1. Introduction
The projection of future change in precipitation (or rainfall) and other moisture variables remains a major topic of research, in part because of the range of changes, for many regions of the globe, that are simulated by climate models. Recent studies have analyzed simulations contributed by many research centers to the CMIP6 project of the WCRP. In the IPCC’s Sixth Assessment Report (AR6), Eyring et al. (2021) compared simulations of the present climate with observational datasets, including the latest ECMWF reanalysis (ERA5; Hersbach et al. 2020), but quantitative skill scores of moisture variables over the globe (their Fig. 3.43) were limited to precipitation and humidity at 400 hPa. Lee et al. (2021) assessed research on the projections of rainfall and other climate variables and presented results from the CMIP6 ensemble for a range of future scenarios. At high latitudes and parts of the equatorial zone, precipitation is projected to increase in a warming climate, while much of the subtropics would have decreases in some seasons (in at least 80% of models; see their Fig. 4.24). Elsewhere, some models simulate an increase and others a decrease. Douville et al. (2021) assessed the broader water cycle and the atmospheric water budget, in particular the difference between precipitation and evaporation, which largely reflects the vertical integral through the atmosphere of horizontal transport or flux of moisture. They noted, however, that there has been limited examination to date of moisture transport from CMIP6. One reason is that the moisture flux vector, with eastward and northward components, has not been routinely output by climate models.
Among recent studies, Zhao and Dai (2022) presented hydroclimatic fields from 25 CMIP6 models but did not assess horizontal moisture flux. Chen et al. (2022) considered a regional moisture budget, approximating the observational moisture flux using the product of monthly means of the component wind and humidity. Various previous studies have taken this approach to provide an indication of moisture transport. Heidemann et al. (2022) and others have studied flux variations associated with ENSO and other modes of variability. However, Zhang et al. (2019) analyzed CMIP5 simulations over the monsoon land regions and found an annual-mean “residual” in the budget calculated with monthly components that reached 5%–9% with respect to precipitation. Deng et al. (2022) note differences between flux calculated from monthly and daily means, specifically due to synoptic processes. Seager et al. (2010) calculated vertically integrated fluxes using daily data from 15 CMIP3 models and used the components to make various decompositions of the fluxes. The submonthly variability contributed to the budget over much of the globe. However, there remained a residual, especially over regions of topography. Even using daily or subdaily data, which is difficult to do in the case of large model ensembles, there is inevitably some approximation from using components that are given at a set of standard pressure levels, rather than a model’s discretization of the atmosphere [see the appendix of Seager et al. (2010)]. It seems that vertically integrated fluxes would need to be evaluated during a model simulation for them to be accurate everywhere.
It is helpful that monthly mean vertically integrated flux is included in the list of variables for submission to CMIP6, although it was not requested for experiments on future climate. Watterson et al. (2021) compared precipitation and flux for idealized past and warmer climates from the “1pctCO2” simulations of the 10 models from which the flux data were available. To date that remains the case, but there are now data for the “historical” run, with climate change forced by realistic constituent changes, and those for several future forcing scenarios. Despite the numerous studies and assessments of these experiments, the available vertically integrated moisture flux data appear to have not yet been used.
This study analyses the two flux components, together with 12 other single-level quantities, from the 10 CMIP6 models and from ERA5. To reduce statistical uncertainty, a longer than usual 40-yr recent climate period is used, 1980–2019, denoted period 1 or P1. For the future climate, period 2 (P2) is 2040–79, from simulations driven by the SSP5-8.5 scenario. The choice was partly because of data availability but it also provides a global warming around the 2°C level. The main aim is to assess the new moisture flux data and its convergence and to examine its relationship to the modeled atmospheric moisture budget and rainfall. Various previous analyses of regional atmospheric moisture processes, including by AR6, can be augmented or improved with the addition of the fluxes.
The following section briefly describes the budget equation for atmospheric moisture, then presents climatological means over P1 for key quantities from ERA5 and from the 10 CMIP6 models. Skill scores representing the similarity of the CMIP6 and ERA5 fields over the globe are presented in section 3, providing novel assessments of moisture transport in climate models. For the basic climate variables, temperature, precipitation, and pressure, the analysis is extended to a further 25 models. The relationships between the moisture skill scores, basic variables, and model resolution are considered. Simulated future changes in the moisture quantities, standardized by the model’s global warming, are put in the context of those in basic variables and atmospheric circulation in section 4. While the range of changes is considered, across the ensemble and across five simulations from a single model, the focus is on the scaled 10-model average change as representing a plausible future climate for a global warming of 2°C. In section 5, the seasonal results over six broad regions are examined in more detail, providing new information on how moisture transport links to rainfall in the present climate and in the future change. The discussion in section 6 briefly addresses the intensification of moisture fluxes and considers the potential usefulness of additional model outputs. The conclusions follow in section 7. Online supplemental material comprises sections S1 and S2, Tables S1–S5, and Figs. S1–S11.
2. Atmospheric moisture budget in ERA5 and CMIP6
a. Vertically integrated moisture equation
All data were obtained as time series of monthly means, then averaged for the standard seasons [December–February (DJF), March–May (MAM), June–August (JJA), and September–November (SON)] and the annual case. The preceding December is used, including from 1979, in forming the 40-yr DJF climatology for P1. (All of 1979 was included in the ERA5 annual case.)
b. ERA5
The climatological annual mean fields for pr, conv, and evap from ERA5 for period 1 are shown in Figs. 1a, 1c, and 1e. For consistency, conv is calculated as for the models. Shown in familiar colors, pr is highest in the equatorial band, extending to the subtropical oceans. Shown in alternative colors, covering both signs, conv has a similar pattern, but is strongly negative in the subtropics. Evaporation, only positive, is largest over the ocean, especially the subtropics.
Climatological annual means from (left) ERA5 and (right) av10. Shading is for moisture budget terms (mm day−1): (a),(b) pr (precipitation), (c),(d) conv (convergence of moisture flux), (e),(f) evap (evaporation), and (g),(h) res (residual). Vectors are winds at 850 hPa [w850, in (a) and (b)], 10 m [w10, in (e) and (f)], and 200 hPa [w200, in (g) and (h)] with reference vectors (m s−1). The moisture flux vector [flux, in (c) and (d)], has reference 500 kg m−1 s−1. Vectors are shown at a spacing of not less than 0.4 the reference vector length (similarly for other figures).
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
In such long-term means, even in a warming climate, the W term in Eq. (1) is very small. Hence, in a balanced budget the residual R, or res, calculated from R = P − E − C should be near zero. As seen in Fig. 1g, the annual mean res from ERA5 is generally small, with some larger values near orography and sharp gradients in pr. Both res and conv also feature some gridpoint “noise,” especially over land. (Note that the 0.25° grid ERA5 fields were linearly interpolated to a 1° grid for this global plot.) Assuming accurate flux fields, much of this is likely related to differing methods of determining the convergence. The ERA5 archive includes two moisture divergence quantities. One (the “vertical integral of divergence of moisture flux”) is similarly noisy to our conv and the other (“vertically integrated moisture divergence”) is somewhat smoother, as can be inferred from the statistics given in Table S1. Gutenstein et al. (2021) used a divergence field from ERA5 in assessing freshwater flux over the ocean.
Naturally, the global mean of a conv field calculated using differences is zero, and for the models the mean res is also near zero (Table S1). However, the mean pr of 2.91 mm day−1 over P1 is 1.6% larger than that of evap in ERA5. Hersbach et al. (2020) show that the difference varies in time, as does the comparison of ERA5 pr with climatologies derived from observational data. They show that the ERA5 quantities are closer to observations than are ECMWF’s previous reanalysis, but further effort is needed to understand such variations.
The mean zonal and meridional flux components, denoted here for convenience (uq, vq), are shown as vectors overlying conv in Fig. 1c. In P1, these tend to be approximately parallel to the vectors for wind at 850 hPa (or w850, with components u850 and v850), shown in Fig. 1a, and at 10 m (w10), shown in Fig. 1e. The annual mean winds at 200 hPa (w200) are shown with res, featuring strong midlatitude westerlies. Also analyzed in the study are W (or “prw”; the CMIP6 short variable name), surface air temperature (“tas”), surface temperature (“ts”), and mean sea level pressure (“psl”), bringing the total number of single-level quantities being analyzed, including the derived conv and res, to 16.
To allow better comparisons, the zonal means of the annual pr, conv, and evap are presented in Fig. 2. Meridional means over the 10°S–10°N band of these three, plus tas, psl, prw, and uq are shown in Fig. 3. The zonal means for each of the four seasonal climatologies of four variables are shown in Fig. 4. Notable features are the north–south shifts between DJF and JJA in the low-latitude peaks of pr (Fig. 4a) and prw (Fig. 4b), and the reversal in sign for vq (Fig. 4c) and v200 (Fig. 4d). In each feature, SON is more like JJA and MAM more like DJF.
Zonal means of annual mean moisture budget terms: (a) pr, (b) conv, and (c) evap. In black are ERA5 (solid), av10 (for P1; long dashed), and fut2 (av10 for the future at a global warming of 2°C, or 2°C GW; short dashed). In colors are the individual models for P1: see legend for the patterns.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
Meridional means, over the equatorial band 10°S–10°N, of annual mean quantities: (a) tas (temperature), (b) psl (pressure), (c) prw (integrated water), (d) uq (eastward flux), (e) pr, (f) conv, and (g) evap (with land fraction in green, from 0 to 1). In blue is ERA5, red av10 (for P1), and dashed red fut2 (av10 for the future at 2°C GW).
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
Zonal means of seasonal mean: (a) pr, (b) prw, (c) vq (northward flux), and (d) v200 (meridional wind at 200 hPa). Shown are ERA5, av10 (for P1), and fut2 (av10 for the future at 2°C GW); see legend for colors and patterns.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
c. CMIP6
The 14 single-level quantities were extracted as monthly means from the CMIP6 archive for the 10 models listed in Table 1. The remaining CMIP6 short variable names (not used here) are evspsbl for evap, (intuaw, intvaw) for the flux, and (uas, vas) for w10, while the other winds are levels from (ua, va). For each model, a continuous series for 1850–2100 was formed by concatenating the “historical” simulation, with concentrations of atmospheric constituents based on observations over years 1850–2014, and the subsequent simulation of the same “variant label” for the high greenhouse gas concentration future scenario SSP5-8.5. In each case, the simulations are those designated as the first (“r1”), with the full set of labels given in Table S2, for the 10 models and an additional 25 models. This approach provides a 40-yr P1 series matching the years used for ERA5. Since the unforced variability in these CMIP6 simulations is unrelated to that observed and there is little dependence on the scenario over 2015–19 there is minimal discrepancy in comparing the P1 seasonal climatological results from the models and ERA5. For convenience, the individual models are designated by the code names given in Table 1. A representative grid length (see Table 1 caption) is given, with that for the 1° grid being 89 km. The 10-model average (av10) length of 130 km closely matches that of the larger 35-model ensemble, at 131 km. Note that the additional 25 models were those for which the basic variables were readily available from both experiments (omitting a few closely aligned model versions). Further details on the models and the data are given in the supplemental material, by IPCC (2021, Annex II), and by Watterson et al. (2021). As for that study, the exception to the above data extraction was the flux fields from two models, code h3l and h3m, for which monthly means from the specific years of P1 and P2 were acquired from the UK Met Office.
Models used in the analysis, a code name, representative grid length (km), and simulated global and annual mean surface air temperature, tas (°C), and precipitation, pr (mm day−1). Values are given for the average over period 1 (1980–2019) and the change to period 2 (2040–79). The change in pr is for the future climate at 2°C GW (global warming) denoted fut2, as a percentage of P1. This is determined by a linear scaling of the P2 change, using the model’s (P2 − P1) for tas (see text). The 10-model average, av10, is also given for tas and pr. For ERA5, the means in P1 are 14.3°C for tas and 2.91 mm day−1 for pr. Length is the side length of a square with the average area of the data grid squares over the globe. Models with code ending in “e” have Earth system components.
The zonal annual means of the moisture budget quantities from the individual models are included in Fig. 2. The curves are generally very similar, although the range in mean pr (highest in model ace, lowest in model cn6; Table 1) is reflected in values at several latitudes, for pr and for evap. The curve for av10 pr (Fig. 2a) is notably larger than ERA5 pr around 10°S, where av10 conv and evap are also larger. [Eyring et al. (2021) discuss the spatial pattern of CMIP6 pr bias in their section 3.3.2.3.] Note that in some models, conv near the poles (Fig. 2b) is affected by spurious polar flux values.
Global annual mean res is negligible in each model, although noise is evident in the res and conv fields, even in the av10 annual fields shown in Figs. 1h and 1d. The patterns in the av10 budget fields match ERA5 well, aside from the well-known differences in the low-latitude oceans. The av10 fluxes (Fig. 1d) are visually almost indistinguishable from those of ERA5 (Fig. 1c). The meridional mean of uq in Fig. 3d does reveal a weaker eastward band in av10 than ERA5 in the Indian Ocean. Otherwise, there is a general similarity of av10 and ERA5 in Fig. 3. The av10 zonal means in Fig. 4 feature the seasonal variations noted for ERA5. Interestingly, the av10 pr (Fig. 4a) exceeds ERA5 most notably in MAM around 10°S, along with larger southward flux (Fig. 4c) near the equator.
The individual model pr fields and flux vectors are illustrated in Fig. 5, for central North America in DJF. All models simulate high pr in the east, with flux from the Gulf of Mexico, and the northwest, with northeastward flux from the Pacific. The higher-resolution models (cnh and h3m) match well the enhanced pr over the Rocky Mountains seen in ERA5. The av10 field is a little smoother. The JJA fields for the same domain are shown in Fig. S1. Flux from the Gulf of Mexico reaches farther west (the “monsoon”). Dryness in the west corresponds with flux from the Pacific turned southeastward, in all the results.
Climatological means for December–February (DJF) in P1 of precipitation (shading; mm day−1) and moisture flux (vector; reference 300 kg m−1 s−1) over the central North American region. The top row shows ERA5 and av10, with the others being the 10 models, labeled by the code name.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
3. Skill scores
a. Basic climate variables
The global mean tas for P1 varies across the 10 climate models in Table 1, a consequence of them being unconstrained over the historical simulation. However, the ensemble average (av10) of 14.4°C is close to the 14.3°C value from ERA5. Likewise, the av10 global mean pr of 3.07 mm day−1 compares reasonably well with 2.91 mm day−1 for ERA5. [Hersbach et al. (2020) showed that ERA5 mean pr exceeds other observational estimates.]
Eyring et al. (2021) provide a comprehensive assessment of the simulation of basic climate variables in CMIP6 models, often in comparison to ERA5, and they conclude that these are improved in skill over CMIP5 models. Their Fig. 3.42 shows the root-mean-square error (deviation from observations) or rmse across the globe for seasonal climatologies of a range of fields, while their FAQ 3.3 section shows the correlation coefficient between model and observations for tas, pr, and psl. Watterson (2015) used the Arcsin–Mielke measure M, where the mse score is nondimensionalized by spatial variance (see section S1), such that a value of 1000 “points” holds for perfect agreement, while M of 0 or less means no skill. For the scalar fields in Fig. 1, the rmse and M comparing av10 and ERA5 over the globe are included in Table S1 along with other statistics. In all cases, both fields are interpolated to the common 1° grid, using a conservative method for ERA5. The best score, M = 845, is for evap, with rmse 0.43 mm day−1. The M scores for P − E are similar to those for pr. The score for conv is a little lower, in part due to noise.
For the basic variables, the M score has been calculated for each season, and the average over the four is given in Table S2 for each of 35 models, with those for our 10 models given also in Table 2. The scores are largest for tas, with its strong latitudinal pattern. The average M values are similar for the 10 models as the 35, further supporting the 10 as being representative of the full ensemble. Watterson (2015) used the average M for tas, pr, and psl as a score for basic overall skill, denoted here Av-3, and included in the tables. Eyring et al. (2021) note that the multimodel mean fields generally improve on those of any individual model. This holds for our av10 fields, with an Av-3 of 852 (Table 2), which is higher than for any of the 35 models.
Climatological skill scores for the 10 models (by code) and for av10, measuring the agreement with the ERA5 climatology for P1 over the globe. The values are the average of the four M scores in points for the individual seasons, for each of eight quantities. The average M for tas, pr, psl ‘Av-3’ is a measure of basic climate skill. The average for the six moisture-related quantities, Av-6 is given. Below, is the correlation coefficient r across the 10 models, between grid length (L) and each column, followed by r for pr score and each column, and for the Av-6 score and each column.
Watterson (2015) provided Av-3 scores of 42 CMIP5 models for a near-global land–ocean domain GLO that excluded the southern polar cap 90°–60°S (see their Table S1). For reference these scores are reproduced in our Tables S3 and S4. To enable a comparison, the CMIP6 scores for this domain are included in Table S3. The 35-model average score is 773 points, which exceeds the CMIP5 average (Table S4) of 745. A similar rise holds if the ensembles are each restricted to 21 models, for which each CMIP6 model is subjectively judged to be related to the paired CMIP5 model. Since this analysis is outside the main aim of the paper it is presented in section S1. While the time periods and observational data are different, the results support the improvement of CMIP6.
b. Atmospheric moisture variables
Aside from pr, global skill scores for the moisture-related variables evap, conv, prw, and the flux components seem not to have been previously calculated. One difficulty is in providing a credible observational field over all regions. Watterson (2015) and more recently Chen et al. (2022) discuss the dependence of skill scores on the dataset and on grid resolution. The assessment here is limited to the similarity of the global fields to those of ERA5. The four-season average M scores for each moisture variable are included in Table 2. All the values exceed 550, indicating that the models have considerable skill in this context. The visual similarity of the pr and flux vectors in Fig. 5 and Fig. S1 to ERA5 supports this. With one exception (prw for h3m), the scores for the av10 fields are higher than any individual model score. The average score for the six moisture variables, Av-6, for av10 is 811, higher than for the top model h3m.
In general, some of the difference between a model simulation and observations can be attributed to unforced or internal temporal variability. Averaging multiple simulations of a model can reduce the statistical uncertainty and give a better representation of its true forced or underlying climate. As an indication of the effect of uncertainty on the results, the same P1 period from each of four other runs (r2–r5) of ACCESS-CM2 has been fully analyzed. The range for M over the five runs for Av-3 is 783 to 789, and for Av-6 738 to 745. These ranges are relatively small, indicating that the single-run results are representative of the model’s overall skill. Averaging the seasonal fields over the 10 models should also reduce the effect of uncertainty in each model’s P1 average. This would contribute a little to the scores for the av10 fields being better.
c. Relationships
1) Correlations with grid length
The average score for both the basic variables (Av-3) and the six moisture variables (Av-6) ranges from a low for model mce to a high for model h3m. Given that mce has the largest grid length and h3m the second smallest, it is not surprising that across the 10 models these M scores are negatively correlated with length, as given in Table 2. This holds for the individual variables also, except for conv and prw, for which model cnh (with smallest length) has reduced scores. Across the 35 models, the correlation between L and Av-3 is r = −0.61 (Table S2). For the GLO scores (Table S3) r = −0.62. As discussed in section S1, based on the regression relationship for GLO, a rise of 20 points would be expected from the average grid length of the CMIP6 ensemble being 43 km less than that of CMIP5. Thus, the improved resolution of CMIP6 appears to relate to much of the rise (28 points) in average Av-3 score.
2) Moisture and other quantities
Given the importance of the simulation of rainfall, it is worthwhile considering how skill in the other variables relates to skill in pr. The correlations between the M scores across the CMIP6 ensemble are included in Table 2 and Table S2. The skill in pr is moderately correlated with that in psl and tas, across 10 and 35 models (Table 2 and Table S2). The skill in pr is well correlated, across 10, with that in the other moisture variables, peaking at r = 0.84 for intvaw, and 0.86 for the overall score (which includes pr). Evidently the meridional transport of moisture is important to the skill in pr. The overall basic skill, Av-3, is well correlated with that for moisture (Av-6). These relationships, although limited by the number of models, are consistent with the interdependence of climate variables. The assessments support the case that all 10 models produce credible simulations of climatological atmospheric moisture. While the resolution may be a consideration, for the larger scale considered here, the inclusion of all 10 is justified. The improved scores for the average fields provide support for the use of av10 as a representative climate for CMIP6, and the focus on results from it.
4. Future change
a. Global warming
Under the SSP5-8.5 scenario of rising greenhouse gases and hence radiative forcing, all 35 models in our CMIP6 ensemble simulate rising global mean surface air temperature (averaged over multiple years). The global warming, for convenience GW, from tas, averaged over the P2 period, 2040–79, relative to P1 ranges from 1.42° to 3.80°C, with an average of 2.46°C (see Table S2). The GW for our 10 models, given in Table 1, is each within this range, but averages a little higher, at 2.70°C. The range of warming is attributed to the different sensitivity of the model systems to greenhouse gas and other changes; see Lee et al. (2021), who give a CMIP6 average warming of 4.0°C under SSP5-8.5, for 2081–2100 relative to 1995–2014. Given the warming rates before each of those periods, this appears consistent with our 35-model average for P2 relative to P1. Lee et al. (2021) also presented an “assessed” future change in GW, based on multiple lines of evidence, that is somewhat lower than the CMIP6 average. From their Fig. 4.11d, the central value for the warming from P1 to P2 is approximately 2°C.
Following the “traditional” pattern scaling methodology (Lee et al. 2021, their section 4.2.4), to provide a pattern for change in each variable and season consistent with this assessed GW, 2°C is used here as a scaling factor to the standardized change from each model. The standardized change or “change per degree” field is calculated from P2 relative to P1, divided by the GW for the model (Table 1). The 10-model average of the standardized change is then multiplied by 2°C, to give the av10 future change for a global warming of 2°C, or 2°C GW for short. Adding this to the P1 climate gives the future climate denoted fut2, which can be taken as representative of P2 under this scenario. Lee et al. (2021) used this approach in their section 4.8. (Scaling the multimodel means, as they did, rather than the mean of the standardized changes, made very little difference to the results here.) An alternative approach, as applied by Zhang et al. (2018) to extreme precipitation, averages data from the period around the target warming for each model. Lee et al. (2021) used this “time shift” method for the case of change in annual pr for 2°C GW in their Fig. 4.32b. Tebaldi and Knutti (2018) found that both methods can be useful in emulating scenario experiments for future climate change. Since both the P1 and P2 means from a single simulation include some effect of internal variability, so does each standardized change field. A brief assessment of this uncertainty is made below.
b. Atmospheric moisture budget
Global annual mean pr increases in each of the 10 models. Table 1 gives the global mean fut2 change as a percentage of the P1 mean. The individual values range from 2.51% to 3.97%. For comparison with the other budget terms, the focus is on the fut2 quantities in mm day−1. The av10 of these is included in Figs. 2–4. The zonal mean pr (Fig. 2a) and conv (Fig. 2b) increases near the equator and at high latitudes, while evap (Fig. 2c) has more uniform small increases. (Douville et al. 2021 provide comparable results for a larger ensemble in Fig. 8.13.) From Fig. 3e, the low-latitude increases in pr are largest over the Pacific. Temperature increases at all longitudes (Fig. 3a), as does prw (Fig. 3c) and the magnitude of uq (a largely westward flux; Fig. 3d). From Fig. 4b, the zonal seasonal mean prw always increases, and the magnitude of vq (Fig. 4c) increases except near tropical changes of sign. The v200 wind (Fig. 4d) barely changes.
c. Seasonal changes
Changes in pr averaged over the full CMIP6 ensemble are well documented by the IPCC AR6, with multimodel seasonal fields for future scenarios and periods shown by Douville et al. (2021, their Fig. 8.14) and Lee et al. (2021, their Fig. 4.24). The pr changes scaled to 2°C GW for each of our 10 models over central North America in DJF are shown in Fig. 6. Increases in the midlatitudes, especially in the east of the domain, occur in all 10, while decreases prevail over Mexico. The patterns of change in flux are also similar, with strengthening of the flux across the northwest coast and in the southeast. However, there is a range of change across the models. The av10 changes in pr, flux, and conv are included in Fig. 6 (top row). The sign of conv change mostly matches that of pr. The corresponding results for JJA are in Fig. S2. Strengthened flux from the Gulf of Mexico and from the Pacific leads to increased conv and pr over much of the United States in JJA. Note that while these changes in pr match well the patterns from the larger ensemble shown in AR6, they may not have been considered robust.
Change for 2°C GW, for DJF over central North America, in pr (mm day−1) and moisture flux (reference 100 kg m−1 s−1). Each field is scaled from the model’s P1 to P2 change (see text). The panels follow Fig. 5, except that the top left is the av10 convergence (av-c) and flux.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
The av10 fut2 change fields for 12 variables are shown, over most of the globe, for DJF in Fig. 7 and JJA in Fig. 8, with MAM and SON shown in Figs. S3 and S4. The left three panels of each figure show the changes in the basic variables, pr, psl, and tas. In a few regions where the av10 is not representative of the av35 result, the shading is overlain with stippling, with the criteria given in the Fig. 7 caption. The pattern of increased pr in the equatorial band and at higher latitudes in all seasons (Fig. 4a) is seen in the av10 fields (Figs. 7a and 8a). Precipitation decreases in much of the subtropics, extending into the midlatitudes in some seasons. The patterns in pr are mostly matched by those in the av10 conv (Figs. 7b and 8b), linked to changes in the mean flux shown by the overlying vectors. It is worth noting the decreases in JJA in Central America, which comprises much of the NH American monsoon region of Zhang et al. (2019). Similarly, they matched decreased pr with decreased P − E. Evaporation increases over much of the ocean (Figs. 7d and 8d), with the moisture transported to support the low- and high-latitude precipitation. Integrated water, prw (Figs. 7f and 8f), rises everywhere, but typically in relatively small amounts over land where pr decreases. In P1 (e.g., Fig. 1), the 10-m and 850-hPa winds are mostly aligned with those in flux but, as seen in the maps, changes often have different directions. Further, flux typically increases in magnitude, even without change in wind. Given the small magnitudes of the change in res (not shown), changes in conv match well those in P − E, or freshwater flux from the atmosphere to the ocean.
Change for 2°C GW from av10, for DJF over (most of) the globe. At left are (a) pr, (c) psl, and (e) tas. Values for pr and psl are stippled where av10 has different sign to av35, except if both values are small (in white band, magnitude given in bottom right). Values for tas are stippled if av10 differs from av35 by more than 10%. At right are (b) conv, with flux vectors, reference shown, (d) evap, with wind at 10 m, and (f) prw, with wind at 850 hPa, all in the usual units.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
d. Range of CMIP6 changes
The av10 fut2 fields provide a single projection based on the 10 models, with broadly compatible changes across our suite of variables, including flux. Even for a specific GW for period 2, there is a range of possible futures for a regional climate in the real world, as evident from the scaled model results for North America seen in Fig. 6. In general, the uncertainty in a climate projection for a future period based on an ensemble of models can be attributed to the uncertainty in the future scenario, that in the forced change or model uncertainty, and to internal variability. Zhou et al. (2020) assessed these sources of uncertainty for global land monsoon rainfall. Douville et al. (2021, their section 4.2) provide a comprehensive discussion of uncertainty, while Watterson and Whetton (2011) incorporated decadal variability into a pattern scaling approach that included uncertainty in global warming. Providing full projections is well beyond the scope of the study, but a consideration of the uncertainty in the results presented is worthwhile. As a simple statistic for the spread of change for each season, the sample standard deviation of the 10 standardized change results was calculated at each 1° grid point. Fields of sd10 for moisture variables in DJF and JJA are plotted in Fig. S5, for the domain of Fig. 6. The global means of the sd10 values, averaged over the four seasons, are given in Table S5. For pr, the average is 0.12 mm day−1 and for flux components (4.6, 2.3) kg m−1 s−1, so an inferred range for 2°C GW would be significant relative to the typical gridpoint av10 changes in Figs. 7 and 8. However, based on simple statistical theory (as presented in section S2), the uncertainty in the av10 values, as the mean of a sample n of a larger ensemble is
While the individual model values were made more certain by using the longer 40-yr periods, there remains statistical uncertainty in the changes at grid points. An estimate of this can be obtained from the ensemble of five standardized change results calculated from the ACCESS-CM2 runs. The corresponding sd5 results are in Fig. S6 and Table S5. The ratio sd5/sd10 of the four-season global means is also given and it ranges from 0.64 for pr to 0.47 for evap. Thus, the statistical uncertainty is smaller but may be significant, with respect to the 10-model range. Averaging over multiple runs, where available, would provide a more certain forced change from each individual model. However, based on standard statistical theory (as presented in section S2), and given the above ratios, adding certainty to the model changes would likely not markedly change the resulting average across the 10 models. In any case, the av10 results are presented as a plausible future projection, while acknowledging the considerable possible range of future change.
5. Moisture transport associated with regional change
With our focus on how the mean flux and its convergence relates to changes in pr, this section considers a selection of other regions and seasons with patterns of change that have been previously studied. The accurate flux data from av10 provide further insight. All the pr changes described are of the sign of those in the 35-model ensemble and the AR6 Atlas (Gutiérrez et al. 2021) although some were assessed as being not robust.
a. Northern South America in DJF
Carvalho et al. (2011) showed the moisture fluxes from the Atlantic that drive the South American monsoon system in DJF, and these are simulated well by av10 (Fig. 9a). Convergence is strongly positive, except in the relatively dry northwest (P1 pr is shown in Fig. S7, along with evap and conv, and change scaled to 2°C GW). The flux increases (Fig. 9b), but more strongly around 15°S, 60°W, resulting in a negative change in conv. Combined with reduced evap, pr declines in the Amazon basin (Fig. 9c). Llopart et al. (2021) calculated a similar budget for that region (their AMZ). To the west, southwest, and east, there is a positive conv change, which drives increased pr. Similarly, Grimm and Zilli (2009) found that pr variability in the east is driven by flux variability.
Conv, flux, and pr fields from av10 for four regions: (a)–(c) northern South America in DJF, (d)–(f) southern Africa in DJF, (g)–(i) southern South America in JJA, and (j)–(l) Europe in JJA. Shown are (left) the conv and flux vectors for P1, (center) the change scaled to 2°C GW, and (right) change in pr as a percentage of P1, stippled where this has a different sign from av35 (except when both av10 and av35 are smaller than 2%).
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
b. Southern Africa in DJF
Dunning et al. (2018) assessed changes in the wet season of regions across Africa and presented changes in moisture flux at 925 hPa for August–October. Maúre et al. (2018) focused on the south, where pr is large during DJF (summer), except in the far southwest. The pr change from downscaled CMIP5 simulations at 2°C GW had an increase near the equator and a wavy pattern farther south. In the av10 budget for P1 (Fig. S8), pr is driven by both conv and evap, with mean fluxes from the Indian Ocean (Fig. 9d) to 26°S. The fluxes are strengthened with 2°C GW (Fig. 9e), but with a pattern of change in conv that largely matches the pattern of pr change (Fig. 9f). The southwest becomes even drier, while northern Madagascar is not as wet.
c. Southern South America in JJA
Winter precipitation in southern South America is heaviest along the southwest coast, where westerlies result in strong moisture convergence along the Andes (see P1 fields in Fig. S9). There is a mean moisture flux from the tropics into the La Plata basin (Fig. 9g), which is also wet. Llopart et al. (2021) analyzed future pr changes in downscaled CMIP5 simulations, featuring a banded pattern, with strong increases in the east and far southwest. A similar pattern occurs in av10 (Fig. 9h), driven by strengthened conv. In the west from 30° to 42°S, conv and pr (Fig. 9i) decrease, coinciding with higher psl (Fig. 8c) and wind changes (Fig. 8d).
d. Europe in JJA
Coppola et al. (2021) presented the future changes in pr over Europe from CMIP6, with mostly increases in DJF, except in the far south. In JJA, decreases extend over most of the continent, which Haarsma et al. (2009) linked to a “heat low” in psl over the Mediterranean region and easterly wind changes over central Europe. Consistent changes are seen in the av10 results in Fig. 8 (and Fig. S10 showing Europe). Llopart et al. (2021) found that pr in the present climate averages over 2 mm day−1 in central and eastern European domains in JJA, despite conv being negative. A similar balance holds in av10, with a strong evap (Figs. S10a–c and Fig. 9j). In the av10 change for 2°C GW (Fig. 9k) the eastward flux is strengthened (contrary to w850; Fig. S10d), as is the divergence, except over the Iberian Peninsula, where evap (Fig. 8d) declines. With the change in res from av10 averaging less than 0.03 mm day−1 over the above domains, the decline in mean pr (Fig. 9l) is well explained by the increased divergence.
e. Polar regions
Douville et al. (2021) project increased poleward flux into high latitudes, based on increased zonal mean P − E. Figure 2 shows an increased annual zonal mean conv and pr in av10 [consistent with the SH results of Bracegirdle et al. (2020)]. The polar plots for winter in each hemisphere, in Fig. 10, and for summer (Fig. S11) show that convergence predominates in P1, except for some northern seas in DJF (Fig. 10a) and some land areas in summer. The mean flux at high latitudes is mostly eastward, but with a poleward component, especially onto the Antarctic coast (Fig. 10d). Like the Antarctic ice sheet “surface mass balance” (P − E) field from Frieler et al. (2015, Fig. 4) the conv is strongest near the coast (Fig. 10d), as are the future increases in both seasons (Fig. 10e and Fig. S11e). Mean flux is strengthened, in general, with particularly large changes over the Arctic Ocean in summer (Fig. S11b). However, the largest percentage increases in pr there are in winter (Fig. 10c), balanced by evap (not shown) rather than conv, which decreases over some seas. There is reduced conv to the north of West Antarctica in winter, enhancing the flux onto the land (Fig. 10e).
As in Fig. 9, but for the polar winter: (a)–(c) the Arctic in DJF and (d)–(f) the Antarctic in JJA. Note the modified scales.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
6. Discussion
The monthly mean atmospheric moisture flux data from 10 CMIP6 models allow the moisture budget to be evaluated with minimal residual in regional means. The seasonal climatological fluxes considered here provide insight into the source of precipitation and how it may change in a future climate. Of course, they do hide the temporal evolution of moisture processes. For example, over midlatitude land the transport of humid air ahead of a front can lead to strong convergence and rainfall. The subsequent evaporation from the surface may lead to a period of divergence, likely not seen in monthly means. Accurate vertically integrated daily or subdaily flux would be valuable in process studies, particularly in the study of atmospheric rivers, as for example by Reid et al. (2022). The field of divergence, as calculated within each model, would be a helpful additional variable.
A key topic in the assessment of climate change, addressed by Douville et al. (2021), is the intensification of the moisture processes that follows from increased saturation humidity. Even with some reduction in mean relative humidity over midlatitude land (Fig. 4.23 therein) the integrated atmospheric water, prw, increases throughout the globe, in our 10-model mean (av10) seasonal fields for the climate (fut2) at 2°C global warming. The global, annual mean prw increases by 14.5%, which is close to the standard Clausius–Clapeyron low altitude rate of 7% °C−1 (their section 8.2.1). The moisture budget terms change more slowly, in fut2, 3.2% for global mean pr (Table 1) and evap, while mean conv is zero in each climate. What about the flux?
Like near-surface wind, the vertically integrated moisture flux is a vector with components taking either sign. A more meaningful percentage change would be of the mean magnitude of flux, say, flxm. Mean wind speed, the time average of speeds from each model time step, is indeed a standard CMIP6 variable and it would be helpful if flxm were also a monthly mean variable, calculated likewise, as the time average of magnitude. Nevertheless, it is interesting to assess the magnitude of the seasonal av10 flux vectors. The flxm fields for DJF and JJA in 1980–2019 are plotted as Figs. 11a and 11b. There are values of over 200 kg m−1 s−1 along the equator and in several subtropical ocean regions, notably the South Asian monsoon in JJA and 40°–50°S in DJF. Midlatitude land values can exceed 50 kg m−1 s−1. There are lines of small flxm, often in the subtropics, where the mean vector is near zero. Averaging over the four seasons raises these minima, so that the percentage change in the four-season mean fields for fut2, shown in Fig. 11d is better defined. Over much of the globe it is comparable to the changes in prw (Fig. 11c), whose field has a minimum value of 5.7%. Smaller values, even reductions, in flxm tend to occur where the change is negative in one or more seasons (as shaded), as can happen along a line of small flxm in a seasonal fut2 field, or in some polar regions. Increases in flxm typically exceed 20% at high latitudes, and can exceed the prw increase, if winds also change. The global mean of the four-season mean flxm increases by 12.5% for 2°C GW, close to the prw value. It would be interesting to see an analysis of true time averages of flxm, if that variable were available.
Averages over four seasons of moisture quantities from av10: the magnitude of seasonal mean flux (flxm) in P1 for (a) DJF and (b) JJA, and the percentage change for 2°C GW of (c) the four-season mean of prw and of (d) magnitude of seasonal mean flux. The values in (d) are shaded if the change in any season is negative. See text for details.
Citation: Journal of Climate 36, 18; 10.1175/JCLI-D-22-0588.1
7. Conclusions
Precipitation and the atmospheric moisture budget are analyzed for 40-yr periods of recent and future climate simulated by 10 CMIP6 models from which the vertically integrated moisture flux is newly available. The atmospheric moisture budget for 1980–2019 is effectively closed, given these accurate fluxes, with the budget residual largely reduced to gridpoint variation associated with the calculation of flux convergence. The zonal annual means of the budget quantities are quite similar in each model. Seasonal climatological fields are compared with those from the ERA5 reanalysis. Using the four-season average M skill score for the globe, precipitation from the 10 models is similar in skill to that from a further 25 models, and likewise for the basic variables surface air temperature and pressure. The three-variable average confirms an improvement in CMIP6, relative to a previous analysis of CMIP5 models. The scores for six moisture variables, including the new flux and its convergence, demonstrate global skill for each model. Skill in precipitation in a model is closely aligned with that in meridional flux. Averaging over the scores for both basic and moisture variables, the best of the models is HadGEM3-GC3.1-MM, while the 10-model average fields have better skill than any individual model.
The global annual mean increase in temperature for 2040–79 in the SSP5-8.5 simulations averaged across the 10 models is 2.7°C. Under pattern scaling, to provide a projection of change for the IPCC’s assessed global warming for this case, the individual “change per degree” fields are multiplied by 2°C. Flux and precipitation changes in winter over central North America from each model are illustrated, with rather similar enhancement of flux, increased precipitation in the north and decreases farther south. The 10-model average global fields for change in precipitation, temperature, and pressure in each season are largely consistent with those of the larger ensemble. The changes in flux, convergence, water column, and winds at three levels are also presented. The role of convergence in balancing precipitation changes over many land regions is evident. The range of the changes across the 10 models is also considered.
To improve the understanding of regional moisture processes, the simulated flux, convergence, evaporation, and precipitation are shown in detail for selected cases. The South American monsoon in December–February features southward flux that is enhanced at 2°C warming. However, the additional convergence is to the west and southeast of the domain, leaving reduced rainfall over the Amazon. In southern Africa in summer flux from the Indian Ocean is also enhanced, boosting rainfall in the southeast. In southern South America in winter, convergence and precipitation are enhanced in the far southwest and the east of the La Plata basin. Over central and southern Europe in summer, eastward flux tends to be enhanced, but so is divergence. Rainfall declines, along with evaporation. Over the polar regions, poleward flux is enhanced, along with convergence over Antarctica and most Arctic land. In winter, especially, precipitation can be further enhanced by increased evaporation over the adjacent regional seas.
The presentation aims to encourage the production of the vertically integrated flux vector as a standard output from climate models, as a monthly mean and, ideally, more frequently. To this can be added the divergence of flux, as calculated by the model, to avoid the limitations of gridpoint differencing, and the mean magnitude of flux.
Acknowledgments.
The author acknowledges the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. I thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data, and the multiple funding agencies who support CMIP6 and ESGF. Much of the data used were obtained from an archive at NCI Australia, where most of the computational work was performed. The ERA5 data are provided by the Copernicus Climate Change Service (2017). The skill score software was developed in collaboration with Roger Bodman. Calculations and plotting have largely been performed using the NCL software (NCAR Command Language, NCAR, Boulder, Colorado) and CDO (Climate Data Operators); see https://code.mpimet.mpg.de/projects/cdo. Very helpful advice was given by two reviewers, along with encouragement for the model skill evaluation.
Data availability statement.
The CMIP6 data are available on the ESGF node at https://esgf-node.llnl.gov/search/cmip6/. Moisture flux data for HadGEM-GC31-LL and HadGEM-GC31-MM were obtained directly from the U.K. Met Office. ERA5 data are downloadable, after registration, from https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels-monthly-means.
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