HadISDH is a multi-variable humidity monitoring product from the Met Office Hadley Centre expressly designed for the monitoring of surface atmospheric humidity. HadISDH includes a simultaneously observed temperature product (Willett et al., 2017) which is included here for direct comparison with humidity variables. HadISDH is based on the sub-daily, quality-controlled station dataset HadISD, which provides temperature and dew point temperature data, amongst other meteorological variables, from 1973 onwards . For the detailed methods used to create HadISDH from HadISD, see , but we reproduce an outline below. A subset of the 6103 HadISD stations was selected on the basis of their length of record and data quality, leaving around 3500 stations (the exact number is dependent on the humidity variable). The sub-daily data from each of these stations were converted to monthly mean values and subsequently homogenised to remove non-climatic features. The pairwise homogenisation algorithm was used for this step, but to ensure consistency across the different humidity variables, an indirect approach was applied using the change point locations derived from the dew point depression and temperature values (see for details).

After homogenisation, the adjusted station monthly means were gridded onto a 5∘×5∘ grid by simple averaging. HadISDH suffers from the spatio-temporal coverage issues common to most in situ global data products; station density is generally sparse outside of the USA and Europe, especially for high latitudes, tropics, South America, Africa, the Middle East and most of Australia. Furthermore, despite extensive efforts to control quality and homogenise, it is highly likely that some errors remain. To account for this uncertainty, estimates arising from the station (measurement, climatology, inhomogeneity) and gridding (spatio-temporal coverage) have also been calculated for each grid box and time. These uncertainties have been included when calculating large-scale average time series along with those arising from incomplete coverage across the globe.

In this analysis we use monthly mean anomalies relative to the 1976–2005 period from HadISDH version 2.0.1.2015p (unless otherwise stated). Global and regional monthly means were calculated for each variable using cosine weighting of the grid box latitude, with annual means calculated from the monthly means.

The CMIP5 has provided a valuable repository for a wide range of climate model data . Over 60 climate models with numerous experiments each have been provided for use by over 20 different institutions. In this study we focus on the set of simulations of the 20th century (1850–2005) with different forcing factors applied. The historical experiments are forced by anthropogenic and natural factors to capture as closely as possible the recent climate. Extra simulations have been run for some models to extend the historical period to 2012 or 2014 (historicalExt). There also exist simulations forced by only natural factors (historicalNat) and those forced only by GHG factors (historicalGHG). Not all models have simulations of these last two experiments run beyond 2005. To study the changes in surface humidity in the CMIP5 archive, especially over the last decade, we select the nine models that have coverage up to at least 2012 in their historicalGHG and historicalNat experiments (see Table ). The historicalExt experiments were merged with the historical runs in which it is possible to provide coverage beyond 2005, though for three models no historicalExt experiments exist. For a more comprehensive description of the different models and their individual forcing factors relevant to this analysis, we refer to Sect. 2 of .

A number of specific features in each of the models could strongly influence their ability to capture changes in humidity measures. Land surface processes such as changes in soil moisture or CO2 fertilisation effects on evapotranspiration can strongly influence the humidity measures. Replication of realistic aerosol forcings, and particularly the date, location and magnitude of volcanic forcings, is also important. Hence, the degree to which models include these effects will impact the degree to which they replicate observed humidity changes.

Anomalies for each experiment run were calculated relative to the 1976–2005 period to match HadISDH. As HadISDH is a land-surface-only dataset and has varying coverage with time, this needs to be accounted for in the model coverage when creating global and regional averages. Each month in the CMIP5 models was regridded to the 5∘×5∘ resolution of HadISDH, and then coverage was matched with the corresponding month in HadISDH. Global and regional monthly means were calculated for each ensemble member using cosine weighting of the grid box latitude, with annual means calculated from the monthly means.

The coupled models from the CMIP5 archive are driven by long-term radiative forcing parameters (including volcanic aerosols, solar activity, GHG emissions, etc). This ensures that they should capture long-term trends and changes. However, they are not expected to match the temporal pattern of short-term variations driven by modes of variability such as the El Niño–Southern Oscillation, for example. Despite this, they are expected to capture the amplitude of these variations successfully.

Atmosphere-only models use observed SSTs and radiative forcings to drive the atmospheric portion of a coupled climate model. This additional constraint should ensure that these models more accurately capture the short-term variations in the observed climate at the same point in time. Furthermore, if there are large-scale changes in the SSTs that are not captured by the coupled models, then an atmosphere-only model should improve the match to the observations.

The land surface has been warming faster than the oceans over the last 10 to 15 years, a characteristic that has not been well captured by coupled climate models. By including a model driven by observed SSTs, we can assess to what extent any land–ocean heating contrast is driving any differences between the modelled and observed humidity measures (see also Sect. ). Also, the representation of large-scale atmosphere–ocean circulation patterns should be improved in an atmosphere-only model, and hence short-timescale variations in the temperature and humidity may be improved as well.

We use the latest version of the Hadley Centre model in its atmosphere-only configuration, HadGEM3-A , to compare with the coupled version of its predecessor, HadGEM2-ES. We use an ensemble of 15 equivalent realisations initialised in December 1959 and run under historical forcings, consistent with the CMIP5 generation of coupled models, and at a relatively high resolution of N216 L85 (∼ 60 km mid-latitudes). This has also been processed to match the HadISDH data in the same way as the CMIP5 models.

show that HadISDH is in broad agreement with the annual time series from a number of reanalyses datasets. Of the most recent products, only ERA-Interim and JRA-55 provide direct analysis of 2 m air temperature and humidity. show that there is better agreement between these two products than between either of them and the MERRA-2 reanalysis , especially for relative humidity. MERRA-2 also shows inconsistencies with other reanalysis products for surface air temperature .

We include the ERA-Interim reanalysis dataset in our assessment as it is in very good agreement with a range of observational products . The specific and relative humidity fields were calculated from the 6-hourly fields of temperature, dew point temperature and pressure. These sub-daily fields were then averaged to monthly values and the data were re-gridded to the 5∘×5∘ grid of HadISDH. Then each month was coverage matched as for the CMIP5 models with identical calculations to obtain the global and regional averages. The climatology period was 1979–2005 to mirror the HadISDH period as closely as possible, as there are no data prior to 1979 in ERA-Interim.

The ERA-Interim reanalysis product, although having the advantages of complete coverage and physics-based algorithms to calculate the humidity parameters, has some limitations in terms of long-term stability. A key example is the change in input SSTs. From 1979 to 1981 the Met Office Hadley Centre monthly HadISST1 was used. This was then swapped to the US National Centers for Environmental Prediction (NCEP) weekly 2D-Var dataset and then again in June 2001 to the daily operational NCEP product. A further change occurred in January 2002, which combined with the June 2001 change resulted in a shift to lower SSTs of approximately 0.15 K globally, which is now accounted for by some studies (e.g. ). In February 2009 the source shifted again to Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA), which has more sea ice and higher SSTs at the poles, but the differences were mostly negligible . Over time there have been various changes to the types and density of observing platforms available. While the assimilation system can mitigate this to some extent, some inhomogeneities occur.

While the main focus of this paper is humidity, it is helpful to also look at temperature as one of the key drivers of changes in specific and relative humidity. Several studies have conducted formal detection and attribution of global land surface temperatures, with the best explanation for recent trends requiring the inclusion of GHG forcing (e.g. ). The observations show strong warming trends for the early, late and full periods (Fig. ). As expected, the atmosphere-only HadGEM3-A model shows the best agreement with observed estimates, whereas the historical runs from the CMIP5 models all have larger positive trends than the observations for the later period (see Sect.  for discussion of the most recent years). Most of the CMIP5 historical ensemble means are consistent with the observations for the globe, Northern Hemisphere and tropics, in that the confidence ranges of linear trends overlap over the entire period of study (see Figs. S1–3, rightmost trend panels). For the Southern Hemisphere however, the majority of CMIP5 historical models have trends that are much more positive than the observed trends, with no overlap of confidence ranges (Fig. S4, rightmost trend panels). Note that nearly all of the CMIP5 historicalNat ensemble mean trends over the full period, although positive, are much smaller and inconsistent (the spread does not overlap) with the historical trends (all regions) and the observed trends (all regions except for the single-member historicalNat runs in NorESM1-M and bcc-csm1-1 in the tropics and these plus IPSL-CM5A-LR in the Southern Hemisphere). In the Southern Hemisphere, the observed trends are more consistent with the historicalNat trends than the historical trends. This suggests that although the CMIP5 models show clear anthropogenically induced changes over all regions that are larger than the observed trends, the contribution of GHGs could be part of the explanation for the observed trends, apart from in the Southern Hemisphere. show in their Fig. 8, that compared to both historical and historicalGHG experiments, both the observations (HadCRUT4; ) and the historicalNat experiment show cooling over the most recent 3 decades. Given the dominance of the oceans in the Southern Hemisphere, this may influence the land-based observations in HadISDH.

Specific humidity in HadISDH exhibits a positive moistening trend in the early period for all regions bar the Southern Hemisphere, with short-term decreases corresponding to the two significant volcanic eruptions in this period – El Chichón

The eruption of El Chichón in 1982 has an apparent delayed effect on the specific humidity because of the 1982–83 El Niño, which cancelled out some of the decrease.

The observed relative humidity exhibits negative trends over the full period, although the early period shows positive trends for the globe and Northern Hemisphere, clearly inconsistent with no trend in the case of the latter region (Fig. ). In contrast, the Northern Hemisphere ERA-Interim does not show strong positive trends in the early period. The Northern Hemisphere dominates the global signal, as is to be expected given the larger spatial coverage over this region. Here the full period trends mask very different behaviour in the early and late periods, even when the temporal coverage of the CMIP5 historical models are taken into account.

For relative humidity, there is far greater spread across the models and different forcings than for temperature and specific humidity, and in general, agreement with the observations is much poorer, even for HadGEM3-A. Although some models show a small positive trend in the early period (GISS-E2-H and GISS-E2-R; Fig. S10), none show such a strong negative trend for the late period. Generally, all models exhibit relative humidity trends that are closer to zero (neutral trend) than in the observed estimates, with the majority showing small negative trends, except over the tropics.

For all regions apart from the Southern Hemisphere, the confidence range of the full period observed trends reaches or crosses the zero line; thus, strictly speaking, although all observed trends are negative, they are only considered significant for the globe and Southern Hemisphere for some models. Over the Northern Hemisphere and globe the CMIP5 full period historical trends broadly agree with the observed negative trends. Over the Southern Hemisphere, where full period observed trends are negative and largest, there is little agreement with the models. When partitioning the observed period into the early and late sections, it is then clear that none of the CMIP5 models show the strong decline in relative humidity observed in the later period in all regions regardless of the temporal coverage used for the observations. The HadGEM3-A averages have a slightly more negative trend than the CMIP5 models, but it is a small improvement to the match with observations. A similar result was noted by in the ERA-20CM experiments, in which the driest conditions were found in the final decade of the 1901–2010 temporal coverage.

The relative humidity time series show larger interannual variability than specific humidity or temperature, especially compared to the magnitude of the changes observed in the latter period compared to the earlier. This is partly due to relative humidity being more sensitive, reflecting both changes in temperature and changes in dew point temperature directly, whereas specific humidity is only directly affected by changes in the dew point temperature. Longer-term increases in temperature do drive changes in specific humidity but these are energetic rather than direct, hence the increased sensitivity of relative humidity measures. The large interannual variability in relative humidity means the linear trends have much larger confidence ranges. This results in broad-scale consistency between the CMIP5 model historical ensemble spread and the observations; most but not all of the full period historical trends and historicalNat trends overlap with the observations over almost all regions, though this is less true for the Southern Hemisphere. However, the interannual and interdecadal variability and the short period trends really are quite different. There is no consistent difference between CMIP5 historical and historicalNat full period trends in that their confidence ranges overlap. Only for the Northern Hemisphere and globe are the historical trends mostly more negative than the historicalNat trends. Hence, unlike temperature and specific humidity, there is no clear GHG-driven signal in the relative humidity in the CMIP5 models.

For large-scale averages, over the current period of record, CMIP5 historical models are in broad agreement with the observed long-term trends for temperature and specific humidity, but not for relative humidity. The CMIP5 models warm and moisten too much in all regions and do not decline in saturation enough in any region, nor do they agree on whether relative humidity should or should not decline over this period. The best explanation for all regions, except the Southern Hemisphere, is when the models include GHGs. Curiously, the models show strong GHG-driven changes in temperature and specific humidity in the Southern Hemisphere that are not present in the observations.

As noted in Sect. , the cooling observed in the Southern Ocean (and also eastern Pacific) may impact the land-based measurements of temperature, but especially humidity. As this cooling is not seen in the historical and historicalGHG models for surface temperature, it is unsurprising that the agreement between the observations and historical experiments is not as good in this region. note that this cooling may be the result of the Southern Annular Mode but also suggest that there may be forcing contributions to these changes . A further complication is whether low cloud cover plays a role as this is naturally associated with humidity close to the land surface but also with aerosols. The same study shows that models that include indirect aerosol effects have better agreement with the observed global temperature trends. The lack of agreement between the historical experiments and observations is also seen in the specific humidity (see Fig. S27), as a cooler ocean would result in less moisture in the air blown onto the land. We note that no clear difference between the different experiments is visible for the relative humidity (see Fig. S13).

For all variables the behaviour of HadISDH is for the most part mirrored by ERA-Interim, including in all the regional averages. The largest differences are observed in the early 2000s, across both variables and all regions. This indicates that this may be the result of the shift in the source of the SSTs used as input to ERA-Interim (Sect. ).

The agreement in decadal variability and short-period trends is actually very poor: best for temperature, less good for specific humidity and worst for relative humidity. This suggests that our conclusion of good agreement in long-term trends may not hold as the record grows year after year.

Monthly global time series are shown in the Supplement (Figs. S5, S14 and S28). The long-term trends calculated from these time series are very similar in magnitude to the ones from the annual time series. Both the models and observations show monthly variability in the temperature and specific humidity, though the magnitudes differ. However, the relative humidity does not show any regular variation on monthly timescales.

The behaviour of the observed and modelled humidity since 1973 suggests that water availability is less of a limiting factor in the models than in the observations. Even though land surface temperatures have warmed more in the models than observed in HadISDH, there appears to still be enough moisture available over land in the models to increase specific humidity at a rate at which the relative humidity remains close to constant, as is also clear in Fig. . From the observed HadISDH, limits on the water availability both over land and in terms of moisture advected from the oceans, combined with increasing land temperatures, have been discussed as possible drivers of a plateau in the specific humidity and a decline in the relative humidity in recent decades .

Even when modes of variability (key drivers of change, e.g. ENSO via SSTs) are aligned, and land surface temperature trends are similar (e.g. by using HadGEM3-A), the trend for specific humidity is still too large, and the agreement for relative humidity is only slightly better than for the coupled models of the CMIP5 archive (Fig. S10). This suggests that specific and relative humidity do not just depend on natural variability or the amount of warming; something else is missing. In the remaining sections of this paper we test a number of possible ideas including different background climatology (Sect. ), different spatial patterns of change (Sect. ) or the possibility of the water limitations that are less for models than observations impacting the strength and shape of temperature–humidity relationships (Sect. ). Observational and model errors could also play a part, and there are many other processes that could affect the models' ability to match the patterns shown in the observations, which may be avenues for further investigation, including evapotranspiration processes (e.g. land-cover type and changes, stomatal conductance or resistance changes under increasing CO2, cloud cover and changes) and differences in the land–sea warming rate.

To provide context for the differences between the observations and models and/or reanalyses, we give a quick description of the climatologies shown in Fig. a to c. The air temperature is unsurprisingly highest in the tropics and lowest at high latitudes, though large high-altitude regions stand out, e.g the Himalayas. The impact of prevailing westerly flows in the mid-latitudes can be seen on the western coasts of both Europe and North America. The relative humidity clearly shows the less saturated areas over the desert belts around the tropics of Cancer and Capricorn. In central Asia this also stretches north of the Himalayas on the Tibetan Plateau. High-altitude areas in the western USA also have lower relative humidities. Coastal areas in the mid-high latitudes along with rainforest regions in South America, western Africa and south-eastern Asia have higher relative humidities. The specific humidity is highest over the tropics and also coastal regions in the mid-latitudes, such as around the Mediterranean Sea. Low values are found in typically arid areas e.g. the deserts of the world and also the high latitudes.

Panels d to i in Fig.  show the frequency of historical CMIP5 models with positive (Fig. d to f) and negative (Fig. g to i) biases relative to the observations; the number of runs across all models and ensemble members that are greater or less than HadISDH at each grid cell. The lower panels (Fig. j to o) show the differences from HadISDH of ERA-Interim and HadGEM3-A.

The historically forced CMIP5 models exhibit a diverse range of differences compared to the HadISDH climatology, both between models and also spatially, within any one model. Overall and across all the models, there is a tendency for the CMIP5 models to be too cool over much of the globe (comparing Fig. g and d), aside from eastern coastal USA, parts of South America, mid-central Europe and eastern Japan, which appear consistently warmer than HadISDH. The CMIP5 models appear drier and less saturated over the lower latitudes (Fig. h, i). Conversely, over higher latitudes polewards of 40∘ N and polewards of 40∘ S, while specific humidity is broadly similar (Fig. e, h), the models tend to be too highly saturated (Fig. f, i). The patterns are more zonal for specific humidity and relative humidity than for temperature. For specific humidity, notably, the largest differences occur in the deep tropics with very small differences found in the high latitudes. For relative humidity the differences appear large throughout. Most of the CMIP5 models have a cooler bias, are drier especially in the tropics and are more saturated in the mid-high latitudes. The CanESM2 and NASA-GISS models stand out from the others as having a warm bias. This is very widespread in CanESM2, which also shows a widespread moist and saturated bias (see Figs. S7, S16 and S30).

Regionally, there are some consistent features across the models. The western and eastern (excluding the central and the east coast) USA, western China, northern Europe and southern South America are cooler and have considerably higher relative humidity (are more saturated) in the historical forced CMIP5 models but with no clear, common differences in specific humidity. Thus, these regions are more saturated in the models, most likely because they are cooler rather than because they contain less moisture (Fig. g). Western and northern Africa tend to be cooler with lower specific humidity (less moisture) in the CMIP5 models but no particularly common difference in relative humidity (saturation). Conversely, the east coast of the USA appears warmer and moister (higher specific humidity) in the CMIP5 models, again with no particularly common difference in saturation level (relative humidity).

The Southern Hemisphere is the region where the observations and models differ most in terms of the regional average time series (Sect. ). However, climatologically, there is not a strong consistent difference between the historically forced CMIP5 models and HadISDH over this region. Some grid boxes appear to be generally warmer, moister and more saturated in the CMIP5 models (but not HadGEM3-A) than in HadISDH, but other grid boxes are cooler, drier and less saturated. Areas of southern Africa, southern Australia and the west coast of South America appear to be cooler, contain more moisture, and be more saturated than HadISDH. Over Antarctica, the few grid boxes present are also cooler and more saturated, but not necessarily more moist. The middle of South America is generally warmer, drier and less saturated. Similarly for HadGEM3-A and ERA-Interim, while the majority of the observed Southern Hemisphere grid boxes are too highly saturated, the Southern Hemisphere does not stand out as a region of large climatological differences compared to HadISDH. As these features are very localised, it is not possible to say that these regions are biased compared to the observations.

HadGEM3-A is generally cooler than HadISDH overall, drier and less saturated over the tropics and more saturated over the mid-high latitudes, consistent with the majority of the CMIP5 models. ERA-Interim shows better agreement with HadISDH overall but has generally similar biases to HadGEM3-A, albeit to a lesser extent and with less spatial consistency. Dry biases relative to synoptic surface observations are also noted in .

Clearly, there are some notable differences between HadISDH and the other datasets (CMIP5 models and ERA-Interim) climatologically speaking, especially for relative humidity. Most importantly perhaps is the tendency for all models (CMIP5 and HadGEM3-A) to be too highly saturated in the mid-high latitudes and too arid in the low latitudes. Given these differences, we expect differences in the spatial distribution of trends, which if large could impact large-scale average time series and trends, as well as T–q and T–rh relationships (Sect. ).

HadISDH spans from 1973 to 2015 inclusive, but the CMIP5 models mainly stop in 2012, with the few without historicalExt runs ending in 2005. We therefore calculate linear trends over 1975–2010 requiring 80 % completeness. The trends are again calculated using the MPW method. For models that have no data after 2005 (IPSL-CM5A-LR and CSIRO-Mk-3-6-0 for historical humidity), these are still included in these calculations. The spatial and temporal coverage has been matched to that of HadISDH. We also calculate the number of historical CMIP5 model runs that have trends greater than (more positive) or less than (more negative) those of HadISDH for the three variables, as well as whether the trend is in the same direction to or opposite direction from HadISDH.

Despite the relatively poor coverage in the tropics, the relative humidity trends indicate increasing saturation in the tropics and also the high latitudes. In the mid-latitudes, however, there are large areas in which the relative humidity has declined. These regions extend further north in Europe than they do in North America and eastern Asia (Fig. c). In comparison, specific humidity shows an increase in moistness almost globally, with the largest increases over the tropics, though the Mediterranean region also stands out. Only a few grid boxes show decreasing trends, at the southern tips of the Southern Hemisphere land masses and also on the west coast of North America (Fig. b). The global temperature has increased in all but a handful of grid boxes, with the strongest warming over eastern Europe and western Asia, and the Northern Hemisphere warming more than the Southern (Fig. a).

There is generally good agreement between the CMIP5 models and HadISDH for both the air temperature and the specific humidity trends. The strongest warming is in the northern high latitudes, and the strongest moistening is in the tropics. There is a quasi-zonal pattern in the air temperature trend differences between the CMIP5 models and HadISDH, with stronger warming across the high latitudes and weaker warming across the mid-latitudes (Fig. e, h). The tropics show mixed signals, with many models showing stronger warming over India and south-eastern Asia and weaker warming over tropical western Africa. The specific humidity in contrast shows stronger moistening over the Americas, eastern Asia, Australia, and southern Africa and weaker moistening over Eurasia, eastern North and Central America, and northern Africa. As only a few boxes in both air temperature and specific humidity have trends opposite to HadISDH (Fig. ), this shows very good agreement in general in terms of the spatial patterns in direction of trends.

However, many of the regions that have very strong moistening in HadISDH have weaker moistening in the CMIP5 models and also stronger warming in these areas. The few areas showing drying in HadISDH are also not replicated in the CMIP5 models and are also seen in Fig. b, e as areas with trends opposite to HadISDH. However, HadGEM3-A shows some areas that do exhibit drying in similar (though not exactly the same) locations as HadISDH (south-western USA, southern South America, southern tip of Africa, but not southern Australia; see Figs. b and S31).

A number of CMIP5 models also show a few isolated grid boxes with a negative trend in the specific humidity (e.g. CSIRO-Mk3-6-0, HadGEM2-ES; Fig. S28). However, these are most likely the result of artifacts of missing data in the observations that, when applied to the model values, result in poor temporal sampling in these very few grid boxes.

For relative humidity, there are spatially cohesive regions of both positive and negative trends in both the CMIP5 models and HadISDH, and weak trends towards less saturation are reasonably widespread in all models (compare Figs. f, i and c, f). More negative trends (decreased rate of saturation compared to HadISDH) over the USA, mid- and northern South America, southern Africa, north-eastern Europe and western Asia, and India are common to most models (Fig. ). Although India is becoming more saturated in the CMIP5 models (but not HadGEM3-A), it is doing so at a slower rate than HadISDH (see Fig. ). More positive trends (increased rate of saturation compared to HadISDH) over southern Europe and eastern China are also common to most models. The drying regions in HadISDH take on a more zonal structure with the drying mostly across the mid-latitudes in both hemispheres.

Broadly, over the mid-latitudes, where HadISDH shows a trend towards less saturation (negative relative humidity), most CMIP5 models show more positive trends (Fig. f, i). Mostly this means that the model trends are still negative, but weaker than HadISDH, but in some cases the model trends are positive, especially over eastern China (Fig. f). Over the tropics and high latitudes, where HadISDH shows a trend towards increasing saturation (positive relative humidity), most CMIP5 models show more negative trends (Fig. c, i). This is a result of mostly weaker positive CMIP5 trends, or, especially over the high latitudes, negative trends. When comparing the direction of trends (Fig. c, f) this is also clear, with CMIP5 models being split between having trends in the same or opposite direction as HadISDH. The relatively high interannual variability in relative humidity in the CMIP5 models compared to the amplitude of the long-term trends contributes to this more mixed signal.

HadGEM3-A, as for temperature and specific humidity, shows similarities to the CMIP5 models, exhibiting some zonal banding of the differences. It does not show the trends of increasing saturation over the high latitudes observed in HadISDH. The prominent increasing relative humidity over India observed in HadISDH and a number of CMIP5 models is not present in HadGEM3-A.

In contrast, the differences between HadISDH and ERA-Interim are more mixed, with few areas showing strong differences in the temperature trends. Moderate differences are apparent with more warming in northern Europe and western Asia and cooling in western Europe and western Africa as well as an area in central Asia. For the humidity measures, the predominant signal is for relative drying and less saturation compared to HadISDH, especially in the deep tropics, western North America and western Europe. Note the changes in ingested SSTs in June 2001 and January 2002 in ERA-Interim that lead to a small downward shift in SSTs (see Sect. ). This could be a contributing factor to the smaller positive land specific humidity trends and larger negative relative humidity trends. Furthermore, in the regional average time series presented (Figs.  to ), the largest differences between HadISDH and ERA-Interim are observed at that time across all variables.

The comparison of spatial patterns in the previous section focusses both on the background annual climatology and long-term linear trends. Note that we have not assessed any spatial correlations between the observations, historical models and reanalysis products.

For air temperature, the CMIP5 models are on the whole too cool over most of the globe, except parts of the mid-latitudes (especially a band stretching eastwards from the Mediterranean Sea). Similarly, the CMIP5 models are too dry in most areas, but areas in the mid-latitudes appear to be too moist. Conversely, the models are more saturated than the observations in the high latitudes but are too arid in the tropical regions. Across all three variables, there is a suggestion of a zonal pattern – with mid-latitudes showing a different signal to the rest of the globe in temperature and specific humidity and a striking contrast between the tropics and high latitudes in relative humidity. However, the Southern Hemisphere, which stood out in the temporal analysis, does not show strong, consistent differences in any of the three variables. HadGEM3-A is on the whole a little cooler and drier than HadISDH, and less saturated in the tropics but is more saturated over mid-high latitudes. ERA-Interim shows a similar pattern but with lower magnitudes.

Comparing long-term trends to the models shows general good agreement between the CMIP5 models and HadISD for air temperature and specific humidity. The directions of the model trends are well aligned to the observed trends for the majority of the globe for these two variables, (Fig. ) though there are regional differences in the magnitude of the trends and a quasi-zonal pattern, especially in the eastern hemisphere. Many of the regions showing strong moistening in the observations show weaker moistening in the CMIP5 models, combined with stronger warming. For relative humidity, there is not even agreement on the direction of the trends. Again, there is an apparent zonal signal, with models having negative trend differences in high latitudes and India but positive ones in the eastern hemisphere mid-latitudes. In both HadGEM3-A and ERA-Interim the largest differences are for the relative humidity trends, with the smallest in air temperature. Both these products show shallower trends in relative humidity in most regions.

Away from the high latitudes, the relative humidity trends in the historical CMIP5 models look similar to the RCP 8.5 multi-model ensemble mean difference between 2071–2100 and 1971–2000. Relative humidity is projected to become less saturated over most of the land mass apart from regions around India, parts of tropical Africa and the southern Arabian peninsula. The more zonal pattern in the observations includes increasing saturation levels over the Caribbean and western Africa, and the high northern latitudes are not present in the future projected changes (Fig. 12.21, Fig. S1). Thus, despite some similarities, the present observed drying appears to be different from the long-term projected trends in drying. This suggests the importance of some decadal-scale variability or driving mechanisms, such as land use change, that are not well represented in GCMs.

There is no evidence that climatologically moister and more saturated regions have stronger moistening trends and weaker or decreasing saturation trends; thus, we cannot conclude that the models are less water limited than the observations from this analysis. Just as with the time series, agreement between the models and observations is better for temperature and specific humidity than for relative humidity. There is arguably better agreement in terms of spatial patterns of drying than the long-term large-scale average time series. This shows how linear trends mask the significant temporal differences that can be seen in the time series. Despite the same modes of variability and SSTs, the spatial pattern of trends in HadGEM3-A do not match the observations very well. The spatial differences from projected future trends in relative humidity suggest that for those regions (Caribbean, high latitudes) a number of possible issues are present: there could be larger observational errors, processes not captured well in the models, more transitional processes associated with the land surface or even modes of variability that could not be expected to persist to centennial timescales nor be captured by climate models.

Both HadISDH and ERA-Interim exhibit positive temperature–specific humidity (T–q) relationships for all regions. They behave reasonably linearly. The steepest observed T–q relationship slopes are in the tropics. This makes sense, given that the tropics (20∘ S to 20∘ N) is the warmest region – a warming trend will drive larger moistening trends there. The smallest observed T–q relationship slopes (close to zero) are in the Southern Hemisphere. Correlation is also lowest in the Southern Hemisphere to the extent that there is no real relationship between temperature and specific humidity there; the observed regions of the Southern Hemisphere appear very water limited. ERA-Interim has smaller slopes and weaker correlations compared to HadISDH but they are broadly similar. The strongest correlations occur in the tropics for HadISDH and in the Northern Hemisphere for ERA-Interim (see Figs. S34 and S35). The location of individual years along with their relative humidity anomaly are shown in the Supplement, Fig. S37.

Overall, the majority of historically forced CMIP5 models exhibit slightly steeper (more positive) temperature–specific humidity relationship slopes, with stronger correlations than HadISDH or ERA-Interim (Fig. ). This supports the concept of T and q being more closely correlated in the models than the observations. However, this is partly to be expected given the stronger warming in the historical CMIP5 models. Clearly, the slight cool bias in the historical CMIP5 climatological temperature is not large enough to significantly change the T–q relationship slope.

This tendency for larger slopes and stronger T–q relationships in the historical CMIP5 models is true for all regions, especially the Southern Hemisphere (Fig. ). Notably, CSIRO-Mk3-6-0 is unique in its similarity to the observations in the Southern Hemisphere. HadGEM2-ES and CSIRO-Mk3-6-0 have slopes closest to HadISDH, and these slopes are slightly smaller than those in HadISDH in the tropics. Like the observations, the CMIP5 models consistently show the largest slopes in the tropics (apart from NorESM1-M, which places the Southern Hemisphere just above the tropics but from few ensemble members) and the majority of historical CMIP5 models also have the highest correlations there as well. CSIRO-Mk3-6-0, CanESM2 and HadGEM2-ES have the strongest correlations in the Northern Hemisphere or globe along with ERA-Interim. However, unlike the observations, all historical CMIP5 models apart from CSIRO-Mk3-6-0 have a larger T–q relationship slope in the Southern Hemisphere than for the globe and Northern Hemisphere, though the correlation coefficients are in some cases relatively low (∼0.3). Overall, the larger slopes and higher correlations in the CMIP5 models suggests that water availability could be less of a limiting factor in the models compared to the observations, especially in the Southern Hemisphere (see also Sect. ). This is supported to some extent by the prevalence of overly moist and saturated historical CMIP5 model grid boxes in parts of the Southern Hemisphere as discussed in Sect. .

Interestingly, most historicalNat CMIP5 models appear more consistent with HadISDH and ERA-Interim over the Southern Hemisphere in terms of small slopes and low correlations. The historicalNat CMIP5 model Southern Hemisphere correlations are notably lower than for other regions, but slopes are not consistently smaller. The difference between and within the historicalNat CMIP5 models suggests that natural variability does contribute to differences in the temperature–specific humidity relationship. However, the consistency between models, which collectively explore a wide range of natural variability at any one point in time, suggests that Southern Hemisphere differences are not strongly driven by natural variability.

It appears that the human forcing component in the models is contributing to humidity changes in the Southern Hemisphere that are not consistent with the observations. We have established that the models are overall biased cool and dry (in absolute moisture terms) relative to the observations, suggesting that climatological biases are not driving differences in the global average.

In all cases, the historically forced CMIP5 models have larger warming trends than the observations, which could be a contributing factor, especially as the trend differences tend to be greatest in the Southern Hemisphere. However, for some models and regions the T–q relationship slope is largest in the historicalNat forced ensemble mean relative to the historically forced runs, even though historicalNat warming trends are much smaller than historical warming trends. This is the case for HadGEM2-ES and bcc-csm1-1 over the globe and Northern Hemisphere, and for CSIRO-Mk3-6-0 over the Northern Hemisphere, although there is an overlap between the range of slopes of the T–q relationship from the individual runs between historical and historicalNat. This suggests that for these models at least it is not just the stronger warming trend in the CMIP5 models that is driving the stronger relationship and that natural variability may play a role in determining how specific humidity changes over time.

The atmosphere-only HadGEM3-A model for the most part has the same patterns of natural variability as the observations. Trends and climatology are fractionally more similar to HadISDH than for the historical CMIP5 models. As expected, the temperature–specific humidity relationship slopes and correlations are substantially more similar to HadISDH and ERA-Interim (Fig. ). The ensemble mean T–q relationship slope for the globe and Northern Hemisphere is slightly smaller than for the observations, as is the spread of the individual runs. For the tropics the ensemble mean T–q relationship slope is slightly larger than for HadISDH and ERA-Interim. Again, the Southern Hemisphere is the region where differences are largest. Although the correlations are similar and the ensemble range of slopes and correlations encompass the HadISDH observed values, the ensemble mean slope is slightly more positive in HadGEM3-A. It is actually more positive than for the Northern Hemisphere, which is not the case in HadISDH or ERA-Interim, but has a lower correlation, indicating that this has lower robustness. Overall, this good agreement suggests that the model physics is reasonable outside of the Southern Hemisphere – when background climatology, variability and trends are similar, the models behave very similarly to the observations in terms of large-scale physical relationships.

Overall, the T–q relationships are reasonably similar to the observations, except for the Southern Hemisphere. Generally the correlations are a little stronger in the CMIP5 models, with steeper slopes. However, in the Southern Hemisphere these differences are larger in CMIP5 and even for HadGEM3-A. Apart from observational error being a possible cause, these differences also suggest some issues with the model physics in the Southern Hemisphere.

In a region that is not water limited, the expectation is that relative humidity should not change with temperature and the slope and correlation should be very close to zero. Given that water availability is limited over land to some extent, and additionally that the land has been warming faster than the ocean, a negative T–rh relationship might be expected. The T–rh relationship slopes are negative for all regions for both HadISDH and ERA-Interim and are the largest (most negative) by a large margin in the Southern Hemisphere (Fig. ). This is to be expected given the lack of relationship between temperature and specific humidity for this region, again suggesting that it is strongly water limited. ERA-Interim consistently has more negative slopes and stronger (more negative) correlations than HadISDH. The strongest correlation for HadISDH is in the Southern Hemisphere but still quite weak at -0.550. For ERA-Interim, all correlations are more negative than -0.5 and are the strongest (most negative) for the globe.

The scatter pattern of both HadISDH and ERA-Interim for the globe and Northern Hemisphere is distinctly different from anything shown in the models (including HadGEM3-A) and very clearly non-linear (Fig. , most clearly seen compared to models with few ensemble members). For both HadISDH and ERA-Interim there appear to be two populations. For all times at which temperature anomalies are lower than ∼0.2 ∘C there appears to be a neutral or small positive T–rh relationship. For all temperature anomalies greater than 0.2 ∘C there is either a very large negative or a neutral T–rh relationship. Either way, this second cluster appears to behave differently than the first. Also, this behaviour is not apparent in the tropics or Southern Hemisphere. In Fig. S23, the T–rh relationship is shown along with the years and the specific humidity anomalies. The positive specific humidity anomaly years (mainly the most recent years) seem to have a different relationship from the negative anomaly years (mainly the earlier years) for the Northern Hemisphere, and to some extent in the tropics.

In general, the T–rh correlations for all models, all regions and the observed estimates are low (Fig. ). This shows that the relationship between temperature and relative humidity is much weaker than for temperature and specific humidity, which is consistent across all models and observations, and that the slopes should be interpreted with caution. However, none of the CMIP5 models exhibit anything like the scatter patterns shown in HadISDH or ERA-Interim. Nevertheless, some interesting common features are apparent. Overall, the majority of historical forced CMIP5 model ensemble members exhibit negative temperature–relative humidity relationships. However, here is far greater variation in the T–rh relationships across the historical CMIP5 models compared to the T–q relationships, with slopes and correlations both steeper–stronger and shallower–weaker than HadISDH. Interestingly, the CMIP5 models exhibit consistently shallower slopes than ERA-Interim. In the Southern Hemisphere, the slopes for the CMIP5 models are on the whole more negative than they are for the globe and for other regions, as in HadISDH and ERA-Interim (except for GISS-E2-H and IPSL-CM5A-LR). The slopes are mostly more negative than HadISDH for the Northern Hemisphere but shallower than ERA-Interim. The models have shallower negative slopes than HadISDH for the Southern Hemisphere and are very mixed for the tropics, with weaker correlations.

HadGEM3-A appears to be closer to ERA-Interim for the globe and Northern Hemisphere than the other models or the observations. The CMIP5 models are closer to the observations for the globe and Northern Hemisphere than HadGEM3A (Fig. ). HadGEM3-A is within the model spread for the tropics and Southern Hemisphere, along with HadISDH. ERA-Interim, however, is with the model spread for the tropics but not for the Southern Hemisphere.

As outlined previously, the specific humidity is closely linked to the surface temperature (assuming no water limitation) and thus a relatively tight correlation is expected, and also seen in all regions apart from the Southern Hemisphere. However, as relative humidity is a more sensitive variable and also no trend is expected under the same assumptions, a higher apparent scatter would be expected. Combined with the necessity of showing each model and experiment realisation compared to the single realisations of HadISDH and ERA-Interim, the qualitative differences in the appearance of the T–q and T–rh plots follow.

We have discussed previously whether the models could have different levels of water limitation compared to the observations when analysing the temporal behaviour over large regions (Sect. ), but overall differences are not clearly evident from the distribution of differences in trends and climatologies (Sect. ). The presence of a negative T–rh relationship shows that the models are water limited to some extent. For the Northern Hemisphere and globe, the generally stronger correlations and steeper negative slopes in the historical CMIP5 models suggest that the models are more water limited than the observations in these regions. Conversely, for the Southern Hemisphere, and to some extent in the tropics, the weaker correlations and shallower negative slopes in the historical CMIP5 models suggest that the models are less water limited than the observations. However, this interpretation does not take into account the complex interdecadal behaviour of the observation-based estimate, especially for the Northern Hemisphere and globe, which is very different from the more linear relationship that is consistently shown across the models. Furthermore, climatological differences point to historical CMIP5 models generally being drier and less saturated across the tropics, which might suggest that they are more water limited than the observed estimates. The higher latitudes appear to be more saturated than the observations, but only polewards of 40∘ N and polewards of 40∘ S. The hemispheric averages included data down to 20∘ N and down to 20∘ S, which would dampen any expected signal. For all other regions, the range of slopes from individual historicalNat CMIP5 model runs encompass the historical CMIP5 model ensemble mean. This suggests that natural variability also plays a strong part in the T–rh relationship over these large scales.

We would expect better agreement between the observed estimates and HadGEM3-A than for the CMIP5 models. However, this does not appear to be the case. For the globe and Northern Hemisphere, the slopes and correlations in HadGEM3-A are much more negative than those in HadISDH and many of the historical CMIP5 models, although they are closer to those in ERA-Interim (Fig. ).

For the tropics, where there is large variability across the CMIP5 models, and the Southern Hemisphere, historical HadGEM3-A and HadISDH are both within the coupled model spread. However, like the CMIP5 models, HadGEM3-A shows shallower negative slopes in the Southern Hemisphere, suggesting that it is less water limited than the observed estimates there.

As in the other analyses, the agreement between models and observations is generally poorer where relative humidity is concerned compared to specific humidity. There is consistency across the CMIP5 models in terms of their negative T–rh relationships, the largest negative relationship occurring in the Southern Hemisphere. In this region, and in the tropics, there is a larger negative relationship in the historicalNat ensemble members compared to historical. The range of slopes from the historicalNat runs are mostly wider than those of the historical runs, encompasses the ensemble mean historical slope and overlap with the historical slope range in most cases for the globe and Northern Hemisphere. This is not the case for the tropics or Southern Hemisphere though. Hence, natural variability appears to be a larger contributing factor than GHGs to the variation observed in the global and Northern Hemisphere averages. The smaller negative slopes in the Southern Hemisphere and also the tropics for historical CMIP5 models relative to historicalNat suggest that in the models, human activity may be driving a weakening of the T–rh relationship, making the region less water limited.

While the agreement between the models themselves and between the models and observations is good for T–q (outside of the Southern Hemisphere), there is much poorer agreement between both the models themselves and the models and observations for T–rh. In general the T–q relationship is strongly positive, whereas the T–rh relationship is weakly negative. The Southern Hemisphere appears unique in that the T–q relationship is generally weakly positive, whereas the T–rh relationship is generally strongly negative, for both models and observations. The CMIP5 models consistently have a stronger T–q correlation that is more steeply positive than HadISDH, ERA-Interim and HadGEM3-A, even in the Southern Hemisphere. Also, reasonable agreement between ERA-Interim and HadISDH suggests some robustness in the observed features. This over-correlation as discussed in could be due to missing processes in the models or errors in the observations or models. As this analysis uses spatially and temporally matched data, it is not the result of coverage issues. The over-correlation may be the result of the models sampling slightly different climatologies for the regions discussed above. If the coverage is sparse and the few areas sampled are climatologically different, then different relationships may be expected.

For T–rh, the CMIP5 models (historical and historicalNat) have much wider spread that encompasses HadISDH in terms of correlation strength and slope steepness but is consistently weaker and shallower in the Southern Hemisphere. This suggests a high sensitivity of relative humidity to model parameterisations or natural variability. Generally, over all regions, the historicalNat T–q correlations and slopes from CMIP5 are weaker or shallower than the historical ones. This suggests some strengthening of the T–q relationship driven by anthropogenic climate change. In the tropics and especially the Southern Hemisphere, the historicalNat T–rh relationships have stronger correlations and steeper slopes than historical experiments, which is consistent with the weaker or shallower historicalNat T–q relationship. This weakening of the T–rh relationship under anthropogenic climate change, while again largely driven by the presence of a strong trend in temperature, suggests less-water-limited conditions under anthropogenic climate change.