Abstract

The goal of the present study is to elucidate and assess the observed closure and annual variations of the water cycles for the Asian continent and its constituent climatic regions. For this purpose, heavy reliance is placed on simulation as well as observational data. The difference between moisture convergence (MC) and runoff (R) is used as an inverse measure of the closure. Areal averages of MC − R are compared between different areas to decide on its scale dependency and also between different climatic regions categorized by Köppen's climate classification to investigate their annual variations. Atmospheric Model Intercomparison Project (AMIP) II standard output data were used for simulation.

The normal annual means of hydrological variables averaged over the Asian continent are similar between the AMIP II ensemble (MOD) data and the observational (OBS) counterparts, even though MOD and OBS do not exactly agree in terms of their respective regions of distinctive features. In the Asian continent, both OBS MC − R and MOD MC − R are small but in the case of OBS the smallness was due to cancellation of two large and opposite MC − Rs for the dry and mesothermal climatic regions. An appraisal of the closure for each climatic regions has been attempted through comparison between MOD MC − R and OBS MC − R. Nevertheless the relatively poor closures in these two climatic regions surely pose a problem for the simulation community.

The mean annual variations of MOD MC and MOD R, averaged for the Asian continent and its climatic regions, respectively, were analyzed for their uncertainty using the Taylor diagram. MOD R in the dry regions and MOD MC in the microthermal and polar regions are unreliable.

1. Introduction

In many studies thus far, the climatological mean atmospheric moisture budgets including moisture convergence have been estimated, but water conservation or a closure problem was raised in the meantime. A careful comparison and discussion on the global atmospheric moisture budget was performed with respect to its computation methods and the results arrived at using several analyses and satellite datasets by Trenberth and Guillemot (1995). The National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis surface water budget was compared to the results simulated with the NCEP global spectral model by Roads et al. (1999). Latitudinal and seasonal variations of freshwater discharges were investigated by Dai and Trenberth (2002). Recently the studies are being extended to examine seasonal and interannual variabilities of the cycle. On the other hand, through the Global Energy and Water Cycle Experiment (GEWEX) project, the hydrological cycles for the last decade in particular have been investigated intensively with the observational data obtained from in situ, radiosonde, and satellite measurements as well as reanalyses data.

Hydrology can be described in terms of water cycles on many different scales. Water cycles, however, have been considered either on local and landscape scales for practical purposes or on a global scale for conceptual purposes. In the previous studies (e.g., Roads 2002), mainly observational or reanalyses data were used for assessing the global water cycle and a closure problem was noted as an apparent ailment to cure. For example, Roads (2002) reported that the global land hydrological cycle might be closed to within around 10% error in terms of the atmospheric moisture convergence and river discharge. He points out, however, that closure on regional scales is not so certain. Further studies on the latter subject are now being carried out through GEWEX's five regional Continental-Scale Experiments (CSEs; e.g., Roads et al. 2002).

The recent success of climate modeling by GCMs (WGNE AMIP Panel 2001) would seem to offer a good opportunity for at least an ensemble of GCMs to reveal the hydrological closure on regional scales (see Henderson-Sellers et al. 2003). Unlike the observational or reanalyses data to incur the mass imbalance or the closure problem, simulation data would exhibit correct mass conservation since GCMs are devised to satisfy mass conservation. Therefore, atmospheric GCM results were used in this study to investigate the climatological annual mean and variation of the water cycle.

The Asian continent is a vast area containing every climate type as its boundary reaches from the equator to a polar region. Thus, the Asian continent has been divided into several climatic regions and the continent's water cycle has been the subject of concern for each climatic region. Section 2 describes the data and methodology used for this study. Section 3 includes a brief discussion on water budget closure and its scale dependency in order to look at how it differs from the global water budget when the water budget is investigated for the Asian continent. Then the climatological annual mean and variation of water cycle including the closure problem are described and discussed for the Asian continent with its climatic regions in section 4 and 5. Finally, the concluding remarks are in section 6.

2. Data and methodology

a. Data

Our strategy for the appraisal of the yet unclear structure of the water cycle for the Asian continent is to use and compare observational and simulation data. The Global Precipitation Climatology Project (GPCP) version 2 combined precipitation data (Adler et al. 2003), National Aeronautics and Space Administration (NASA) Water Vapor Project (NVAP) precipitable water data (Randel et al. 1996), and the University of New Hampshire–Global Runoff Data Centre Composite Runoff Fields V1.0 (UNH–GRDC) runoff data (Fekete et al. 2000) were used as observational data. Evaporation was computed from latent heat flux as done by Trenberth and Guillemot (1998) and Roads (2002) with NCEP/ Department of Energy (DOE) reanalysis data (Kanamitsu et al. 2002). The observational data were calculated to arrive at the climatological mean monthly fields for 12 yr from 1988 to 1999, but the UNH–GRDC climatological mean monthly data were used for runoff. The combination of these observational datasets is denoted as OBS hereafter and the data sources are summarized in Table 1.

Table 1.

List of the data sources for OBS

List of the data sources for OBS
List of the data sources for OBS

The AMIP II standard outputs were used as simulation data and the models that produced the outputs are listed in Table 2. The data period is 17 yr from 1979 to 1995 and the climatological mean monthly fields were calculated over this period. The AMIP II ensemble (MOD) was calculated with spatially averaged values on each model's own resolution. The ensemble members were selected under the condition that mean annual precipitation minus evaporation and runoff values averaged over the global land are in the range of one standard deviation among the whole models listed in Table 2.

Table 2.

List of the AMIP II models whose standard outputs were used for this study. The models selected for the AMIP II ensemble are denoted by letters A–J (see Figs. 3 and 6)

List of the AMIP II models whose standard outputs were used for this study. The models selected for the AMIP II ensemble are denoted by letters A–J (see Figs. 3 and 6)
List of the AMIP II models whose standard outputs were used for this study. The models selected for the AMIP II ensemble are denoted by letters A–J (see Figs. 3 and 6)

b. Water budget and global adjustment to balance

Assuming no changes in water storages, in order to conserve total water mass globally, the total amount of precipitation has to globally balance that of evaporation. When this balance of global water budget is satisfied, the global mean precipitation minus evaporation must be zero. However, the simulation data as well as the observational data did not satisfy the stipulated balance. They showed nonzero global mean ɛs as defined as the following:

 
formula

where P is precipitation, E evaporation, θ a latitudinal angle, ϕ a longitudinal angle, and a the radius of the earth, and the overbar means long-term average over the given periods. Therefore, prior to an analysis of the climatological water cycle for the Asian continent, the global water budget was constrained to balance on a long-term annual average so that the global average of climatological mean annual precipitation minus evaporation was set to be zero for both the observational and the simulation data. Thus we produced a globally adjusted precipitation minus evaporation, that is, PEɛs such that

 
formula

where ɛs is the global mean value of PE as given by (1).

The values of ɛs are listed for the AMIP II ensemble members and OBS in Table 3. The magnitude of these values can matter with the water closure problem in the Asian continent during discussion in the following sections. What the sources of these errors are was not figured out, and it was handed over to a future further study.

Table 3.

Global average values of climatological mean annual precipitation minus evaporation of each dataset. The capital letters represent each member of the AMIP II ensemble. MOD represents the ensemble mean, and OBS the GPCP precipitation minus NCEP/DOE evaporation. (Units: mm day−1 )

Global average values of climatological mean annual precipitation minus evaporation of each dataset. The capital letters represent each member of the AMIP II ensemble. MOD represents the ensemble mean, and OBS the GPCP precipitation minus NCEP/DOE evaporation. (Units: mm day−1 )
Global average values of climatological mean annual precipitation minus evaporation of each dataset. The capital letters represent each member of the AMIP II ensemble. MOD represents the ensemble mean, and OBS the GPCP precipitation minus NCEP/DOE evaporation. (Units: mm day−1 )

Seven models out of ten resulted in ɛs less than or equal to 0.01 mm day−1, and three models resulted in ɛs of 0.08 ∼ 0.10 mm day−1. MOD showed the global water budget imbalance of 0.03 mm day−1 which corresponds to almost 1% of its global mean precipitation 2.98 mm day−1.

On the other hand, OBS revealed the large imbalance of global water budget with ɛs of −0.52 mm day−1. Most of this error comes from the exaggerated NCEP/ DOE evaporation (Roads 2002; Henderson-Sellers et al. 2003).

Water budget equations expressing water cycle over land are given as follows.

 
formula

where MC is moisture convergence and R total runoff rate. In (4) surface water includes not only soil moisture but also snow amount. The terms on the left side of (3)–(5) are changes in atmospheric water storage, surface water storage, and their sum, respectively. The atmospheric water storage change can be estimated from precipitable water, and the surface water storage change results from changes in soil moisture and accumulated snow amount. The storage changes are negligible on the climatological annual average, but they are not on the climatological monthly averages. Especially the monthly change of surface water storage plays an important role in the surface water budget showing considerable phase difference between PE and R in their seasonal cycles.

In this study, the water cycle for the Asian continent was investigated in terms of moisture convergence and runoff. Thus the right-hand terms of the total water budget equation (5) have been examined as a major concern of this paper. Changes in water storage are assumed to be negligible and therefore long-term trends are not accounted for in this study.

c. Estimation of moisture convergence

Moisture convergence across the boundary of a region may be obtained by using wind and water vapor data at the boundary. Six-hourly or more frequent data are recommended for a decade or so in order to calculate the climatology of moisture transport (Gaffen et al. 1997). In the case of observational data, such data are rarely available for the present. Only reanalysis and simulation data are suitable for the calculation, but they still require a correction of the wind velocity for mass conservation (see Trenberth and Guillemot 1994, Roads et al. 1992, and Roads et al. 2002), which is violated due to an inappropriate treatment of topography or their low vertical resolution while interpolating a variable from a model coordinate onto pressure coordinate (see Trenberth and Guillemot (1995) for detailed discussion on the computation methods of vertically integrated moisture convergence). Most of the variables in the AMIP II standard outputs are provided as monthly data at 17 pressure levels from 1000 to 10 mb. Only several variables are provided as 6-hourly data, but at a few pressure levels such as 850, 500, and 200 mb. After all, neither the observational data nor the AMIP II standard outputs are available with sufficient temporal and vertical resolution for a decade or longer period. Reanalysis data or an individual model integration can be used for the calculation, but they are not on target for the present study.

Hence daily accumulated freshwater flux (i.e., precipitation minus evaporation) and precipitable water are used to estimate moisture convergence as their residual following the atmospheric water budget equation (3). The change of atmospheric water storage would be obtained from monthly precipitable water by means of linear interpolation as given in (6). Here, monthly precipitable water data were regarded as giving the values for the midmonth days (indicated by an integer subscript i):

 
formula

where Δt is one-month time interval and the half-integer subscripts i − 1/2 and i + 1/2 indicate respectively the first day and the last day of the ith month.

d. Köppen climate classification for the Asian continent

The Asian continent is a vast area reaching polar regions to equatorial regions, and contains diverse climate types within the area. We thus divided the continent according to Köppen climate classification (see Lutgens and Tarbuck 1995, chapter 15). Figure 1 shows the climate distribution in the Asian continent. Both the observation data and the AMIP II ensemble data were regridded into a 2.5° × 2.5° array. Climatic Research Unit TS 2.0 data (Mitchell et al. 2003, manuscript submitted to J. Climate) were used to get the Köppen climate distribution for OBS. Ensemble mean precipitation and surface air temperature were used to show MOD's Köppen climate distribution in Fig. 1. However, MOD results analyzed in this study were calculated based on each model's Köppen climate distribution. The areal percentage of the climatic regions in the Asian continent is shown in Table 4.

Fig. 1.

The Asian continent and its Köppen climatic regions. (a) The Asian continent of UNH–GRDC. Köppen climate classification for the Asian continent obtained from (b) the observational data of CRU 2.0, and (c) the ensemble of the AMIP II models

Fig. 1.

The Asian continent and its Köppen climatic regions. (a) The Asian continent of UNH–GRDC. Köppen climate classification for the Asian continent obtained from (b) the observational data of CRU 2.0, and (c) the ensemble of the AMIP II models

Table 4.

Areal percentage of Köppen climatic regions of the Asian continent. MOD and OBS are defined in the text. STD is the inter model standard deviation among the MOD members

Areal percentage of Köppen climatic regions of the Asian continent. MOD and OBS are defined in the text. STD is the inter model standard deviation among the MOD members
Areal percentage of Köppen climatic regions of the Asian continent. MOD and OBS are defined in the text. STD is the inter model standard deviation among the MOD members

3. Water budget closure for the global land and for the Asian continent

a. Water budget closure and its scale dependency

Assuming that the storage changes on the left-hand side of the budget equations (3)–(5) are negligible on a long-term average, closure of the water budgets can be expressed as

 
MC = PE = R
(7)

at every grid point, where PE is the globally adjusted freshwater flux to satisfy (2). The left equality in (7) implies closure of the atmospheric water budget, and the right equality that of the surface water budget, and thus

 
MC = R,
(8)

the closure of the total water budget. Because MC has been estimated as a residual from (3), the closure of the atmospheric water budget is trivial, and the closure of the total water budget becomes indistinguishable from that of the surface water budget.

The magnitude of MC − R can be used as a measure of nonclosure of the total water budget. Figure 2 shows the distributions of OBS and MOD MC − R over the global land. Equation (8) is a local requirement, but it is hardly satisfied on many parts of the global land as seen in Fig. 2. There are gross errors in both distributions even though MOD MC − R is much less than OBS MC − R. One might assume that any nonzero values of MC − R should be of random nature, and expect that MC − R becomes smaller when averaged over larger area. This assumption may be right because in the previous studies (e.g., Roads 2002; Henderson-Sellers et al. 2003) it was noted that MC − R is small on the average over the global land but much larger on the averages over continental regions. This would mean the scale dependency of MC − R. As seen in Fig. 2, OBS MC − R, however, has distinctive structures with large values in South America and in the southern rim of the Tibetan Plateau. The large OBS MC − R in South America, in particular, would make the mean value for the global land to be larger than that for the Northern Hemisphere.

Fig. 2.

Global distribution of MC − R. The interval of isolines is 1. Negative values are shaded. (Units: mm day−1)

Fig. 2.

Global distribution of MC − R. The interval of isolines is 1. Negative values are shaded. (Units: mm day−1)

The areal averages of MC − R are shown in Table 5 for the global land, the Northern Hemisphere land, and the Asian continent. They are respectively −0.12, −0.04, and −0.06 mm day−1 in OBS, while they are also respectively 0.00, −0.02, and −0.04 mm day−1 in MOD. As a result, OBS MC − R do not support the scale dependency whereas MOD MC − R do. Those three land areas include all types of Köppen climate. Discussion on the scale dependency can be made clearer through looking into MC − R on regional scales as in Table 6 for the Asian continent and its climatic regions. Referring to the areal percentage of each climatic region from Table 4, the scale dependency does not appear manifest for both OBS and MOD. Instead these results give an idea that there may exist some regional characteristics in water budget imbalance depending on climate type. For this reason the water cycle for the Asian continent in this study has been investigated according to Köppen climate classification.

Table 5.

Hydrological components P, E, MC, R, and MC − R for the climatological mean annual water budget for the global land, the Northern Hemisphere land, and the Asian continent. (Units: mm day−1 )

Hydrological components P, E, MC, R, and MC − R for the climatological mean annual water budget for the global land, the Northern Hemisphere land, and the Asian continent. (Units: mm day−1 )
Hydrological components P, E, MC, R, and MC − R for the climatological mean annual water budget for the global land, the Northern Hemisphere land, and the Asian continent. (Units: mm day−1 )
Table 6.

Same as in Table 5 except for the Asian continent and its climatic regions

Same as in Table 5 except for the Asian continent and its climatic regions
Same as in Table 5 except for the Asian continent and its climatic regions

b. Effect of the global adjustment of P − E on water budget closure

Table 5 shows some other interesting features of the areal averages of MC − R. First of all, all OBS MC − R averages have been considerably improved by the global adjustment, that is, −0.12 from −0.64 for the global land, −0.04 from −0.56 for the Northern Hemisphere land, and −0.06 from −0.58 for the Asian continent (units in mm day−1). This improvement is irrelevant to the present quality of runoff data.

Nonzero MC − R after the global adjustment of PE may be produced somewhat from 1) the independency between OBS MC and OBS R (in the aspect of data) for OBS; 2) the fact that PE was globally adjusted regardless of R for both OBS and MOD, and; 3) the long-term trends in soil-water storage that may exist (see Henderson-Sellers et al. 2003 for the case of AMIP II). According to Henderson-Sellers et al. (2003), closure of the water budget can be considered achieved within an “acceptable margin” of 0.05 mm day−1. For both OBS and MOD, MC − R is within the acceptable margin for the Northern Hemisphere land and the Asian continent. However, some errors happen in these results, in that every component of OBS was modified to one land mask (the calculated results from its own land mask are shown in the second line of a row in Table 5), and the magnitude of intermodel standard deviation of MOD (the values in parenthesis in Table 5) is already comparable or even larger to this margin.

c. Uncertainty of the MOD closure

Figure 3 shows the individual models' MC − R averaged over the global land, the Northern Hemisphere land and the Asian continent, respectively. MOD MC − R is within the acceptable margin for all of the three types, but the number of models whose MC − R is within the margin for the regions is only two (C and I). On the other hand, two models (B and F out of the 10 models) show the scale dependency, while five models (A, C, G, I, J) show rather the reverse scale dependency. It is stated for reference that B and F (which show the scale dependency) use the simple simplified biosphere land surface model (SSiB; Xue et al. 1991) and the Meteorological Office Surface Exchange Scheme (MOSES; Cox et al. 1999), respectively, as a land surface model. Models A, G, and J (which show the reverse scale dependency) use a bucket land surface model.

Fig. 3.

Imbalance of simulated climatological water budget for the global land, the Northern Hemisphere land, and the Asian continent. The capital letters on the abscissa represent each member of the AMIP II ensemble. (Units: mm day−1)

Fig. 3.

Imbalance of simulated climatological water budget for the global land, the Northern Hemisphere land, and the Asian continent. The capital letters on the abscissa represent each member of the AMIP II ensemble. (Units: mm day−1)

As seen from the individual model results, the magnitudes of MOD MC − R are diminished due to cancellation between large positive and negative individual model errors. Therefore, it is believed to be premature that we persist in the scale dependency of MOD MC − R. Nevertheless, the scale dependency of MOD MC − R will be significant for the present from the point of view that the models which show the scale dependency use the most recent land surface model.

4. Annual mean and closure

a. Climatological annual mean

OBS and MOD's mean annual P, E, MC, and R are enumerated for the Asian continent and its climatic regions in Table 6. OBS and MOD's MC − Rs are similar to each other (−0.06 and −0.04 mm day−1, respectively) in the Asian continent, but they are very dissimilar within each of its climatic regions. Especially in the tropical rainy and dry regions, both OBS and MOD show relatively large magnitudes. Henderson-Sellers et al. (2003) reported the same result in these climate types even if the regions did not belong to Asia. In the microthermal region, OBS and MOD's MC − Rs are very small.

In the dry regions, OBS R is almost zero, but OBS MC is large and seems to be produced owing to the global adjustment of OBS PE. In the mesothermal region, OBS MC − R diminished by the adjustment, but it still shows a large negative value. The positive OBS MC − R in the dry regions and the negative OBS MC − R in the mesothermal region cancel each other in total amount within the areas (see Tables 4 and 6). As a result, OBS MC − R for the Asian continent becomes very small near zero.

MOD MC shows a negative bias in the dry regions and positive biases in the other climatic regions. MOD R shows a large negative bias in the mesothermal region and a large positive bias in the polar region. MOD MC − Rs especially in the tropical rainy and dry regions are −0.08 and −0.09 mm day−1, respectively, which are beyond the acceptable margin. In the other climatic regions, they are within the margin.

The spatial distributions of OBS and MOD's mean annual P, E, MC, and R are shown for the Asian continent in Fig. 4. Generally, in the continent, MOD shows a similar distribution to OBS, but different maximum regions from OBS. In particular, OBS P shows its maximum in Bangladesh to the north of the Bay of Bengal, but MOD P shows its maximum in the Chengdu basin surrounded with mountain regions. The spatial patterns of MC and R follow the distribution of P. This is a common feature among most of the models and is more certain locally in the models (C, E, F) with relatively high horizontal resolution.

Fig. 4.

Climatological mean annual P, E, MC, and R from top to bottom. (left column) The results from GPCP P, NCEP/DOE E, and UNH-GRDC R, and (right column) the results from the AMIP II ensemble (MOD). The interval of isolines is 0.5 between −2 and 2, and elsewhere the interval is 1 for P, E, and MC, and 2 for R. Values >2 mm day−1 are shaded. (Units: mm day−1)

Fig. 4.

Climatological mean annual P, E, MC, and R from top to bottom. (left column) The results from GPCP P, NCEP/DOE E, and UNH-GRDC R, and (right column) the results from the AMIP II ensemble (MOD). The interval of isolines is 0.5 between −2 and 2, and elsewhere the interval is 1 for P, E, and MC, and 2 for R. Values >2 mm day−1 are shaded. (Units: mm day−1)

Figure 5 shows the biases of MOD MC and R. MOD MC shows positive bias in mountainous area but negative bias in plain area overall. In a similar fashion, MOD R shows large negative biases in Bhutan, around the Himalayas and along the east and south coasts of China, and large positive bias in the Chengdu basin. Consequently, this suggests that the effect of topography be one of the problems that the AMIP II models retain.

Fig. 5.

The MOD's bias distribution for (a) MC and (b) R. The interval of isolines is 0.5 between −2 and 2, and 1 elsewhere. Negative values are shaded. (Units: mm day−1)

Fig. 5.

The MOD's bias distribution for (a) MC and (b) R. The interval of isolines is 0.5 between −2 and 2, and 1 elsewhere. Negative values are shaded. (Units: mm day−1)

b. Uncertainty of the MOD annual means

Individual models' MC − Rs are shown for the Asian continent and its climate types in Fig. 6. Half of the models (A, C, G, I, J) showed MC − R near zero for all climate types. Out of the five models, three models (A, G, J), which showed the reverse scale dependency as mentioned in section 3a, satisfied the water budget balance for all climate types. Recall that the three models commonly use a bucket model. Model F should have shown almost zero MC − R for all climate types without the global adjustment of PE (i.e., 0.09 mm day−1 from Table 3). In this case of model F, the global adjustment rather exaggerated MC − R and is regretful. Although MOD MC − R is lesser than OBS MC − R, some models' MC − Rs are much greater than OBS MC − R in magnitude for all climate types.

Fig. 6.

Same as in Fig. 4, except for the Asian continent and its Köppen climatic regions

Fig. 6.

Same as in Fig. 4, except for the Asian continent and its Köppen climatic regions

5. Annual variation and closure

a. Climatological annual variation

Moisture convergence for this study is estimated from (3). Prior to estimating MC, changes in the atmospheric water storage is calculated with precipitable water from (6). Figure 7 shows annual variations of not only the changes in atmospheric water storage (right column), but also, precipitable water (left column). The amplitudes of the variations are relatively large in the tropical rainy and the mesothermal regions including the monsoon region, compared to the other climatic regions. The annual variations of OBS and MOD show almost the same amplitude but different phase, with coherence for all of the climatic regions. For every climatic region, OBS precipitable water reaches its maximum in June, while MOD precipitable water reaches its maximum 1 or 2 months later, that is, July to August. The OBS and MOD annual variations of the atmospheric water storage change show about 1-month phase difference relative to each other.

Fig. 7.

Climatological annual variation for the Asian continent and its Köppen climatic regions. (left column) Monthly precipitable water, and (right column) the change in atmospheric water storage. Dashed lines denote OBS; solid lines denote MOD, and the error bars along the solid lines are the intermodel standard deviation among the ensemble members. (Units: mm day−1)

Fig. 7.

Climatological annual variation for the Asian continent and its Köppen climatic regions. (left column) Monthly precipitable water, and (right column) the change in atmospheric water storage. Dashed lines denote OBS; solid lines denote MOD, and the error bars along the solid lines are the intermodel standard deviation among the ensemble members. (Units: mm day−1)

The estimated MC and R are shown together in Fig. 8. The annual variations of OBS R and MOD R are generally similar to each other, but those of OBS MC and MOD MC are not, except in the tropical rainy region. In the Asian continent, R increases in March to May, is maintained during the rainy summer, and decreases from September to November. OBS MC reaches its maximum in August, while MOD MC reaches its maximum in July. MOD MC, however, shows positive bias from March to June and negative bias from August to November.

Fig. 8.

Same as in Fig. 7, except for (left) MC and (right) R. The numbers next to OBS and MOD are their annual mean and standard deviation

Fig. 8.

Same as in Fig. 7, except for (left) MC and (right) R. The numbers next to OBS and MOD are their annual mean and standard deviation

In the tropical rainy region, OBS MC and MOD MC show a maximum of 5 mm day−1 or so in July or August, and they are consistent. In the dry regions, OBS MC shows a similar variation to MOD MC, but shows positive bias of around 0.5 mm day−1 during the year except for June. On the other hand, MOD MC shows moisture divergence during the spring and fall seasons. It should be noted that the global adjustment amount of 0.52 mm day−1 (see Table 3) is comparable to the positive bias of OBS MC, and thus the difference between OBS MC and MOD MC would seem to be quite artificial in the dry regions. Then the exaggerated NCEP/DOE evaporation which was believed to lead the global adjustment (see section 2b) was not valid for the dry regions, and thus, the adjustment was not proper for the dry regions. In these dry regions, however, the MOD moisture divergence during the spring and fall seasons is a notable feature. In the mesothermal region, OBS MC and MOD MC show the maximum of about 2.5 mm day−1 in July and June, respectively. While OBS MC is nearly negligible from October through April of the following year, MOD MC reaches its minimum in October and increases consistently until June of the following year. Accordingly, MOD MC has positive bias from February to May. In the microthermal region, OBS MC decreases during the early part of the year, shows significant moisture divergence from April to June (related to the minimum of OBS MC in the Asian continent in April and May), then increases from July to August, and maintains a consistent value of about 1 mm day−1 until the end of the year. Unlike the annual variation of the OBS MC, MOD MC adheres to around 0.6 mm day−1 throughout the year. Note that MOD MC has a quite certain structure in this microthermal region because its intermodel variability is particularly small. In the polar region, MOD MC shows large positive bias, especially during summertime. Here, OBS MC has a maximum of about 1.3 mm day−1 from August to September and MOD MC about 2.3 mm day−1 in July.

In the Asian continent during the first half of the year, the bias in MOD MC results from the overestimated precipitation and underestimated evaporation which is systematic during that period among AMIP II models (see Fig. 9). This systematic bias is coherent for precipitation in the microthermal and polar regions and for evaporation in all of the climatic regions except for the polar region. Therefore, this bias in MOD MC arises mainly from the evaporation bias in the mesothermal region, precipitation and evaporation biases in the microthermal region, and precipitation bias in the polar region, respectively. On the other hand, in the Asian continent during the second half of the year (from July to December), the bias in MOD MC may be caused by the global adjustment of PE.

Fig. 9.

Same as in Fig. 7, except for (left) precipitation and (right) evaporation

Fig. 9.

Same as in Fig. 7, except for (left) precipitation and (right) evaporation

In all of the Asian climatic regions, OBS R and MOD R are close to zero from November to March or April of the following year. Especially in the dry regions, they are almost zero throughout the year. The bias in MOD R is manifested mostly in the mesothermal and polar regions during summer. In these regions, the biases in MOD R compensate for each other, and thus in the Asian continent, the bias in MOD R has been reduced. Nevertheless, comparing Fig. 8 and Fig. 9, Rs in the tropical rainy and mesothermal regions follow the pattern of precipitation. The Rs in the microthermal and polar regions show their maximums before summer. Snow melting may have an influence on this result, but deeper discussion regarding biases of R is beyond the scope of this paper.

b. Uncertainty of the MOD annual variations

In order to look into the annual variations of individual models as well as that of MOD more specifically, a Taylor diagram (Taylor 2001) was shown in Fig. 10. In this figure, annual variation is expressed as a circle representing an individual model. A solid circle represents annual variation of model's MC, and an open circle that of a model's R. The unit point (a reference point) on the abscissa represents an annual variation of MOD. Thus, this diagram compares a model point to the reference point. In a Taylor diagram, the length of a segment from the origin to a model point is the standard deviation of an annual variation, and the angle that the segment makes with the abscissa is a correlation coefficient between the annual variations of MOD and a model. A scale mark for the correlation coefficient is given on the arc outline of the diagram. The distance from a model point to the reference point is the root-mean-square difference (rmsd) between the annual variations of MOD and a model. In this figure, the standard deviation and rmsd of the annual variation of a model are normalized by the standard deviation of the annual variation of MOD. A model point whose distance from the origin is longer than 1 has a larger amplitude of annual variation than that of MOD's annual variation. Figure 10 shows only the models that have positive correlation with MOD.

Fig. 10.

Taylor diagram for the annual variations of MC (solid circles) and R (open circles) in the Asian continent and its Köppen climatic regions. The unit point on the abscissa represents the annual variation of MOD, and each circle represents an individual model. The length of a radial ray is the annual standard deviation of a model normalized by that of MOD, and the angle between the ray and the abscissa is the correlation between the annual variations of MOD and a model

Fig. 10.

Taylor diagram for the annual variations of MC (solid circles) and R (open circles) in the Asian continent and its Köppen climatic regions. The unit point on the abscissa represents the annual variation of MOD, and each circle represents an individual model. The length of a radial ray is the annual standard deviation of a model normalized by that of MOD, and the angle between the ray and the abscissa is the correlation between the annual variations of MOD and a model

In the tropical rainy region (Fig. 10b), from the viewpoint that the model points gather near the reference point, the annual variations of MOD MC and R are quite reliable. As seen from Fig. 8, the annual mean of MOD R in the dry regions is close to zero, and the annual variation of that has a very small standard deviation. The annual variation of an individual model normalized by the standard deviation of MOD R has a considerably large nondimensional amplitude, and thus, in Fig. 10c, the dispersion of the model points for R become quite scattered. Similarly, in the microthermal region, MOD MC also shows a very small amplitude of annual variation (see Fig. 8), and thus, the dispersion of the model points for MC become scattered in Fig. 10e.

Correlation between an individual model's annual variation and MOD's annual variation is high in every climatic region of the Asian continent except for the dry region, and mostly shows the coefficients of 0.7 or higher. Especially in the tropical rainy region, the correlation coefficient is over 0.9.

To measure quantitatively dispersion of the model points expressed in the Taylor diagram, variances among the model points were calculated for every climate type and enumerated in Table 7. A variance of the model points (xm, ym) (where m = 1, 2, … , 10 is a model identification index) is given as

 
formula

where xm = (σm/σr) cosθ, ym = (σm/σr) sinθ, x and y are, respectively, average values of xm and ym, N(=10) is the number of models, θ is arc cosine of a correlation coefficient between the annual variations of MOD and a model, and σm and σr are standard deviations of the annual variations. When all the models gather at the same point, V2 = 0. When the measure of dispersion of the models is the same as the amplitude of the annual variation of MOD, V2 ≃ 1. Although the measure of dispersion of the models V2 itself does not mean uncertainty of the annual variation of MOD, it provides a major source of that uncertainty.

Table 7.

A measure of uncertainty of the MOD annual variation for MC and R in the Asian continent and its climatic regions. The values have been obtained by using Eqs. (9) and (10). Nondimen sional units

A measure of uncertainty of the MOD annual variation for MC and R in the Asian continent and its climatic regions. The values have been obtained by using Eqs. (9) and (10). Nondimen sional units
A measure of uncertainty of the MOD annual variation for MC and R in the Asian continent and its climatic regions. The values have been obtained by using Eqs. (9) and (10). Nondimen sional units

The uncertainty of MOD's annual variation must be expressed to the extent of how far the model points are from the reference point. For this,

 
formula

is proposed as a measure of the uncertainty. Here rmsdm is a rmsd between the annual variations of MOD and mth model normalized by the standard deviation of MOD's annual variation.

As seen from Table 7, confidence for MOD MC is relatively high in the tropical rainy, dry, and mesothermal regions. From this table, MOD R is not reliable at all in the dry regions. Accordingly, AMIP II models simulate the annual variation of MC well in warmer climate regions, but they do not in colder climate regions.

6. Concluding remarks

In this paper, it is found that the closure of the water budget raises a problem from two viewpoints. First, because the global mean PE of the climatological OBS was not zero, an adjustment was required so as to render it to zero. Second, in spite of or due to the adjustment, climatological MC − R was not zero, neither in the Asian continent nor in its climatic regions. In the Asian continent, MC − R is more or less than −0.05 mm day−1 in OBS and MOD. The global adjustment especially for OBS is considered to lead the water budget closure (MC = R) successfully in the Asian continent. Consequently, in each of the Asian climatic regions except for the dry regions, the global adjustment for OBS improved closure of the water budget. However, OBS MC − R shows a large positive bias in the dry regions, while OBS MC − R still shows a large negative bias in the mesothermal region. Hence, it may be problematic to define the global adjustment as a constant. This implies that it is important to recognize a regional contribution to the global adjustment amount (−0.52 mm day−1) for every climate type.

Particularly, the discrepancy between MC and R in the dry regions results from the artificial increment through the global adjustment. This judgment for the result became possible by means of comparison of the annual variations between MC and R. In this manner, the characteristics of a regional closure of water budget in terms of MC − R can be revealed through analyzing the structure of its annual variation.

In the Asian continent, the global adjustment for OBS MC had influences on the MOD's bias, that is, decrease during the first half of the year and increase during the second half of the year. As seen from Fig. 9, there is no significant bias in both precipitation and evaporation during the second half of the year. Therefore, the bias in MOD MC during the second half of the year is almost entirely caused by the global adjustment. On the other hand, the bias in MOD MC during the first half of the year is caused by overestimated precipitation and underestimated evaporation as in Fig. 9. In this way, the characteristics of bias in MOD MC are suggested to be analyzed in a climatic region with distinctive seasons of the year.

In the microthermal region, the annual variation of MOD MC has a much smaller amplitude than that of OBS MC, but has a stable structure among all AMIP II models. From this context, it may be informative and helpful to analyze ensemble results as well as observational data for careful study about the water cycle.

In spite of the uncertainty captured from the results of MOD, the validity of the following results may not be reduced in the near future: 1) The closure of MOD MC = R is achieved within the error of 0.1 mm day−1 in the Asian continent and its climatic regions; 2) The moisture divergence in the dry regions during the spring and fall seasons possibly retain a significant physical reason though it was not explained in this paper. Of course, the latter statement should be proved in a further study.

Last, we suggest that the water cycle and water budget for a region with a distinctive climate type be analyzed only after the areal mean MC − R is corrected to be zero.

Acknowledgments

The present study was supported by the Meteorological and Earthquake R&D programs of the Korea Meteorological Administration. The GPCP combined precipitation data were developed and computed by the NASA Goddard Space Flight Center's Laboratory for the Atmosphere as a contribution to the GEWEX Global Precipitation Climatology Project. The NVAP precipitable water data were obtained from the NASA Langley Research Center Atmospheric Sciences Data Center. The authors would like to thank PCMDI and AMIP II modelers for allowing us to use the AMIP II standard outputs for the present study. The authors also thank the editor and reviewers. The reviewers' comments were very helpful in the revision.

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Footnotes

Corresponding author address: Ho-Jeong Shin, Global Environment Laboratory, Yonsei University, 134 Shinchon-dong, Seodaemun-ku, Seoul 120-749, South Korea. Email: shj@atmos.yonsei.ac.kr