Stable water isotopes (D and 18O) in precipitation have large spatial and temporal variability and are used widely to trace the global hydrologic cycle. The two models that have been used in the past to examine the variability of precipitation isotopes are Rayleigh-type models and isotope-atmospheric general circulation models. The causes of short-term (1–10 day) variability in precipitation isotopes, however, remain unclear. This study seeks to explain isotope variability quantitatively at such scale. A new water isotope circulation model on a global scale that includes a Rayleigh equation and the use of external meteorological forcings is developed. Transport and mixing processes of water masses and isotopes that have been neglected in earlier Rayleigh models are included in the new model. A simulation of 18O for 1998 is forced with data from the Global Energy and Water Cycle Experiment (GEWEX) Asian Monsoon Experiments (GAME) reanalysis. The results are validated by Global Network of Isotopes in Precipitation (GNIP) monthly observations with correlation R = 0.76 and a significance level >99% and by daily observations at three sites in Thailand with similar correlation and significance. A quantitative analysis of the results shows that among three factors that cause isotopic variability, the contribution of moisture flux is the largest, accounting for 37% at Chiangmai, and 46% globally. This highlights the importance of transport and mixing of air masses with different isotopic concentrations. A sensitivity analysis of the temporal and spatial resolution required for each variable is also made, and the model is applied to two additional data sets. The more accurate Global Precipitation Climatology Project (GPCP) precipitation data set yields improved model results at all three observation sites in Thailand. The National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis allows the simulation to cover 2 years, reproducing reasonable interannual isotopic variability.
 Stable isotopes of water, D and 18O, have been used as tracers of the hydrologic cycle for more than 50 years. The first studies that considered isotopes focused on isotopic enrichment and the isotopic uniformity of seawater [Gilfillan, 1934; Epstein and Mayeda, 1953; Friedman, 1953]. Dansgaard  made the first successful trial to quantitatively understand the water isotopes in precipitation. Subsequent studies used isotopic characteristics to analyze precipitation at different spatial and temporal scales, as classified by Welker . The studies have revealed great heterogeneity in the temporal and spatial distributions of precipitation isotopes. These precipitation characteristics are well known as several isotopic effects [e.g., Clark and Fritz, 1997].
 Past studies frequently used Rayleigh's distillation process (the Rayleigh equation as described below) and developed models [e.g., Dansgaard, 1964; Jouzel and Merlivat, 1984; Ciais and Jouzel, 1994] to help explain spatial and temporal variability in precipitation isotopes. The physical basis behind the Rayleigh equation that governs precipitation isotope is that isotopes are exchanged between moisture in rising air and falling droplets and precipitation essentially “forgets” any isotopic label from in-cloud processes as isotopic equilibrium with the ambient air is established [Friedman et al., 1962; Gat, 2000].
 A common weakness in Rayleigh models is oversimplification of the full complexity of the global hydrological cycle [Hoffmann et al., 2000]. In particular, Rayleigh models were assumed to be unable to account for the mixing of air masses of different origin and the high variability of vapor pathways from the site of evaporation to the site where condensation takes place and finally the water precipitates. Consequently, Rayleigh equations have been used only for qualitative explanations of observed isotopic characteristics, for example, isotopic depletion of precipitation far from the ocean or at high altitudes.
 Therefore it was a big step when Joussaume et al.  incorporated the physics of water isotopes into an atmospheric general circulation model (AGCM), the model of the Laboratoire de Meteorologie Dynamique (LMD). Subsequently, Jouzel et al.  embedded the water isotopes in the Goddard Institute for Space Studies (GISS) model, Hoffmann et al.  embedded the water isotopes in the European Center model modified in Hamburg (ECHAM) model, Mathieu et al.  embedded the water isotopes in the Global Environmental and Ecological Simulation of Interactive Systems (GENESIS) model, and Noone and Simmonds  embedded the water isotopes in the Melbourne University GCM (MUGCM). Thereafter, recent similar studies have been trying to couple stable isotopes with mesoscale models inquiring into more precise isotopic phenomena such as internal structure of storms [e.g., Gedzelman et al., 2003; Lawrence and Gedzelman, 2003]. AGCMs already take account of the complexity of the atmospheric processes leading to the global hydrological cycle, which is oversimplified in Rayleigh-type models. AGCMs that include isotopes should be better at reproducing observed spatial and temporal heterogeneity of precipitation isotopes. Indeed, isotope-AGCM studies have reasonably reproduced the major isotopic features in precipitation, and have revealed the large-scale characteristic of observed isotope-climate relationships [Mathieu et al., 2002].
 Such reproductions, however, have been reasonable only for monthly or annual averages. Many regional isotopic studies have shown that short-term isotopic variability in precipitation is much greater than that over a season or a month. Such studies include those by Jacob and Sonntag  for western Europe, Njitchoua et al.  for Africa, Rindsberger et al.  for Israel, Welker  for the United States, Shimada et al.  for Japan, and the present study for Thailand, as detailed below. As Hoffmann et al.  noted, isotope-AGCM studies cannot reproduce this short-term isotopic variability, perhaps because of spatial resolution limitations. They noted that rain formation processes that influence isotopic signals of single precipitation events occur on small spatial scales, about 30 km in the horizontal [Ehhalt and Öestlund, 1970], and current models, with horizontal resolutions of more than 100 km, cannot accurately account for such processes.
 The failure of isotope-AGCMs to reproduce short-term variability may have other causes, however. Isotopic variability with time has been observed at spatial scales of greater than 100 km in the horizontal, despite rain formation processes on smaller horizontal scales. For example, Yamanaka et al.  showed that spatial variability of the temporal variability at 18 observation sites in a 150 km by 150 km region around Tokyo, Japan, was small compared to event-based temporal variability. In addition, daily precipitation isotopic data have been collected and analyzed at three sites in Thailand (Bangkok, Sukhothai, and Chiangmai; see Figure 1) since 1998. These data show similar temporal variability (Figure 2), even though Bangkok and Chiangmai are 600 km apart and single precipitation events on small spatial scales are common during the rainy season in Thailand. This spatially uniform temporal variability suggests that large-scale moisture transport dominates the control of short-term isotopic variability. Furthermore, regional processes at smaller scales, such as the formation of cloud liquid and solids in single storms and their convective redistribution within the clouds, are of secondary importance. If so, the cause of the failure is likely due to the fact that short-term-averaged meteorological field from AGCMs are less realistic than monthly averaged or annual-averaged values. Short-term isotopic variability hence has not been accurately reproduced.
 This paper will quantitatively explain the short-term variability of precipitation isotopes, focusing on whether moisture transport at large scales is important. A new model is developed that simulates the global circulation of atmospheric water and its isotope. Unlike isotope-AGCMs, the new model incorporates external meteorological data sets that are more realistic than the internally generated circulation fields in the AGCMs. The more realistic external data sets are taken from reanalyses that include long-term gridded global data sets of key variables constrained and assimilated by observations [Bengtsson and Shukla, 1988]. It is difficult, however, to incorporate all atmospheric physics including in-cloud microphysical processes or convection activities, because of the limited number of variables included in the reanalyses. It is hence useful to include a Rayleigh equation to simulate isotopic fractionation in the precipitation. The Rayleigh equation, as noted above, describes an isotopic equilibrium relationship between precipitation and ambient air, regardless of any isotopic variability introduced by in-cloud processes. Thus the Rayleigh model, which includes previously neglected transport and mixing of water masses and their isotopes, is also suitable for evaluating the impact of transport at large scale on precipitation isotope. The new model is therefore named a Rayleigh-type isotope circulation model that is intermediate between Rayleigh-type models and isotope-AGCMs.
 The second section briefly introduces the fundamentals of the Rayleigh equation and of stable isotopes in water. The Rayleigh-type isotope circulation model is detailed in the third section. This is followed in the fourth section by a description of, and results from, a control simulation. A quantitative analysis of short-term isotopic variability is also demonstrated. The fifth section includes sensitivity experiments and simulations using different meteorological data sets. The last section contains a summary and conclusions.
2. Fundamentals of Water Isotopes
 The stable water isotopes D and 18O are measured in units of parts per thousand (‰) relative to a standard (standard mean ocean water (SMOW)) composition. For example, δ18O values are calculated by
where RA and RS denote the ratios in the sample and standard, respectively, of the heavy to light isotope (18O/16O).
2.2. Fractionation and Fractionation Factor
 Because of mass differences, H and D and 16O and 18O have different chemical and physical properties. Such differences are manifested as a fractionation effect. When water changes phase from liquid to gas, the heavy isotopes preferentially enrich in the liquid. The fractionation is expressed as the isotope fractionation factor α
where RA and RB are the isotope ratios of phase A and phase B, respectively. When αA,B > 1, the heavy isotopes are enriched in phase B. When αA,B < 1, the heavy isotopes are depleted in phase B.
2.3. Rayleigh Equation
 As water changes phase, the evolution of the isotopic composition is described by a Rayleigh equation with fractionation factor α as follows for 18O,
where R0 and R are the initial and final isotope ratios, δ18O0 and δ18O are the respective δ-values, and W0 and W are the initial and final amounts of water in the final phase.
3. Model Description
 The isotope circulation model used in this study is simpler than those of previous isotope-AGCM studies. The model consists of a global grid (1.25° × 1.25° or 2.5° × 2.5° and one vertical layer), and each grid is approximated as a trapezoid. As illustrated in Figure 3, the model computes water transport by maintaining the atmospheric water balance [Oki et al., 1995] with the upstream scheme in each grid at every time step. The model time step (Δt) is 10 min. This scheme, however, often does not satisfy Courant-Friedrichs-Lewy (CFL) condition near the Poles because of the short distance between grid points there. Calculations are therefore not performed poleward of 85N or 85S, and a constant value (−30‰) for the isotope composition of vapor is assigned there. This abbreviation may cause uncertainties in the model at high latitudes, but isotopic influence of those polar regions on main target areas of the present study, the tropics and the subtropics including Thailand, is assumed as negligible. Finally, during every time step in water transport calculation, the isotopic compositions (δ-value) of both vapor and precipitation are calculated using isotopic mass balance and Rayleigh fractionation as described below.
 One notable feature of the model is its single layer in the vertical. Vertical profiles of water and isotope composition are included as vertical integrations. In this way, processes that influence the local isotopic composition of precipitation, including the formation of cloud liquid or solid and their redistribution by convection [e.g., Hoffmann et al., 2000], all cancel out. Indeed, the model considers only the fractionation generated by condensation at large horizontal scales using the fractionation factor α. Here, “large-scale condensation” means the spatially averaged accumulating precipitation in each grid.
 There is one more distinctive model characteristic. When the model calculates the atmospheric water balance, it uses forcing variables computed from external meteorological data sets such as reanalyses or observations. Thus the model can reproduce the water cycle more realistically than isotope-AGCM studies.
where W, −∇ · , P, and E represent precipitable water, horizontal water vapor flux convergence, precipitation and evaporation, respectively. is the vertically integrated vapor flux vector; its components are the zonal and the meridional fluxes, Qλ and Qϕ, respectively. Qλ, Qϕ, and W are defined as follows:
where q, u, v, g, p, and p0 are specific humidity, zonal wind speed, meridional wind speed, gravitational acceleration, atmospheric pressure, and surface pressure.
 Here, we tried a test calculation using −∇ · , P, and E from the Global Energy and Water Cycle Experiment (GEWEX) Asian Monsoon Experiments (GAME) reanalysis [Yamazaki et al., 2001]. Figure 4 shows the results, and the monthly change in precipitable water is unrealistically large, up to 150 mm per month. Such problematic results have occurred in similar atmospheric water balance studies [e.g., Bosilovich and Schubert, 2001; Kanae et al., 2001] because the balance equation is not always closed. In fact, if external meteorological data are used, the unclosed nature of the balance equation is inevitable. The water balance equation (4) is discretized
Regarding the fact that the water balance is not closed, calculated W(t+Δt) is used for the isotopic balance equations given below. In the next time step, however, precipitable water on the right side of equation (8) is taken from observed (or reanalyzed) precipitable water instead of using W(t+Δt) in the previous time step.
3.2. Isotope Mass Balance Coupled With Rayleigh Fractionation
 Discretized water balance equation (8) is combined with isotopic mass balance to yield
where δw, δe, and δp are the isotope ratios of precipitable water, evaporation, and precipitation. The term ∇ · is defined as
where Rc is radius of the Earth and λ and ϕ denote longitude and latitude, respectively. If only precipitation causes isotope fractionation, the Rayleigh equation (3) can be rewritten as
where W and δ w are the precipitable water and its isotopic ratio, respectively; W* and δw* are those just before precipitation occurs (W* = W + PΔt); and α is the fractionation factor. Then, if mass and isotope balance are conserved, the isotope ratio of the precipitation is
where f = W/W*. Finally, the weighted daily mean precipitation isotope ratio is calculated.
4. Control Simulation
 The model domain for the control simulation is 1.25° × 1.25° and one vertical layer. Simulation results will be validated by monthly and daily observations. However, for the moment, daily data are only available in Thailand, sampled at three sites as part of the activities of the GEWEX Asian Monsoon Experiment (GAME). The focus of this study is therefore an area influenced by the Asian Monsoon, specifically Thailand. A reanalyzed data set that is achieved also by the GAME activities, called the GAME reanalysis version 1.5, is used for all forcing variables, such as W, , E, P. The GAME reanalysis has been constrained by many assimilated observations in the Asian Monsoon region. Moreover, the data set resolution is finer on temporal (6-hourly) and spatial (1.25° × 1.25°) scales than other reanalyses. The use of the GAME reanalysis is therefore reasonable for the control simulation, despite the short 7-month period reanalyzed (0000 UTC 1 April to 1800 UTC 31 October 1998).
 This study focuses on the short-term variability of 18O for the present, and the circulation of 18O will be simulated. The fractionation factor α is set to 1.0094 at 25°C [Majoube, 1971]. Further, to help determine the δ18O value of the evaporating vapor, δe, the global surface is divided into three parts: seas, land between 40°N and 40°S, and everywhere else. The values for the three regions are −9.4‰, −10‰, and 15‰, respectively. These values are grounded on the following assumptions, respectively: isotopically uniform (0‰) and limitless seawater is assumed to make uniform −9.4‰ evaporating vapor by equilibrium fractionation at 25°C (α = 1.0094) over all seas; the weighted zonal averages of observed annual mean δ18O in precipitation between 40°N and 40°S are quite uniform, approximately −5‰ [Mathieu et al., 2002], a composite of half transpiration from plants (with no isotopic fractionation [Zimmerman et al., 1967]) and half evaporation from bare soil and watery surface (with fractionation at normal temperature) makes −10‰ for δe in 40°N–40°S; and more isotopic depletion of the weighted mean precipitation isotopes for the rest of regions (>40°N and >40°S), approximately −10‰, makes −15‰ for δe using the same assumption as above. Note that isotopic behavior that accounts for interactions between land surface and atmosphere is still uncertain because of model complexity and lack of observational validity [Mathieu and Bariac, 1996], so that the constant values in time series and the rough spatial division into two parts are made for δe on land.
 Specifications for the control simulation are displayed in Table 1. An initial δ-value of atmospheric water δw0 is set to 0‰ at all grid points. The model runs for the first month (April 1998) to reach an isotopic steady state, and reruns from 1 April with the δ-value on 30 April in the first run at each grid point.
Table 1. Control Simulation Specifications
1.25° × 1.25°
1 April 1998 to 31 October 1998
W (precipitable water)
α (fractionation factor)
δe (isotope ratio of E)
−9.4 (‰) on sea
−15 (‰) on high-latitude land
−10 (‰) on low-latitude land
4.2.1. Comparison With Monthly Global Observations
 First, monthly and global simulation results are validated. Global maps of δ18O in monthly precipitation are shown in Figure 5. The “latitude effect” and “continental effect” [e.g., Ingraham, 1998] are clearly reproduced on a global scale. Seasonality is also evident. For example, differences between April and August are significant, especially the depletion in the northern subtropics and the enrichment near the equator. Further, we can see isotopic depleted bands near the equator in all the panels, and they probably correspond with the Intertropical Convergence Zone and its seasonal shift.
Figure 6 shows a comparison in August with monthly Global Network of Isotopes in Precipitation (GNIP) observations (International Atmoic Energy Agency-World Meteorological Organization, Global Network of Isotopes in Precipitation: The GNIP database, 2001, accessible at http://isohis.iaea.org). The GNIP data are weighted monthly means of precipitation for several years, but interannual variability is not as large as seasonal or daily variability, so these values can be used for comparison.
Figure 6a displays the success of the model in reproducing features in the oceans, northern Eurasia, South America, Australia, Africa, and Southeast Asia, within 6‰ error range. Figure 6b shows that the model successfully reproduced spatial characteristics on a global scale. The correlation coefficient was 0.76, with a significance level exceeding 99%, and the root mean square error (RMSE) was 4.80‰. A quantitative comparison of these values with earlier similar studies is quite difficult because the previous isotope-AGCMs emphasized the relationship between local temperature and isotope. However, some of the earlier studies include error contour maps as in Figure 6a, and according to those maps, their one-to-one results seem less accurate than their temperature-isotope results. For example, Mathieu et al.  has errors as large as 14‰ for mountainous regions such as Tibet or the Rocky Mountains. In addition, a recent isotope-AGCM study by Vuille et al.  includes the results of different isotope-AGCMs and several one-to-one comparisons for the weighted annual means in Americas. The reported correlation coefficients are in the range between 0.44 to 0.79. Thus the present model results are accurate enough for a first-order global estimate. However, isotope ratios are sometimes smaller than observed values. These underestimates suggest that the model needs to be improved.
 The GNIP data set for this comparison includes only 389 observation points. The observation network is therefore not dense enough to describe global precipitation isotope distributions accurately. Furthermore, the minimum temporal unit in the GNIP data set is as long as a month, but monthly observation data are not always available. Observations with finer spatial and temporal scales, such as the observations for Thailand shown above, are required for global validation.
4.2.2. Comparison With Daily Observations in Thailand
 The previous discussion highlighted the good agreement between global and monthly 18O simulations and observations. Figure 7 shows the simulated results and a comparison with daily observations at three sites in Thailand, which indicates that the model reproduced the variability of the precipitation isotopes at both short and seasonal timescales. In detail, at Chiangmai, a depleted peak near 1 July, a following enrichment until 6 July, and a depletion again until 11 July were well reproduced. A continuous increasing trend from the end of July to the middle of August and a sudden depletion around 20 August were also traced. The correlation coefficients and RMSEs are 0.76 and 4.23‰ at Chiangmai (18.8°N, 99.0°E), 0.72 and 4.10‰ at Sukhothai (17.0°N, 99.8°E), and 0.56 and 3.50‰ at Bangkok (13.8°N, 100.5°E). All correlation coefficients are significant at a level exceeding 99%.
 In contrast to the good reproduction of the isotopic variability, however, the discrepancy of overdepleted values in the simulation by 4‰ is apparent, as is the case with the global monthly results (previous section). This may be due to several uncertainties in the model (discussed in the last paragraph of section 6) and the errors included in the external variables, the GAME reanalysis, to some extent (discussed in the next section). It is meaningful, though, that however much those uncertainty and errors are included, good reproduction of the short-term variability is made by the simple Rayleigh-type circulation model.
 To explain the control factors of isotopic variability, we will focus on the results for Chiangmai. Figure 8 shows the temporal fluctuations of δ18O in vapor and precipitation, and the forced precipitation. There is a little negative correlation between precipitation and its isotopic composition (R = −0.34). On the other hand, there is a very strong correspondence between the isotopes in the vapor and the precipitation (δp ≃ δw + 9, R = 0.99).
 This indicates that the impact of the amount of precipitation at Chiangmai, i.e., “amount effect,” is insufficient to explain the short-term isotopic variability in the precipitation. On the other hand, the isotopic composition of the precipitation is strongly dependent on the isotopic composition of the vapor above the site. Obviously, this close relationship is due to a link between water vapor isotopes and precipitation isotopes through the fractionation factor. It tells us, however, that what controls the water vapor isotopes also controls the variability of the precipitation isotopes. The present model calculates isotopic composition of water vapor by taking into account horizontal water vapor transport that is influenced by precipitation and evaporation along the transport trajectory. In other words, water and isotopic mass balance on over 100 km horizontal scale control variability of water vapor isotopes. The good agreements between the model results and the daily and monthly observations therefore imply that moisture transport at large scales (>100 km) dominantly controls the short-term isotopic variability of precipitation, particularly over Thailand. The following section provides a more precise account of the control factors of the short-term variability.
4.3. Control Factors of Short-Term Isotopic Variability
 The control factors of short-term vapor isotopic variability will be quantitatively analyzed in this section. This model includes only four forcing variables, , E, W, and P, to simulate atmospheric water circulation. Of the four, the change of precipitable water is dependent on other forcings, as shown in discretized water balance equation (8). Therefore precipitable water has little impact on short-term isotopic variability. Furthermore, because isotope-related parameters such as α and δe are constant for the period in the control simulation, the three forcings , E, and P must govern the isotopic circulation and generate spatial and temporal variability in the water vapor isotopes.
 From the isotope balance equation (9), the change in the isotopic ratio in the precipitable water Δδw consists of three terms by each derivation
If the sizes of these terms are calculated, the impacts of each forcing on the isotopic variability can be quantitatively examined. Results for the control simulation are given in Figure 9. Moisture flux both depletes and enriches the isotopes, but precipitation only depletes and evaporation only enriches. More significantly, the fluctuations in and (Δδw)P are very large relative to the nearly constant (Δδw)E. Thus it is likely to be precipitation or moisture flux that generates any sudden isotopic depletion or enrichment in precipitation isotope variability. The daily average of the absolute value is 1.02‰ for , 0.73‰ for (Δδw)E, and 1.01‰ for (Δδw)P. In Chiangmai for the simulation period, isotopic variability is controlled to some degree by moisture flux and precipitation, and to a lesser degree by evaporation. The averaged contributions to the isotopic variability are 37% for moisture flux, 37% for precipitation, and 26% for evaporation.
Figure 10 shows the global distribution of each contribution to the isotopic variability. The panels show clear geographical distinctions. Moisture flux has a dominant role in arid regions, precipitation dominates in rainy regions, and evaporation is important over warm maritime regions. Over the entire globe, the contribution of moisture flux is the largest. The means weighted by the amount of precipitable water are 46.3% for moisture flux, 23.2% for evaporation, and 30.5% for precipitation. The simple arithmetic means are 47.3%, 23.5%, and 29.2%, respectively.
 In this analysis, the contribution of precipitation at the site was only evaluated. In other words, the impact of precipitation at the surrounding grids was not considered. However, equation (10) shows that the impact of moisture flux on isotope circulation is dependent on the spatial isotopic concentration gradient (∇δw). The concentration gradient is generated by precipitation, because only precipitation causes fractionation in this model. Thus, if the effect of surrounding grid points is accounted for, it becomes difficult to separate the distinctive impacts of moisture flux and precipitation on the isotopic concentration gradient. Although there may be uncertainties as raised above, the quantitative findings discussed here concerning the control factors of short-term isotopic variability are meaningful because there has been no quantitative explanation for the control factors in previous studies.
5. Simulations Using Different Data Sets
5.1. Sensitivity Experiments
 Several numerical experiments elucidated the sensitivity of the simulated isotopic field to temporal variations in the forcings and the modeling design. Table 2 outlines each experiment. Experiments 1 through 4 test the impacts of the seasonality of each forcing variable, E, W, (Qλ, Qϕ), and P, on the isotope variability. In the respective experiments, each forcing is replaced with an averaged value, Ē, , , and , for the simulation period in each grid. Global distribution maps of correlation coefficients between the time series fluctuations of the experiments and the control simulation are created to evaluated sensitivities. The results in Figures 11a–11d show that the isotopic field is more sensitive to moisture flux and precipitation P than to evaporation E and precipitable water W. This indicates that temporal constant values of precipitable water and evaporation are acceptable to use for this simulation, particularly at low latitudes and in nonmaritime regions.
Table 2. Description of Sensitivity Experiments
averaged evaporation amount for each grid
averaged precipitable water for each grid
averaged moisture fluxes for each grid
averaged precipitation amount for each grid
averaged daily forcings calculated from four 6-hourly forcings
2.5° × 2.5° rough spatial resolution design
 Experiment 5 tests the sensitivity to the diurnal cycle of the forcings. All 6-hourly forcings from the GAME reanalysis are averaged to daily values. No significant difference is detected in the results shown in Figure 11e. The use of the daily forcings instead of 6-hourly forcings is therefore acceptable.
 Finally, in experiment 6, increasing the model horizontal resolution to 2.5° × 2.5° tests the sensitivity of results to horizontal resolution. Results are similar over the globe, as shown in Figure 11f. Thus 2.5° × 2.5° spatial resolution is fine enough for simulation of isotopic circulation.
5.2. Precipitation From GPCP
 Daily grid precipitation data from the Global Precipitation Climatology Project (GPCP) [Huffman et al., 2001] are used instead of the data from the GAME reanalysis. The data, originally 1° × 1°, are resampled to 1.25° × 1.25°. The suitability of using daily data instead of 6-hourly data has been confirmed by the sensitivity experiments. Table 3 shows that both the correlation coefficients and the RMSEs relative to the observations at all three sites are improved. Figure 12 shows results for Chiangmai that compare with the control simulation and the observation. Isotopic depleted peaks on 1 July, 10 July, 10 August, 23 August, and 8 September and enriched peaks on 6 July, 12 July, and 13 August are better reproduced than the control simulation. The correlation coefficient has increased to 0.80 (from 0.76) with a significance level exceeding 99%, and the RMSE has decreased to 2.9‰ (from 4.2‰). The better results yielded by the more accurate precipitation in GPCP indicate that the closer the results are to mass balance, the closer the isotope variability is to reality. These results securely support the remark in the last section, i.e., that moisture transport at large scales controls the short-term isotopic variability of precipitation over Thailand.
Table 3. Results of the Simulation Using Precipitation Values From GPCP
0.76 → 0.80
4.2 → 2.9
0.74 → 0.77
4.1 → 2.8
0.56 → 0.60
3.5 → 2.8
0.76 → 0.75
4.8 → 5.2
5.3. NCEP/NCAR Reanalysis
 The GAME reanalysis includes only several months in 1998, and the simulated isotope circulation in this study was verified with observations made in 1998 only. To produce a longer model run, 2 years of the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis [Kalnay et al., 1996] are used. These daily data are provided on a global 2.5° × 2.5° grid. Only precipitable water W and vertically integrated moisture fluxes are calculated from the NCEP/NCAR data. Evaporation and precipitation are not included in the NCEP/NCAR data, so the averaged evaporation is taken from the GAME reanalysis and the daily precipitation is from GPCP. The suitability of these temporal and spatial resolutions and of using the averaged evaporation has been confirmed by the sensitivity experiments above.
Figure 13 shows the results of the simulation for Chiangmai, Sukhothai, and Bangkok for 1998–1999. Table 4 shows that the 2-year-averaged correlation coefficients and RMSEs with observations remain at levels comparable to the control simulation. This figure and table suggest that the model accurately simulated interannual isotopic variability. For instance, the observations for July in 1999 show more enriched values than in 1998 (see Figure 2; most observed values are in the range of −4 and −12 in July 1998, 0 and −8 in July 1999), and the model reproduced the difference (see Figure 13; most predicted values are in the range of −8 and −16 in July 1998, −4 and −12 in July 1999). Obviously, there still exists the discrepancy of the consistent underestimation by the model, so the model requires further improvement as suggested in the last section.
Table 4. Results of the Simulation Using NCEP/NCAR Dataa
Precipitation is from GPCP, and evaporation is from GAME reanalysis.
Figure 14 shows the global seasonal variability in δ18O (weighted monthly mean for 2 years) compared to GNIP observations at eight sites that represent high-latitude, temperate, subtropical, and tropical zones in the Northern and Southern Hemispheres. Correlation coefficients range from 0.50 to 0.94, which indicates good agreement with observations of regional isotopic characteristics, despite the large spatial variability. For all of the 389 GNIP sites, the correlation was a respectable 0.62. Results are not included for polar regions, which have been the main focus of many isotope-AGCM studies. Recall that the CFL condition for the model fails near the Poles. There is an obvious need for model improvement at very high latitudes.
6. Summary and Conclusion
 A new water isotope circulation model that includes a Rayleigh equation and the use of external meteorological forcings has been developed. A simulation for 1998 was forced with data from the GAME reanalysis. The results from this simulation were validated by GNIP observations of δ18O. Comparisons of monthly precipitation yielded a correlation coefficient of 0.76 with a significance level of >99%. The model also reproduced daily isotopic variability at Chiangmai, Thailand, with R = 0.76 and a significance level >99%. There was relatively poorer correlation with the rainfall amount at the site, so that “amount effect” is insufficient to explain the short-term isotopic variability in precipitation. What controls the variability in the present model is the moisture transport system at large scales: in other words, reasonable water and isotopic mass balance on more than 100 km horizontal scale. The good reproduction of the model supports the dominance of the effect of the large-scale moisture transport system on the short-term isotopic variability in Thailand during the rainy season. Regional processes of rain formation account for less of the isotopic variability.
 A quantitative analysis of the short-term variability was made. The change in δ18O in atmospheric vapor is caused by three factors: moisture flux, evaporation, and precipitation. At Chiangmai from April to October 1998, moisture flux and precipitation both caused 37% of the isotopic variability; evaporation accounted for 26% of the variability. Globally, the contributions from each of the three factors have clear geographical distributions: moisture flux is most important in arid regions, precipitation dominates in regions of persistent rain, and evaporation is important in warm maritime regions. Globally, the averaged contribution of moisture flux was the largest, 46%. Thus moisture flux (in other words, the transport and mixing of moist air masses with different isotopic concentrations) is the prime generator of isotopic variability, and should be considered in similar studies.
 Furthermore, sensitivity experiments revealed that the seasonality of precipitable water and evaporation had less impact on isotopic variability than did moisture flux and precipitation. The diurnal cycle and horizontal model resolution had little effect on the model results of isotopic variability. Therefore at least daily moisture flux and precipitation and monthly or annual evaporation and precipitable water at 2.5° × 2.5° in the horizontal are required for acceptable simulation results of the Rayleigh-type isotope circulation model.
 Then, the model was applied to two additional data sets. The more accurate GPCP precipitation data set yielded improved model results at all three observation sites in Thailand. For example, at Chiangmai, the correlation increased to 0.80 from 0.76, and the RMSE decreased to 2.9‰ from 4.2‰. A 2-year simulation using the NCEP/NCAR reanalysis data set produced very good agreement with the observed interannual variability in Thailand, and the simulated 2-year-averaged seasonalities corresponded to GNIP observations at about 400 sites spanning the globe, with a correlation of 0.62.
 Finally, we shall suggest some issues to be further pursued to diminish the discrepancy of the consistent overdepletion by the model. First of all, some aspects of isotopic physics that are lacking in this model might have caused the underestimation. For example, evaporation from a falling droplet enriches the isotopic composition of surface precipitation to some extent. The second uncertainty is the use of the constant three types of evaporating isotopic ratio (δe). As Bosilovich and Schubert  show, the rate of land-evaporated water in precipitation (a water recycling ratio) is remarkably high in inland regions. δe is obviously affected by precipitation isotopes while “ recycling” in a region. Even though the isotopic interactions between land and atmosphere have not yet been reliably established as noted above, an isotopic evapotranspiration model by Gat and Matsui  could possibly be a good model to incorporate. Further, not only on land surfaces but also on sea surfaces, the spatial and temporal variability of δe derived from the isotopic variability in sea surface water should be incorporated (G. A. Schmidt et al. Global seawater oxygen-18 database, 1999, accessible at http://www.giss.nasa.gov/data/o18data/). Third, the spatially uniform equilibrium fractionation scheme in the model includes uncertainty, too. In addition to the equilibrium fractionation, the kinetic fractionation that depends on the ambient temperature and humidity should be taken into account. When we incorporate the fractionations into the model, the external forcings are used. Some simplification is required because of the limited number of variables, but the temperature and humidity at the representative condensation level can be obtained, and they result in appropriate kinetic and equilibrium fractionation by using the equations given by Merlivat and Jouzel  and Jouzel and Merlivat . It is necessary to consider the kinetic effects for both D and 18O to simulate variability of d-excess (d = δD − 8 × δ18O).
 We are indebted to Thada Sukhapunnaphan and the staff of the Chiangmai branch of the Royal Irrigation Department for their cooperation in sampling precipitation and to Nobuo Yamazaki of the Meteorological Research Institute for his assistance in using the GAME reanalysis. An anonymous reviewer provided inspiring comments and helped us to improve our manuscript. Parts of this study were supported by Core Research for Evolutional Science and Technology (CREST), the Japan Science and Technology Corporation (JST), and the Research Institute for Humanity and Nature (RIHN).