except JJA) showing values in excess of 4000 km. The shortest fetches are found in subtropical regions during the local rainy season. Parts of subtropical South America, southern Africa, and northwestern Australia show typical distances of less than 500 km, as does a band across the Sahel to Ethiopia, particularly during JJA. These areas show some persistence of the relatively short transport distances, even in the dry season. Surprisingly, the distances are somewhat longer in the deep tropics. The effect of the annual cycle of winds and terrestrial evaporation are evident over the middle and high latitudes of the Northern Hemisphere. Distances are shorter in the summer when land evapotranspiration is greatest and winds are lighter.

Fig. 4.
Fig. 4.

As in Fig. 3, but for distance to the center of mass of the mean evaporative source distribution for each land grid point (km).

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

The remainder of the paper discusses the quantification of evaporative sources associated with hydrologic extremes. To do so requires quantification of the deviation of an evaporative source from its climatology. The method of relative entropy was described in section 2. Figure 5 shows the average value of the relative entropy calculated between the climatological pattern of evaporative sources and each of the 27 individual years on a monthly basis then aggregated to seasonal, calculated for every land grid point. Small values suggest there is very little variation in the probability distribution, represented by the normalized evaporative source like those depicted in Fig. 2 for area totals. Small values predominate over the tropics, monsoon regions during the wet season, and humid regions in general. Large values are most likely over arid regions, suggesting a great deal of interannual variability in moisture sources there.

Fig. 5.
Fig. 5.

The average relative entropy at each point (dimensionless) calculated between the climatological evaporative moisture source and the source for each of the 27 yr by season. Large values indicate greater interannual variability in the source of moisture supplying local precipitation. Regions with climatological rainfall rates less than 0.1 mm day−1 or where the RE calculation failed because of divisions by zero are masked in white.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

However, there is not a one-to-one correspondence between precipitation and the interannual variability in moisture sources. For example, northern Australia shows very large RE values during MAM and a minimum during SON, even though DJF is the wet season and JJA is the core of the dry season. Likewise, over the western Great Plains there is a clear maximum in relative entropy, and thus peak year-to-year variability in moisture sources, during SON, which is a period of transition from a late spring peak to a winter minimum in total precipitation.

Similarly, the correspondence between variability and fetch (Fig. 4) is not systematic. While the arid zones tend to have high variability, those in the Northern Hemisphere have the longest fetches, while arid zones in the Southern Hemisphere often have short fetches. As another example, during boreal summer variability and fetch are clearly positively correlated, while over North America there is a weak negative correlation.

4. Extremes

The relative entropy statistic provides a handy measure of the difference between any two patterns of evaporative sources. As an example of the application of the relative entropy calculation, we quantify the differences between the global patterns of evaporative sources of terrestrial precipitation using the two different estimates of precipitation, as was shown in Fig. 1. Scaling the evaporative sources in each case by the global totals to maintain the notion of a comparison of probability distributions, relative entropies of 0.30, 0.76, 0.37, and 0.14 are found for MAM, JJA, SON, and DJF, respectively. This corroborates what can be seen in the bias maps in the lower half of Fig. 1; the largest differences appear during JJA, and the two estimates for DJF are rather similar on a global scale. Recall that the RE estimate provides information on the patterns only, not biases in the means.

Here we use relative entropy to determine the difference from the climatological pattern of evaporative sources at each land grid point for specific climatic categories, namely, the months and years with the greatest or least precipitation. With this approach, we may determine whether changes in the sources of moisture supplying precipitation (i.e., changes in circulation, moisture advection, and remote evaporation) are significant contributors to precipitation extremes. For locations where the answer is negative, other causes may be at play, such as local conditions like atmospheric stability, convective potential or land surface feedbacks, or possibly other large-scale factors not discernible from our back-trajectory analysis.

Figure 6 shows the relative entropy calculated at each point between the evaporative source averaged over just the three driest years, based on GPCP precipitation, and the 27-yr climatological evaporative source. The largest values of relative entropy are over arid and semiarid regions, suggesting when these areas suffer drought, there are large changes in the pattern of evaporative moisture sources. Humid areas show smaller values and thus smaller absolute variations in the patterns of evaporative moisture sources. However, the areas of significant variations are widespread and are not limited to any specific climate regime. Nevertheless, some general patterns emerge. During DJF, there is little significant connection between changing moisture sources and drought across the Southern Hemisphere. Summer is also the season with the least coverage of significant moisture transport across most of the Northern Hemisphere. At high latitudes in winter, changing moisture sources are significant. This is consistent with the strong limitations on precipitable water in the Clausius–Clapeyron relationship; in cold regions and seasons, precipitation is strongly correlated with temperature, which is often tied to prevalent wind direction. We also see that monsoon regions in North America and Asia and, to a lesser extent, Africa show significant relative entropies in the transition seasons, where late onsets or early retreats of monsoon rains seem to be connected to circulation anomalies.

Fig. 6.
Fig. 6.

Relative entropy (dimensionless) between the climatological evaporative source distribution and the evaporative source distribution for the three driest years calculated for each ice-free land grid point using monthly data and then averaged for each season. Regions with climatological rainfall rates less than 0.1 mm day−1 are masked in white. Areas where the relative entropy is not significant at the 90% confidence level are shaded dark gray.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

The same relative entropy calculations were performed for the three wettest years at each location, shown in Fig. 7. Here we find few points with statistically significant changes in evaporative sources. There is a plausible reason for this: whereas droughts are the result of a deficit of precipitation over an extended period of time, typically several months or more, floods often result from one or a few very heavy precipitation events occurring over brief periods of days. A wet month or season could be the result of an anomalous moisture source, like that brought by atmospheric rivers, which lasts only a few days (Dettinger et al. 2011). These events can easily become lost when monthly or seasonal statistics are calculated. However, one might expect midlatitude wet spells caused by persistent circulations such as cutoff lows or nearby blocking ridges to induce significant changes in moisture sources. We do not see evidence of this in the monthly data.

Fig. 7.
Fig. 7.

As in Fig. 6, but for the wettest three years.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

Seasonal mean values of relative entropy were recalculated using the original pentad-by-pentad estimates of evaporative sources. The results for the three wettest cases, based on pentad GPCP precipitation data, are shown in Fig. 8. No significance test has been applied because of computational expense with the bootstrap approach on this larger dataset. In all seasons, changes in the evaporative source are a larger factor in flood events over Arctic areas and the Southern Hemisphere subtropics. Mountainous areas of North America and the Himalayas also have persistent high values of RE. For any specific location, one can see evidence of seasonality, with a particular part of the year having the highest likelihood of floods to be associated with changes in evaporative source regions.

Fig. 8.
Fig. 8.

As in Fig. 7, but calculated using pentad instead of monthly data. No significance screening has been applied.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

The impact of the choice of time scale is clearly evident in Fig. 9. The figure shows the natural logarithm of the ratio of the relative entropy at each point—pentad versus monthly. Positive values dominate, indicating that changes in the evaporative source regions are more of a factor in precipitation anomalies on pentad intervals than monthly. Globally, the largest discrepancies are most widespread during JJA, especially over the monsoon regions and other locations experiencing the wettest part of the year. There is also some indication of coincidence with the season of most frequent tropical storm landfall (e.g., over East Asia and the Atlantic coast of the United States and Canada in JJA). The minimum impact is during DJF for most of the Northern Hemisphere, but this is the peak time for the impact of shorter-duration flood events over much of the Southern Hemisphere. However, the midlatitude regions with the strongest positive values over Northern Europe and western North America correspond well with longitudes where blocking is most frequent (Tibaldi et al. 1994). However, it should be noted that a comparison of these two relative entropies, which have inherently different sample spaces being calculated from estimates made at different time scales, may not be strictly appropriate in a statistical sense.

Fig. 9.
Fig. 9.

As in Fig. 6, but for the natural logarithm of the ratio of the relative entropy calculated with pentad data (rather than calculated with monthly data).

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

5. Summary and discussion

The quasi-isentropic, back-trajectory scheme of Brubaker et al. (2001) has been applied to data from MERRA. Estimates of the surface evaporative sources of moisture supplying precipitation over land for the period 1979–2005 are presented. Results are consistent with previous analyses (e.g., Brubaker et al. 2001; Dirmeyer and Brubaker 2007; Dirmeyer and Kinter 2010), but the higher spatial resolution of the MERRA dataset reveals more structure. Systematic biases in MERRA precipitation have a large effect on the surface water budget, which also impacts the estimates of evaporative sources. Thus, precipitation estimates have been corrected using gridded data from GPCP, and evaporation data come from the MERRA-Land offline replay also driven by observationally based precipitation.

The methodology allows for estimates of moisture recycling and the partitioning of local precipitation between terrestrial and oceanic sources, as well as estimates of the distance over which moisture typically travels in the atmosphere prior to falling as precipitation over any location. Recognizing that the two-dimensional distributions of evaporative moisture source are tantamount to probability distributions, we have used the statistical metric of relative entropy to compare evaporative sources for any region under different conditions, namely, cases of drought or flood based on local precipitation anomalies.

We find that changes in local and remote surface evaporative sources of moisture supplying precipitation over land are more a factor behind droughts than wet anomalies over most regions of the globe. Examining results grouped by season, much of the globe shows significant differences in evaporative moisture sources for the driest ~10% (3 out of 27) of the time periods. On the other hand, very little area appears to pass significance tests for comparable wet anomalies. Some of this discrepancy is due to the difference in time scales underpinning droughts and floods: when pentad data are considered instead of monthly data, relative entropy estimates for floods increase. Figure 9 suggests that phenomena such as winter midlatitudes blocking episodes may manifest more strongly on pentad-scale relationships between evaporative sources and excess precipitation than on monthly time scales.

The finding that droughts are more strongly tied to changes in evaporative sources than floods seems to run counter to previous findings with this method that link floods to anomalous advection of moisture (e.g., Dirmeyer and Brubaker 1999; Reale et al. 2001; Turato et al. 2004; Dirmeyer and Kinter 2009, 2010) and, more generally, link atmospheric rivers and extreme precipitation events (e.g., Dettinger 2004). It may be that our screening for the wettest years conflates such cases with extreme rainfall events that have more localized causes. In this study, we have not tried to identify specific cases of atmospheric rivers as those previous studies did. Rather, we conditioned the data based simply on a ranking of precipitation amounts.

To try to discern whether there is more of a change in moisture transport for droughts than floods, we revisit the metric shown in Fig. 4—mean distance to the evaporative source. Distances to the center of mass of evaporative sources have been calculated for the three wettest and driest years for each month, the same cases in Figs. 5 and 6, and then averaged for seasons. The differences in the mean distances (wet minus dry), expressed as a percentage of the 27-yr climatological mean distance to evaporative source, are shown in Fig. 10. On average, distances to moisture sources are greater during droughts than wet periods—as much as 12% during SON for the global mean. Distances are actually greater, averaged globally, for both extremes, but the differences from climatology for wet cases are less than half that for droughts on average. The figure shows that there are significant regional variations. Semiarid and arid regions, where precipitable moisture often has a relatively long path, generally have more distant fetches during droughts than wet intervals (blue shading). This may reflect the near-total lack of evaporation in the drought regions, meaning any moisture must come from relatively farther away. When conditions are wet, there can be excess local evaporation. Indeed, calculations of the difference between wet conditions and climatology (not shown) indicate moisture transport distances are shorter over arid zones.

Fig. 10.
Fig. 10.

Difference (three wettest minus three driest years) in the average distance between precipitation at each land point and the evaporative source supplying that precipitation, expressed as a percentage of the climatological average distance. Positive values indicate dry conditions have closer moisture sources than wet.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-13-053.1

Previous studies have suggested that floods over the eastern United States may tap more distant sources of moisture from the Caribbean Sea (e.g., Brubaker et al. 2001; Dirmeyer and Kinter 2010) whereas droughts draw on local sources (e.g., Bosilovich and Schubert 2001), and Fig. 10 supports that conclusion. Droughts here are often associated with high pressure and weak advection, rendering remote moisture sources unavailable. We do not find a similar signal for lower and central California in winter, where long atmospheric rivers are often implicated in floods. Other red-shaded regions also tap more distant moisture sources during wet periods than dry.

Significant changes in evaporative moisture sources found in this analysis during times of drought could have several causes. The calculation of evaporative sources depends not only on the atmospheric circulation (horizontal wind field), but also on column integrated precipitable water and surface evaporation rates, which are used to determine the contribution of each upstream grid box to the overall moisture supply for downstream precipitation. In this study, we have not attempted to differentiate between these dynamical and hydrological factors, and even in Fig. 10 they remain conflated.

Furthermore, a lack of significant contribution to precipitation extremes from changing moisture transport, estimated using relative entropy, does not indicate what other phenomena may be the cause. Alternative factors may include local increases in atmospheric stability (buoyancy or shear), regional changes such as large-scale subsidence, increased entrainment of dry air at the top of an otherwise favorable boundary layer, or a change in coupled land–atmosphere feedbacks caused by anomalous land surface conditions. Further diagnoses would be helpful to better understand the combination of events that contribute to precipitation extremes around the globe.

Acknowledgments

This research was supported by National Aeronautics and Space Administration Grant NNX09AI84G. Much of the data used in this effort were acquired as part of the activities of NASA's Science Mission Directorate and are archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC).

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