Temporal and spatial variability of the global water balance
Gregory J. McCabe, U.S. Geological Survey, Denver, Colorado (gmccabe@usgs.gov)
David M. Wolock, U.S. Geological Survey, Lawrence, Kansas (dwolock@usgs.gov)
Objectives
Measured 2000-2009 precipitation was compared to mid-21st century GCM-simulated
precipitation (from 16 models) by computing mean annual P departures for 5-degree
latitudinal bands (Figure 4). The GCM-simulated P departures for 5-degree latitudinal
bands are highly variable for most of the globe, except for the high northern latitudes
where the GCM-simulated P departures are similar for all models. The large differences
among GCM-simulated P departures suggest a large amount of uncertainty in model
projections of future precipitation. A notable result is that the means of the GCMestimated P departures co-vary with the measured P departures (r = 0.89, p < 0.01) for the
region from 40oS to 40oN (Figure 4).
In this study we treat the 20th century as an experimental period during which we examine
changes in the spatial and temporal patterns of global water-balance components
(precipitation [P], actual evapotranspiration [AET], runoff [Q], and potential
evapotranspiration [PET]). The Earth warmed during this period, and our goal is to determine
how the components of the water balance have responded to the increases in temperature
(T). In particular, we assess how the partitioning of precipitation into evapotranspiration and
runoff has changed and evaluate whether these temporal changes in water-balance
components are consistent with global climate model predictions for a warmer world.
Figure 4. Mean departures of annual precipitation (P)
for 5-degree latitudinal bands estimated from 16
general circulation models (GCMs) for the mid-21st
century (gray lines), the mean departures from the 16
GCMs (thick black line), and measured P departures for
2000 through 2009 from the CRUTS3.1 data set (red
line).
Methods and Data
Water-balance components (AET and Q) for this analysis were computed using a monthly
water-balance (WB) model because there are few long-term (50 to 100 years in length) global
measurements of these hydrologic variables. The WB model uses an accounting procedure to
compute the allocation of water among various components of the hydrologic system based
on monthly time series of P, T, and PET. The WB model includes the concepts of climatic water
supply and demand, seasonality in climatic water supply and demand, snow accumulation and
melt, and soil-moisture storage.
Monthly T, P, and PET data for the globe were obtained from the Climate Research Unit at East
Anglia, United Kingdom [the CRUTS3.1 dataset]. The spatial resolution of this dataset, which
covers the land areas of the globe, is 0.5 degree (o) by 0.5o and spans the period 1901 through
2009. In our analysis, CRUTS3.1 data poleward of 70° North latitude and 60° South latitude
were not used because many of the monthly temperature and precipitation values for these
grid cells were generated from sparse meteorological observations; the exclusion of these grid
cells left 57087 grid cells for analysis. Potential evapotranspiration from the CRUTS3.1 dataset
is computed using a modified Penman-Montieth equation.
Figure 1. Time series of mean global departures of annual, October
through March (Oct-to-Mar), and April through September (Apr-to-Sep)
precipitation (P), actual evapotranspiration (AET), runoff (Q), and potential
evapotranspiration (PET). Note that positive (negative) departures of P
and Q are shaded blue (red), whereas positive (negative) departures for
AET and PET are shaded red (blue). Using this shading scheme, blue
depicts positive contributions to water supply and red depicts reduced
contributions and/or increased demand for water.
Results
Global average PET departures (Figure 1) show an increase of about 30 mm during the 105year analysis period; the majority of the increase in PET occurred during the Northern
Hemisphere warm season. The PET time series shows little change from 1905 to 1980 and
then an abrupt increase starting in the 1980s and continuing to 2009. Three periods of higherthan-average P are evident beginning around 1950 (Figure 1).
Latitudinal differences in the temporal variability of P, AET, Q, and PET were
examined for each of three latitudinal bands (60o South (S) to 20oS, 20oS to 20o
North (N), 20oN to 60oN). These three latitudinal bands generally correspond to:
the Southern Hemisphere mid-latitudes; the tropics and sub-tropics (hereafter
referred to as tropics); and the Northern Hemisphere mid-latitudes, respectively.
The temporal patterns in the WB-model estimated variables, AET and Q, reflect the temporal
patterns in the forcing variables, P and PET (Figure 1). The increases in AET since about 2000
are related to increases in PET and P; increased PET creates greater climatic demand for water,
and increased P comprises water available to satisfy this demand. The increases in PET since
about 2000, which are caused by increases in global temperature, are large and
unprecedented during the 1900s. The periods of higher than average Q during the analysis
period coincide with periods of higher than average P (Figure 1). This result reflects the
concepts and structure of the WB model—on an annual basis, Q is the amount of P in excess
of AET—and the global average value of P is greater in magnitude than the global average
value of AET.
The time series of departures for P, AET, Q, and PET for the Northern
Hemisphere mid-latitudes are generally smaller than the departures for the
Southern Hemisphere mid-latitudes (Figure 2). The muted departures for the
Northern Hemisphere mid-latitudes may be due to the larger land area—and
hence greater number of grid cells included in the aggregate value—for
Northern Hemisphere mid-latitudes compared with the Southern Hemisphere
mid-latitudes. Also the Northern Hemisphere mid-latitudes include a larger
amount of desert area, such as parts of central Asia. The exception to this
pattern, however, is that PET departures in the Northern Hemisphere and
Southern Hemisphere mid-latitudes are of comparable magnitude and have
increased since about 2000 (Figures 2D and 2L).
An interesting aspect of the response of the global water balance since 2000 to global climate
is that, on an annual basis, Q increased even as PET increased significantly. This result can be
understood by examining the WB components at a seasonal scale. Toward this end, monthly
data were used to compute global mean departures of P, AET, Q, and PET for the October
through March (Oct-to-Mar) and for April through September (Apr-to-Sep) periods (Figure 1).
Although Figure 1 shows global-average water-balance component values, the majority (74%)
of global land area (excluding Antarctica) is in the Northern Hemisphere and, therefore, the
global departures strongly reflect the Northern Hemisphere cool (Oct-to-Mar) and warm (Aprto-Sep) seasons. The P departures for these two seasons indicate that P increases since about
2000 were largest for the Oct-to-Mar months (Figures 1B), whereas increases in PET during
Oct-to-Mar months were small (Figure 1K). Thus, the relatively large increases in P during Octto-Mar months resulted in increases in Q during Oct-to-Mar months (Figure 1H) and on an
annual basis (Figure 1G). Increases in PET since about 2000, in contrast, are largest during Aprto-Sep months (Figure 1L) and account for most of the increase in annual PET observed during
the recent time period (Figures 1J and 1L). The large increases in PET during Apr-to-Sep
months had little effect on annual runoff because during these months (in the Northern
Hemisphere), PET is greater than P and little water is available for runoff; thus increases in PET
during these months do not result in additional decreases in runoff.
Figure 2. Mean annual departures of precipitation (P), actual
evapotranspiration (AET), runoff (Q), and potential evapotranspiration (PET)
for latitudinal bands.
Departures of mean annual water balance variables averaged for the last ten years
of the analysis period (2000-2009) were mapped to show the spatial pattern of
recent values for water-balance components compared to the long-term average.
Positive departures of P occur for a large part of the globe (Figure 3A) except for
negative P departures in the western US, northern Africa, the Middle East, India,
eastern China, and southeastern Australia. The spatial patterns of departures for Q
(Figure 3C) and P (Figure 3A) are similar and significantly correlated (r = 0.86,
significant at a 99 percent confidence level (p < 0.01)). The pattern of mean annual
departures for PET (Figure 3D) are positive for most of the globe and generally are
more extreme than those for P, AET, and Q. Negative PET departures primarily are
located in eastern North America, northwestern South America and northern
Australia. The pattern of departures for AET (Figure 3B) is more similar to the
pattern of departures for P (r = 0.61, p < 0.01) and Q (r =0.33, p < 0.01) than it is for
PET (r = 0.15, p < 0.01).
The P and Q time series for the tropics (Figures 2E and 2G) show larger variability
than the P and Q time series for the mid-latitudes. The time series of AET and
PET (Figures 2F and 2H) for the tropics, however, indicate relatively small
variability and relatively small increases in PET and AET since about 2000. The
low variability in AET and especially PET indicates low year-to-year variability in
temperatures for this region.
Although there is a difference in magnitudes, there exists a symmetry in the
variability of water balance variables in the Northern and Southern
Hemispheres. For example, the annual P time series of Northern Hemisphere
and Southern Hemisphere mid-latitudes are positively correlated (correlation
coefficient (r) = 0.60, p < 0.01) as are the Q time series (r = 0.49, p < 0.01). The
PET time series, as well as the AET time series, for the Northern Hemisphere and
Southern Hemisphere mid-latitudes also are positively but weakly correlated (r =
0.33 for both variables, p < 0.01).
Our analysis of departures of water-balance variables suggests substantial variability and
increases in all variables since about 2000. To place these temporal patterns in a different
context, changes in the magnitudes (as opposed to departures) of the water-balance
variables are examined. To make these comparisons, we computed mean annual time
series of P, AET, Q, and PET for the three latitudinal bands using the raw data (in units of
millimeters) (Figure 5). These results show that variability in the water balance
components is small compared to their magnitudes for the latitudinal bands. For the
Northern Hemisphere mid-latitudes, the time series of the water balance variables appear
as nearly flat lines, although the increase in PET near the end of the record is slightly
discernible. In the tropics, the time series of AET and PET also appear as nearly flat lines,
but the time series of P and Q co-vary and show year-to-year variability. For the Southern
Hemisphere mid-latitudes, the water-balance variables display some year-to-year
variability, and an increase in PET at about the year 2000 is noticeable.
Figure 5. Mean annual precipitation (P),
actual evapotranspiration (AET), runoff (Q),
and potential evapotranspiration (PET) for
latitudinal bands.
Conclusions
Figure 3. Mean departures of annual precipitation (P), actual
evapotranspiration (AET), runoff (Q), and potential evapotranspiration
(PET) during 2000 through 2009. One color bar is used for P and Q and a
different color bar is used for PET and AET. For both color bars, red
indicates less surface water and blue indicates more surface water.
A monthly water-balance model was used to examine the variability of global P, PET, AET,
and Q during the past century. The analyses indicate that P has been the primary climate
factor driving the variability in Q, even during periods when PET has increased. Around
2000, there was an increase in P, AET, Q, and PET for nearly the entire globe. During this
recent period, PET increased substantially on an annual basis but increases in P,
particularly during the Northern Hemisphere cool months (Oct-to-Mar), resulted in an
overall increase in Q. When viewed in terms of departures from the long-term means, the
variability and changes of water balance variables are clearly evident, particularly after
about 2000. When the changes are examined in the context of raw data time series,
however, the changes are small and indicate little change during the past century. Even if
these temporal changes are small compared to the magnitude of the water-balance
components, these slight variations are important for the management of water
resources and ecosystems. This implies that sensitivity analyses are needed to identify
hydrologic, socio-economic, and ecosystem variables and processes that are sensitive to
small changes in the hydro-climate. These analyses should include the combined effects of
changes in precipitation and temperature. Additionally, given the large uncertainty of
GCM projections of changes in precipitation, sensitivity analyses may be the best
approach to develop water and environmental management plans for the future.