Long‐Term Wetting and Drying Trends in Land Water Storage Derived From GRACE and CMIP5 Models

Long-Term Wetting and Drying Trends in Land Water Storage Derived From GRACE and CMIP5 Models L. Jensen1, A. Eicker1, H. Dobslaw2, T. Stacke3, and V. Humphrey4 1Geodesy and Geoinformatics, HafenCity University Hamburg, Hamburg, Germany, 2Helmholtz Centre Potsdam, German Research Centre for Geosciences (GFZ), Potsdam, Germany, 3Max Planck Institute for Meteorology, Hamburg, Germany, 4Institute for Atmospheric and Climate Science, ETH Zürich, Zürich, Switzerland Abstract Coupled climate models participating in the CMIP5 (Coupled Model Intercomparison Project Phase 5) exhibit a large intermodel spread in the representation of long-term trends in soil moisture and snow in response to anthropogenic climate change. We evaluate long-term (January 1861 to December 2099) water storage trends from 21 CMIP5 models against observed trends in terrestrial water storage (TWS) obtained from 14 years (April 2002 to August 2016) of the GRACE (Gravity Recovery And Climate Experiment) satellite mission. This is complicated due to the incomplete representation of TWS in CMIP5 models and interannual climate variability masking long-term trends in observations. We thus evaluate first the spread in projected trends among CMIP5 models and identify regions of broad model consensus. Second, we assess the extent to which these projected trends are already present during the historical period (January 1861 to August 2016) and thus potentially detectable in observational records available today. Third, we quantify the degree to which 14-year tendencies can be expected to represent long-term trends, finding that regional long-term trends start to emerge from interannual variations after just 14 years while stable global trend patterns are detectable after 30 years. We classify regions of strong model consensus into areas where (1) climate-related TWS changes are supported by the direction of GRACE trends, (2) mismatch of trends hints at possible model deficits, (3) the short observation time span and/or anthropogenic influences prevent reliable conclusions about long-term wetting or drying. We thereby demonstrate the value of satellite observations of water storage to further constrain the response of the terrestrial water cycle to climate change. 1. Introduction The terrestrial branch of the global water cycle is an important component of the Earth's coupled climate system: Water available in the soil critically determines biomass production that effectively takes up carbon dioxide from the atmosphere and thus constitutes the land cover and consequently also the albedo of the Earth's surface. The availability of water at the surface influences the rate of evapotranspiration and thereby the amount of latent heat absorbed by the atmosphere locally and advected to distant regions along with the tropospheric winds; and water in the form of snow cover thermally isolates the soil from the air above it. The accurate representation of the terrestrial water dynamics and its various feedbacks to the atmospheric water, energy and carbon cycles is thus critically important for interactively coupled global numerical climate models that are used to infer information about the current state and the future evolution of the Earth's climate conditions (Trenberth, 2010). Due to their direct effect on the availability of freshwater resources, investigating climate change impacts on the global water cycle is of great societal relevance. Changes in terrestrial water storage (TWS) might reflect long-term wetting or drying in various regions of the world, and the identification of such regions is of substantial importance for water resources management. However, coupled climate models used to predict future climatic conditions still exhibit a spread in the representation of long-term trends in soil moisture and other land water related variables (Guo & Dirmeyer, 2006; Figure 12.23 in Berg et al., 2017; Collins et al., 2013; Yuan & Quiring, 2017). Comparing the output of numerical models with observations is crucial to demonstrate their reliability and to test predictive capacities, but measurements of water storage changes are difficult to obtain. A classical RESEARCH ARTICLE 10.1029/2018JD029989 Key Points: • By comparing terrestrial water storage trends from CMIP5 models and GRACE satellite data, we identify hot spot regions of wetting and drying • Model analysis reveals that regional long-term trends start to emerge from interannual variations after 14 years • Large model spread in water storage trends demonstrates importance of GRACE to constrain response of the water cycle to climate change Correspondence to: L. Jensen, [email protected] Received 14 NOV 2018 Accepted 17 AUG 2019 Accepted article online 29 AUG 2019 ©2019. The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. JENSEN ET AL. 9808 Published online 3 SEP 2019 Citation: Jensen, L., Eicker, A., Dobslaw, H., Stacke, T., & Humphrey, V. (2019). Long‐term wetting and drying trends in land water storage derived from GRACE and CMIP5 models. Journal of Geophysical Research: Atmospheres, 124, 9808–9823. https://doi.org/ 10.1029/2018JD029989 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 approach for the determination of TWS at basin scale is the integration of the water balance equation (precipitation minus evapotranspiration minus runoff), see Rodell et al. (2004). However, this is challenging on a global scale, since streamflow measurements are sparse and evapotranspiration is generally difficult to measure (Wartenburger et al., 2018). Especially, trends in water storage cannot be recovered well by this method due to biases in the water flux observations (Hirschi & Seneviratne, 2017). Complementary to conventional meteorologic observations of atmospheric water fluxes, the satellite mission Gravity Recovery And Climate Experiment (GRACE; Tapley et al., 2004) in operation from 2002 to 2017 allowed for the first time the observation of water storage changes with global coverage from space. By evaluating relative distance changes between two spacecraft at very low altitudes of 400–500 km, time variations in the Earth's gravity field are mapped that can be unambiguously related to changes in TWS. Due to the indirect observation concept, GRACE essentially senses water mass anomalies independently of their surface exposure and thus integrates all mass changes vertically from the surface down to the deepest aquifers. This unique capability of the gravimetric method makes GRACE highly complementary to alternative radiometric satellite techniques of soil moisture remote sensing that are only sensitive to changes in the top few centimeters of soil (Dorigo et al., 2015). GRACE mission data have been used in various hydrometeorological applications, for example, Famiglietti and Rodell (2013), and it is rated among the top five priorities of the future Earth observation capacity by the most recent National Aeronautics and Space Administration decadal survey (Committee on the Decadal Survey for Earth Science and Applications from Space et al., 2018). The successor mission GRACE-FO (Follow On), launched in May 2018, is expected to continue this important observational record over the next decades (Flechtner et al., 2016), which will facilitate the separation between interannual variability and long-term climatological trends in TWS. Because the limited time span of GRACE data makes the identification of climate-related signals still challenging, this study aims to investigate how GRACE TWS trends could (and should) be compared to model-derived trends. TWS as observed with GRACE has already been used to validate both global hydrological models (Döll et al., 2014; Eicker et al., 2014; Güntner, 2008; Syed et al., 2008) and land surface models (Scanlon et al., 2018; Zhang et al., 2017) which are driven by a prescribed meteorological forcing. In this study, we focus on interactively coupled Earth System Models (ESMs) participating in CMIP5 (Coupled Model Intercomparison Project Phase 5, Taylor et al., 2011). Comparing GRACE trends with long-term coupled climate model projections is challenging in mainly two aspects: (i) In contrast to GRACE TWS (i.e., the full integrated water column, including all water reservoirs), TWS in the models is reflected typically only by means of snow storage and soil moisture. The representation of the latter critically depends on the depth of the soil column and the number of vertical layers considered. In particular, current ESMs do not explicitly simulate groundwater storage changes. As groundwater-surface interactions play an important role in the global hydrological cycle, this poses an additional source of uncertainty in long-term model projections of wetting and drying. (ii) Coupled runs in CMIP5 starting from preindustrial conditions and extending over the whole historical period until the present day are forced with temporally variable solar radiation, aerosols, CO2concentrations, and land use. Those experiments are thus expected to reproduce the climate variability in a statistical sense only. As a result, different realizations of the interannual and decadal climate variability are superimposed over the climatological trends so that a direct comparison with the 14-year GRACE TWS time series only has limited explanatory power. While a regional study for the Mississippi Basin (Freedman et al., 2014) showed reasonably good agreement for the annual amplitude of GRACE data and a subset of CMIP5 models, Fasullo et al. (2016) found the trends from historical CESM1-CAM5 runs compared to GRACE to be dominated by internal variability rather than by the forced response. Different drivers of TWS trends observed by GRACE were investigated by Rodell et al. (2018), who also made use of CMIP5 model precipitation projections to attribute wetting and drying tendencies in some regions to climate-driven precipitation changes. To our knowledge, an extensive global comparison of soil moisture and snow trends modeled over more than two centuries (in the following referred to as bicentennial) against GRACE observations has never been conducted with an ensemble of models such as CMIP5. In response to these challenges, we focus in this study in particular on the correspondence of bicentennial trends in TWS as simulated by the majority of CMIP5 models and TWS tendencies as observed by GRACE and investigate regions of agreement and disagreement on wetting or drying trends in models and satellite observations. JENSEN ET AL. 9809 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Figure 1. TWS trends from ITSG-Grace2018s (preliminary) for the time span April 2002 to August 2016 (without Greenland, Svalbard, Gulf Coast of Alaska, and Antarctica). Stippling indicates regions with nonsignificant trends (𝛼=0.05). This paper is structured as follows: First, we compute global maps of TWS trends from GRACE data (section 2) and CMIP5 models (section 3) together with an evaluation of the variability among different models and within historical and future time spans. We estimate the influence of the different time series lengths for GRACE and models by means of two model studies using model TWS tendencies from time periods ranging from 14 to more than 200 years (section 4). The TWS trend maps from GRACE and CMIP5 models are subsequently compared (section 5). Next, we investigate hot spot and noncompliance regions of wetting and drying trends regarding their uncertainty (section 6), which might be caused by model deficits or natural interannual variability and human impacts affecting the GRACE-derived trends. Section 7 summarizes the results and addresses future work. 2. TWS Trends From GRACE Data To obtain a global grid of observed TWS trends we use the ITSG-Grace2018s trend Level 2 data (Mayer-Gürr et al., 2018), which was obtained from estimating a long-term mean gravity field model together with linear trend and annual cycle from all available GRACE Level 1B RL03 data. The ITSG-Grace2018s trend used here is a preliminary version containing Level 1B data of the time span April 2002 to August 2016 (∼14 years). It will be updated once the complete time series of Level 1B RL03 data (April 2002 to June 2017) is available. However, for the trend only minor changes are expected by extending the time series by less than 1 year. The spherical harmonic coefficients (Level 2) of the trend in gravitational potential are given up to degree nmax =120 and are postprocessed as follows: The effect of geocenter motion is taken into account by augmenting the GRACE data with the linear trends of degree 1 harmonic coefficients provided by Swenson et al. (2008). The zonal Δc20 trend coefficient is replaced using a result from Satellite Laser Ranging (Cheng et al., 2013). To reduce mass trends originating from glacial isostatic adjustment (GIA), we subtract a model from A et al. (2013) and to mitigate the effect of correlated noise a DDK4 filter (Kusche, 2007) is applied. We calculate the TWS trend on a 2◦×2◦geographical grid (Figure 1) according to tws(𝜆, 𝜃)= M 4𝜋R2𝜌w nmax ∑ n=1 n ∑ m=−n (2n+1) (1+k′ n)ΔcnmYnm(𝜆, 𝜃)(1) where 𝜆and 𝜃denote the spherical coordinates, Mand Rare the mass and the radius of the Earth, 𝜌w=1,000 kg/m3is the density of water, k′ ndenote the Load Love Numbers (Lambeck, 1988), Δcnm are the filtered spherical harmonic coefficients of the gravitational potential, and Ynm(𝜆, 𝜃)are the surface JENSEN ET AL. 9810 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 spherical harmonic functions. Corresponding standard deviations of the TWS trends are obtained by variance propagation from realistic error assumptions provided with the Δcnm coefficients of the ITSG-Grace2018s trend. The significance of the trend can be tested with a parameter test. The estimated trend divided by its estimated standard deviation is compared to the critical value of the normal distribution for a certain significance level 1−𝛼which we set to 95% in this study. Generally, the reliability of trends from GRACE is high. Among the solutions of different GRACE processing centers trends over the same time period are very similar (Scanlon et al., 2018), even if a different representation (mascons instead of spherical harmonics) is chosen. Thus, selecting another GRACE solution (e.g., from JPL or CSR) does not alter the findings of our study (not shown). GRACE-derived trends might not originate purely from TWS changes everywhere, as residual tectonic effects from GIA (Caron et al., 2018), postseismic deformation after large earthquakes (Han et al., 2008, 2010), or residual atmospheric mass variability (Fagiolini et al., 2015) can overlay TWS trends. Furthermore, leakage of signal into neighboring grid cells due to filtering and residual noise that could not be removed during filtering might also distort TWS trends. As the GRACE TWS trends are only calculated from 14 years of data, the results can be dominated by low-frequency climate variability related to El Niño–Southern Oscillation (Ni et al., 2018; Phillips et al., 2012), the solar cycle (Bhattacharyya & Narasimha, 2005), the quasi-biennial oscillation and other coupled climate modes (Gray et al., 2018), and episodic events as volcanic eruptions (Iles et al., 2013), which may either conceal the long-term trend or produce a spurious transient trend. Approaches to reduce these interannual variabilities in the GRACE record are currently being discussed (e.g., Eicker et al., 2016). 3. TWS Trends From CMIP5 Model Data As CMIP5 models do not provide a standard output variable for total water storage, we use the sum of total soil moisture content (mrso) and surface snow amount (snw) as an approximation of it. In the remaining part of the paper we refer to this TWS approximation as model TWS (mTWS). The mTWS differs in several aspects from GRACE-derived TWS: Soil moisture layers in ESMs have a depth that can vary widely between just a few and up to tens of meters depending on the model and thus does not necessarily capture the full soil moisture content at every location. Furthermore, groundwater and surface water are not explicitly included in mTWS as these states are generally not represented in CMIP5 models. However, a certain fraction of these quantities might be implicitly included in total soil moisture as the transport to ocean and atmosphere is limited and the water balance is largely closed by most of the models (Liepert & Lo, 2013). Moreover, historical CMIP5 runs do not contain regional anthropogenic intervention other than land use changes in their setup (e.g., groundwater depletion or dam building is not represented), whereas GRACE observations include their consequences. The representation of mTWS differs from model to model due to different root depths, number of soil layers, and model physics (Huang et al., 2016). Snw also exhibits large intermodel differences in representation (Brutel-Vuilmet et al., 2013). We therefore note that mTWS of different models might not be fully compatible. After adding monthly mrso and snw for each model, we concatenate the corresponding mTWS simulations of the historical runs (1850–2005) and the RCP8.5 scenarios (2006–2100) to calculate trends for time spans that go beyond the year 2006. For those models, where more than one run is available, we calculate the ensemble mean which we regard as the most robust realization for long-term mTWS trend estimates. Afterward, the mTWS values are remapped to a common 2◦×2◦geographical grid. A bicentennial mTWS trend map (time span January 1861 to December 2099, i.e., earliest/latest common date of all models for historical/RCP8.5 experiments) is calculated from the time series of mTWS grids for each model. For each grid cell the linear trend is calculated by fitting a function 𝑓(t)=a+b·t+c·cos(𝜔t)+d·sin(𝜔t)+e·cos(2𝜔t)+𝑓·sin(2𝜔t)(2) with parameters for bias (a), linear trend (b), annual and semiannual cycle (c,d,e,f) to the time series by means of least squares adjustment. The standard deviation of the trend is estimated from the postfit residuals. Note that we exclude the glaciated regions of Greenland, Svalbard, Gulf Coast of Alaska, and Antarctica, since not all models properly represent glacier mass balance dynamics dominating TWS in those regions. JENSEN ET AL. 9811 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Figure 2. Correlations of the bicentennial mTWS trend maps for 34 CMIP5 models. In total 34 CMIP5 models provide at least one run for mrso and snw. However, as some of these 34 models are either different versions of the same model or are runs with partly identical components (land surface and/or atmosphere model), it cannot be assumed that each model produces a completely independent estimate for the mrso and snw fields (Knutti et al., 2013). In order to obtain an unbiased multimodel average mTWS trend map and a reliable conclusion about model consensus, we identify the independent models by comparing the similarity of mTWS trend maps for all models. As a measure for the similarity of two maps we use the Pearson product-moment correlation coefficient r2calculated from the vectorized maps, giving every land pixel of the 2◦×2◦grid equal weight. As trend outliers in single pixels can distort the correlation coefficient we apply a simple threshold to the mTWS trend maps, excluding absolute trend values above 23 mm/year. This is the 2𝜎boundary of the 14-year GRACE TWS trend (Figure 1), thus it is very unlikely that bicentennial trends above these threshold are realistic. The correlations of the bicentennial mTWS trend maps (after applying the 23 mm/year threshold) are calculated for all 34 models and arranged in a matrix (Figure 2). Detailed information and references for the models listed in Figure 2 are given, for example, in Flato et al. (2013) and are not reiterated here. As expected, models that use common atmosphere or land surface components exhibit a very high correlation. In order to only consider models that are independent and to justify the application of equal weight to each model result, in the remaining part of the study we use only one instance from each group of models that are highly correlated (r2>75%). In Figure 2 the models that are excluded due to this threshold are denoted in gray font and the remaining 21 models are highlighted in bold font. The criteria for choosing a specific model among highly correlated models was based on its estimated age (most recent publication), degree of specialization (most general), or spatial resolution (closest to 2◦×2◦). Generally, after excluding all but one from the highly correlated models, the correlation among trend maps from different models is very low (mean r2=10%, maximum r2=67%) and for some pairs of models it is even negative (minimum r2=−55%). This analysis demonstrates the large inhomogeneity among CMIP5 models regarding trends in mTWS. In order to further investigate model spread we define different time spans (Table 1) for which we calculate and discuss mTWS trend maps in the following. First, the 21 models that remain after excluding highly correlated models, are used to calculate a median trend map for the bicentennial time span January JENSEN ET AL. 9812 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Table 1 Notation for Different Time Spans That Are Investigated for mTWS Trends Time span Notation Jan 1861 to Dec 2099 bicentennial trend Jan 1861 to Aug 2016 historical trend Sep 2016 to Dec 2099 RCP8.5 trend Jan 1986 to Dec 2035 50a tendency Jan 1996 to Dec 2025 30a tendency Apr 2002 to Aug 2016 14a tendency 1861 to December 2099 (Figure 3a), that is, for each geographical grid cell the median of the trends of all models is determined. We use the median instead of the arithmetic unweighted mean because it is much less affected by outliers and thus can be assumed to be a more robust estimate for the trend. However, to identify nonsignificant trends in the median map (stippled regions in Figure 3a) we carry out error propagation for the arithmetic mean, because this is not straightforward for the median. Figure 3a is not affected by a model drift in mTWS, as trends from preindustrial control simulations (i.e., model runs only forced with natural, nonevolving atmospheric concentrations) of the same CMIP5 models were found to be an order of magnitude smaller and thus are negligible (not shown). According to the 21 models, the largest trends occur mainly in southern Europe and Turkey, in Central America and in the west of North America, in the north of South America and in the Himalaya region. The climatological trends derived here are in agreement with the results of a previous study (Berg et al., 2017) that focused on total soil moisture, even though significant differences are present in high latitudes since mTWS also includes snowpack. To assess the reliability of the median mTWS trends, we compute the level of consensus of the 21 models, that is, the number of models with the same bicentennial trend direction for a given grid cell (Figure 3b). The higher the consensus, the higher the certainty that the agreement is not by chance, for example, if 15 or more of 21 models agree on the sign, the probability that this is just chance is only 4% or less (Dirmeyer et al., 2013). Hence, the higher the consensus in a grid cell, the more we can trust the direction of the trend in this grid cell according to the models. In many regions high consensus corresponds to large trends and vice versa. However, this is not valid everywhere, meaning that also the sign of small trends can be represented by a majority of models (e.g., India) and inversely, there might be model disagreement about the direction of large trends (e.g., Northern Russia). For the bicentennial mTWS trend, we find 39% of the global land area to exhibit a drying (30%) or wetting trend (9%) that is supported by at least 71% (15 of 21) of the models. These findings are not free of uncertainties as the consensus map (Figure 3b) might be affected by systematic deficits in CMIP5 models, such as in particular the lack of groundwater storage in aquifers at different depth and thus very different residence times (Pokhrel et al., 2014). To investigate if mTWS trends as calculated for the bicentennial time span are in principle already detectable in observational records available today, we compute (in addition to the bicentennial time span) mTWS trends for a historical time span January 1861 to August 2016 (until the end of the GRACE time span; Figure 4a). For comparison, also the mTWS trends for the RCP8.5 time span September 2016 to December 2099 are displayed (Figure 4b). Overall, we find a similar pattern for the historical and the RCP8.5 trend (pattern correlation of 55%), though the historical trend has a much smaller magnitude (only about 20% of RCP8.5). Furthermore, the portion of land area where the median trends are not significant (stippled areas, 95% confidence level) is larger for the historical time span than for the RCP8.5 time span. However, in 73% of the land area the historical trend is already significant and in 68% it is in agreement with the RCP8.5 trend map. In high-consensus regions (agreement of bicentennial trend sign in ≥71% of the models, Figure 3b) to which we restrict the analysis in section 5 and 6, the area of agreement between significant historical and RCP8.5 trends is 92%. This indicates that in most regions the current trends are set to continue in the same direction and even increase in the future, thereby suggesting that the processes shaping the climate change footprint on TWS are already acting today. The consensus among the CMIP5 models is generally lower for the historical time span (Figure 4c) than for the RCP8.5 time span (Figure 4d), which is related to the fact that stronger trends generally imply higher consensus and RCP8.5 is the scenario with the strongest climate change signal. The patterns of the consensus maps are similar for all three time spans (bicentennial, historical, and RCP8.5), thus we infer that regions of large model agreement are largely independent from the selected time span (for centennial trends). 4. Influence of Observation Time Span From Figures 3 and 4 it can be concluded that for centennial time spans a temporally stable pattern of drying and wetting trends exists in the models. However, we cannot expect to readily find these trend patterns in JENSEN ET AL. 9813 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Figure 3. (a) Median of bicentennial mTWS trend maps from 21 CMIP5 models (without Greenland, Svalbard, Gulf Coast of Alaska, and Antarctica). Stippling indicates regions where the mean trend is not significantly different from zero (𝛼=0.05). (b) Consensus map for bicentennial mTWS trends from 21 CMIP5 models. Red colors indicate that ≥#models agree on a negative (i.e., drying) trend, blue colors indicate that ≥#models agree on a positive (i.e., wetting) trend. a short time period of only 14 years for which GRACE observations are available. For short time periods, interannual variations may be dominating the trend estimation in many regions of the world. To estimate the influence of the observation time span on the expected agreement with the bicentennial trend, we perform two model studies using tendency maps for different time spans calculated from the CMIP5 models. In the first model study we investigate after which time span long-term climatic trends in mTWS might be clearly distinguished from interannual variations. In the second model study we estimate the degree to which even after long time spans the observed trends might still be in disagreement with the long-term climatic trend. In contrast to the other sections of the paper, where we rely on the ensemble means, for these model studies we only use one individual run (r1i1p1) per model in order to preserve interannual variability. This is important as natural variations would largely average out by calculating ensemble means. By using CMIP5 model output for simulating differently long observation time spans, we presume that individual model runs represent natural variability realistically in terms of relative magnitude, frequency, and duration. JENSEN ET AL. 9814 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Figure 4. (top) Median of mTWS trend maps from 21 CMIP5 models for (a) historical (January 1861 to August 2016) and (b) RCP8.5 (September 2016 to December 2099) time span. Stippling indicates regions where the mean trend is not significantly different from zero (𝛼=0.05). Please note the different color scales in (a) and (b). (bottom) Consensus maps for bicentennial mTWS trends from 21 CMIP5 models for (c) historical and (d) RCP8.5 time span. For the first study we fit trends in a least squares sense for time spans of different lengths ranging from 14 to 100 years in steps of 5 years with the center year 2010. Examples for tendency maps obtained for the 50a, 30a, and 14a time periods are given in Figure 5. The median tendency maps for all 18 time spans are each correlated to the bicentennial median trend map (Figure 5a). For the 14a observation period the global correlation is only 23%, but with increasing time span it asymptotically approaches 100% (blue curve in Figure 5a). After the 30a time span the global correlation is 57% which is the same order of similarity that we find for the historical and RCP8.5 time spans (55%). Thus we conclude that around 30 years of TWS observations would be the minimum time to globally obtain a TWS trend comparable to long-term model results. However, even though the agreement between trend patterns might be low at 14a globally, this might not be the case locally, for instance, when only considering regions that exhibit strong model agreement. When calculating the correlation of the 14a tendency and the bicentennial trend only for grid cells with a model consensus of ≥71%, the correlation coefficient increases to 39% (red curve in Figure 5a), when additionally excluding nonsignificant grid cells, it increases to 52% (yellow curve in Figure 5a). In this model study we evaluate the (global) spatial pattern correlation which only contains limited information about the agreement of trends for individual grid cells. This means that though this experiment brings out what to expect from the similarity of the spatial patterns, it does not provide the likelihood for a local mTWS tendency computed from a certain time span to actually match the bicentennial trend in that grid cell. As we are interested in regions where 14a GRACE TWS tendencies agree with bicentennial mTWS model trends and want to rate the results with respect to what to expect from this short time span, we perform a second model study: For each of the 21 CMIP5 models we cut 22 slices of 14a mTWS data with a distance of 5 years (centered around the year 1970) and estimate 22 14a tendencies. For each grid cell the fraction of tendencies that agree or disagree (in terms of sign) with the bicentennial mTWS trend from that particular model is calculated. Subsequently, the global mean of all fractions and all models is computed. This procedure is repeated for different time spans from 1 to 100 years in steps of 5 years (Figure 6). According to the models the probability that a 14a tendency is in agreement with the long-term trend is on average 53%, which is slightly better than random chance. Even after a century there is still a chance of 27% that an individual tendency does not match the bicentennial trend even though the global pattern correlation is already high with 87%. This indicates that there is natural variability in the models even over long time periods of 100 years and more, which Laepple and Huybers (2014) found to be caused by sea surface temperature JENSEN ET AL. 9815 Journal of Geophysical Research: Atmospheres 10.1029/2018JD029989 Figure 5. (a) Correlation of the mTWS tendency maps for different time spans (center year 2010) with the bicentennial mTWS trend map. (b–d) Median of mTWS tendency maps from 21 CMIP5 models for (b) 50a time span, (c) 30a time span, and (d) 14a time span. Each time span is centered around the year 2010. 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