A Hydrological Cycle Model for the Globally Resolved Energy Balance Model ( GREB ) v 1 . 0

This study describes the development of the hydrological cycle model for the Globally Resolved Energy Balance (GREB) model. Starting from a rudimentary hydrological cycle model included in the GREB model, we develop three new models: precipitation, evaporation and horizontal transport of water vapour. Precipitation is modelled based on the actual 10 simulated specific and relative humidity in GREB and the prescribed boundary condition of vertical velocity. The evaporation bulk formula is slightly refined by considering differences in the sensitivity to winds between land and oceans, and by improving the estimates of the wind magnitudes. Horizontal transport of water vapour is improved by approximating moisture convergence by vertical velocity. The new parameterisations are fitted against the Global Precipitation Climatology Project (GPCP) data set and reanalysis data sets (ERA-Interim). The new hydrological cycle model is evaluated against the 15 Coupled Model Inter-comparison Project phase 5 (CMIP5) model simulations, reduction in correction terms and by three different sensitivity experiments (Annual Cycle, El Niño Southern Oscillation and Climate Change). The skill of the hydrological cycle model in the GREB model is now within the range of more complex CMIP5 Coupled General Circulation Models and capable of simulating key features of the climate system within the range of uncertainty of CMIP5 model simulations. The results illustrate that the new GREB model’s hydrological cycle is a useful model to study the climate’s 20 hydrological response to external forcings and also to study inter-model differences or biases.

only needed as a zero order estimate to model the latent heat in the energy balance and the atmospheric water vapour levels. ' We changed the word on page 1 Line 9 to 'rudimentary' to not cause confusion with order of numerical convergence or order of accuracy.
6. Page 2 Line 6: Authors may consider mentioning the computational efficiency of idealized model here.
Response: We changed Page 2 Line 6-7 to: 'Because of their simplicity, they help to develop hypotheses about the processes involved and they can be run fast. The GREB numerical code computes one model year in a few seconds and on a standard personal computer. It therefore is a relatively fast tool, which allows conducting sensitivity studies to external forcing within minutes to hours (Dommenget & Floter, 2011)' 7. Page 2 Line 23: I suggest re-organizing the paragraphs that describe the GREB model. For example, the modl layer configuration and resolution in Page 3 Line 10 can be introduced before the description of the NCEP climatological fields used in the original GREB model. This may make introduction of the GREB model framework smoother.
Response: We moved the paragraph describing the GREB model to the beginning of chapter 2

Page 2 Lines 25-26: Any specific reason generating topography from an atmospheric model? Why not using ETOPO dataset?
Response: We adopted the approach form the original GREB model. 9. Page 2 Line 29: I suggest providing brief explanation for the reason of changing dataset here and directing further details to section 3.4. Also, the NCEP reanalysis datasets are used during 1950-2008, whereas the ERA-Interim reanalysis data during 1979-2015. Therefore, long-term mean climatology values may be different. What is the results using the NCEP data during 1979-2015? 1. I believe, however, that the authors need to explain better how this model can be used. While I realize that this is a technical paper describing the model, I think there needs to be some justification as to why we need this model in the first place.
Response: We plan to apply the model for studying biases in CMIP models. This could be done by replacing boundary conditions through CMIP boundary conditions. We revised the manuscript to better highlight the use of the GREB model. For example we added the following to page 12 line 11 (also to address RC1.2): 'A very recent study by Yang et al., 2018 links circulation biases in CMIP models to biases in precipitation and moisture. Forcing GREB with the circulation of CMIP models could shed more light how discrepancies in circulation between CMIP models effect the hydrological cycle in the GREB model.' 2. It is nice that the new version of GREB is more successful in reproducing certain aspects of the hydrological cycle. On the other hand, given that the new version has more fitting parameters, is this really surprising? Using more parameters gives you a better fit but also carries the risk of overfitting. In particular, the model might be too constrained by present day climate to be useful for climate change projection because basic features of the present climate, such as the width of the Hadley circulation or the position of the ITCZ, may change.
Response: We addressed the problem of overfitting by different approaches: first we tested the development of the model in step-wise building up the complexity (see section 3). Secondly, we did a number of response experiments that test the model's skill beyond the information used to fit the parameters. For this we did three tests: Seasonal cycle, El Nino and climate change. In all three the new model showed skills in simulating changes in the hydrological cycle that would not have been achieved by overfitting the model. We added some additional information in the introduction of Section 4 to better highlight this problem.
3. Another way the model could be used is for understanding the climate change response of more complex models. For this purpose, it would seem that GREB's mixture of basic principles (e.g. energy balance), ad-hoc parameterization (e.g. standard deviation of omega), and fitting to observations (e.g. mean omega) does not lend itself to interpretation any more than model output itself.
Response: We agree that the mixture of basic principles and ad-hoc parameterisations helps understanding the climate change response of more complex models (i.e. their biases). The boundary conditions of GREB could for example be replaced with climatologies of CMIP models (i.e. replacing horizontal winds from ERA-Interim with horizontal winds from one CMIP model). By replacing only one or all boundary conditions would help to gain insight where changes in RCPscenarios come from or where biases in the hydrological cycle originate from. This is indeed what we think could be a useful application of this GREB model. We added the following to page 12 line 11 (also to address RC1.2 & RC2.0): 'A very recent study by (Yang et al., 2018) links circulation biases in CMIP models to biases in precipitation and moisture. Forcing GREB with the circulation of CMIP models could shed more light how discrepancies in circulation between CMIP models effect the hydrological cycle in the GREB model.' 3. section 3.3 What causes f to be 2.5 rather than 1.0? Could there be an error in the calculation? Is this mismatch horizontally uniform?
Response: There are several sources of uncertainties: • Response: U_star is the absolute wind climatology explained in Table 2. We introduced Table 2 before any equation is mentioned in section 2. models: precipitation, evaporation and horizontal transport of water vapour. Precipitation is modelled based on the actual 10 simulated specific and relative humidity in GREB and the prescribed boundary condition of vertical velocity. The evaporation bulk formula is slightly refined by considering differences in the sensitivity to winds between land and oceans, and by improving the estimates of the wind magnitudes. Horizontal transport of water vapour is improved by approximating moisture convergence by vertical velocity. The new parameterisations are fitted against the Global Precipitation Climatology Project (GPCP) data set and reanalysis data sets (ERA-Interim). The new hydrological cycle model is evaluated against the 15 Coupled Model Inter-comparison Project phase 5 (CMIP5) model simulations, reduction in correction terms and by three different sensitivity experiments (Annual Cycle, El Niño Southern Oscillation and Climate Change). The skill of the hydrological cycle model in the GREB model is now within the range of more complex CMIP5 Coupled General Circulation Models and capable of simulating key features of the climate system within the range of uncertainty of CMIP5 model simulations. The results illustrate that the new GREB model's hydrological cycle is a useful model to study the climate's 20 hydrological response to external forcings and also to study inter-model differences or biases.

Introduction
One topic in climate change that deserves urgent attention is the changing pattern of the hydrological cycle (Donat et al., 2016). Changes of rainfall have direct impact on the environment and on human health (Dai, 2011;Parry et al., 2004;Patz et al., 2005). The projections on how rainfall is changing are primarily based on Coupled General Circulation Models 25 (CGCMs). CGCMs evaluated by the Intergovernmental Panel on Climate Change (IPCC) for the fifth assessment report are among the most complex simulations of the climate system. However, it is far from trivial to understand even simple aspects of the climate system as several processes interact with each other (Dommenget & Floter, 2011).
Rainfall is generated by a multitude of different systems (e.g. mid-latitude cyclones, tropical convection), which makes it one of the most complex processes in the climate system to model and thus to forecast. Yet many aspects of the hydrological 30 cycle (i.e. high precipitation in the inner tropical convergence zone (ITCZ)) seen in complex CGCMs can be found in  (Petoukhov et al., 1999), the 'UVic earth system climate model' (Weaver et al., 2001) or the simple atmosphere-ocean-sea-ice model developed by Wang and Myask (2000).
Additionally, idealized models like the omega and humidity based model by Pendergrass and Gerber (2016) or the simple enhanced advection model by Chadwick et al. (2016) are capable of representing many aspects of the climate change response seen in complex CGCMs. Simplified climate models and energy balance considerations, are capable of explaining 5 the large-scale features of the climate system and climate change (e.g. arctic amplification and land-sea contrast (Dommenget & Floter, 2011;Izumi et al., 2015). They provide a framework to conceptually understand the hydrological response to climate change. Because of their simplicity, they help to develop hypotheses about the processes involved. The GREB code computes about one model year per second on a standard personal computer. It therefore is a relatively fast tool, which allows conducting sensitivity studies to external forcing within minutes to hours (Dommenget & Floter, 2011). 10 This paper will present a simple hydrological cycle model for the Globally Resolved Energy Balance (GREB) model (Dommenget & Floter, 2011). The aim of this hydrological cycle model is to present a simple and fast model for studies of the large-scale climate in precipitation, its response to climate variability (e.g. El Niño or climate change) and external forcings. The GREB model was originally developed to simulate the globally resolved surface temperature and in particular its response to a CO 2 forcing. The hydrological cycle in the GREB model was only needed as a zero order estimate to model 15 the latent heat in the energy balance and the atmospheric water vapour levels. We now aim for a representation of the hydrological cycle that will allow the study the hydrological cycle in the GREB model by itself. We will improve three separate parameterisations in the model: precipitation, evaporation and the circulation of water vapour. The model will be based on the dynamical variables (surface temperature, atmospheric temperature and humidity) in the GREB model and on the boundary conditions of the GREB model (horizontal and vertical winds). 20 This paper is organised as follows, the following section will present the data sets used, the original GREB model and the methods. In Section 3 the new parameterisations of the hydrological cycle model in the GREB model are described. Section 4, will present three different sensitivity experiments to test the new hydrological cycle model. Finally, we give a discussion and summary of the results.

Data and Methods 25
The GREB model is a three layer (surface, atmosphere and deep ocean) global climate model on a 3.75 x 3.75 horizontal latitude-longitude grid. The GREB model simulates the thermal (long-wave) and solar (short-wave) radiation, heat transport in the atmosphere by isotropic diffusion and advection with the mean winds, the hydrological cycle (evaporation, precipitation and water vapour transport), a simple ice/snow albedo feedback and heat uptake in the sub-surface ocean. The tendency equations of the model (i.e. tendency equation of specific humidity) are solved with a time step of 12 hours. For the 30 atmospheric transport equations, a shorter time step of 0.5 hours is used. This is necessary for the model to remain numerically stable. The daily cycle of incoming solar radiation is not resolved, instead the 24 hours mean incoming solar radiation is used. The tendency equation of surface temperature, deep ocean temperature and specific humidity are flux corrected towards reanalysis data. The wind and cloud cover fields are seasonally prescribed boundary conditions. Thus, the GREB model is conceptually very different from the CGCM simulations in CMIP5, as atmospheric circulations and cloud cover are not simulated but prescribed as external boundary conditions in the model. The effect of ocean circulation on the atmosphere is represented only through the sea surface temperature, but is not explicitly simulated. Additionally, the GREB 5 model has no internal variability, as atmospheric fluid dynamics (e.g. weather systems) are not explicitly simulated. Subsequently, the model will converge to its equilibrium points (all tendency equations converge to zero), if all boundary conditions are constant. The control climate or response to forcings can therefore be estimated from one single year. The original GREB model used climatological fields from the NCEP reanalysis data from 1950 to 2008 (Kalnay et al., 1996) for surface temperature, T surf , specific humidity and horizontal winds. The cloud climatology is taken from the International 10 Satellite Cloud Climatology Project (Rossow & Schiffer, 1991). The ocean mixed layer depth is taken from Lorbacher et al. (2006). Topographic data is taken from the ECHAM5 atmosphere model (Roeckner et al., 2003). For more details refer to Dommenget and Floter (2011). For the development of the new GREB hydrological cycle model we replaced the NCEP reanalysis boundary conditions for T surf , specific humidity and horizontal winds by using ERA-Interim reanalysis data from 1979 to 2015 (Dee et al., 2011). ERA-Interim reanalysis has a higher accuracy than NCEP and a better agreement with 15 observations (Liu et al., 2017). The reasoning for the changed data sets is further explained in section 3.4. Precipitation observations are taken from the Global Precipitation Climatology Project (GPCP) (Adler et al., 2003). The climatological boundary conditions and constraints for the GREB model are summarised in Figure 1. In the following we will refer to these datasets as observations.
The observed hydrological cycle in terms of the annual mean and its seasonal cycle for precipitation, evaporation and 20 moisture circulation are shown in Figures 2 and 3. The global pattern of precipitation is marked by the ITCZ, its seasonal cycle and by the storm tracks of the midlatitudes. The evaporation is strongest over subtropical oceans and has a complex seasonal cycle with generally more evaporation in the warm season over land. The horizontal moisture transport (Figures 2c and 3c) is dominated by large scale convergence and divergence zones over the oceans and their seasonal shift.
Model simulations, pre-industrial (pi-Control) and representative concentration pathway 8.5 (RCP8.5), from the Coupled 25 Model Inter-comparison Project phase 5 (CMIP5) database are used for comparison (Taylor et al., 2012). All datasets are regridded to a horizontal resolution of 3.75 x 3.75 to match the GREB model grid. See Table 1 for a complete list of models used.
The original GREB hydrological cycle model, which is the starting point for this study, is shortly presented below. All variables and parameters are listed and explained in Table 2. The precipitation is proportional to the specific humidity 30 with Eq. (1), which corresponds to an autoregressive model with a decorrelation (recirculation) time of about 14 days (Dommenget & Floter, 2011). Evaporation, !" %/+ , in the original GREB model is calculated using an extended bulk formula: Deleted: Table 1 Deleted: The GREB model is a three layer (surface, atmosphere and deep ocean) global climate model on a 3.75 x 3.75 horizontal 50 latitude-longitude grid. GREB simulates the thermal (long-wave) and solar (short-wave) radiation, heat transport in the atmosphere by isotropic diffusion and advection with the mean winds, the hydrological cycle (evaporation, precipitation and water vapour transport), a simple ice/snow albedo feedback and heat uptake in the 55 sub-surface ocean. The model main time step is 12hrs and the daily cycle of incoming solar radiation is not resolved (e.g. 24hrs mean incoming solar radiation). The tendency equation of surface temperature, deep ocean temperature and specific humidity are flux corrected towards reanalysis data. The wind and cloud cover field are 60 seasonally prescribed boundary conditions. Thus, the GREB model is conceptually very different from the CGCM simulations in CMIP5, as atmospheric and the oceanic circulations are not simulated.
The saturation water vapour pressure is calculated after (Dommenget & Floter, 2011;James, 1995): 5 Together, this leads to the complete tendency equation of specific humidity in GREB with the diffusion term c ⋅ d e " +'$ , the advection term 4 ⋅ d" +'$ and the flux correction term !" &<$$%&7 . The simulated annual 10 mean and seasonal cycle for precipitation, evaporation and mean horizontal moisture transport are shown in Figures 2 and 3 for the original GREB model as discussed above. The diffusion term is only one fifth of the magnitude of the advection term in global average (not shown) but is more important in some locations and therefore not ignored in the GREB model. The original GREB model simulated some of the main features of the regional differences in the precipitation and evaporation, but many important details are missing (e.g. ITCZ, subtropical dry regions or extra-tropical storm tracks). However, 15 horizontal moisture transport is not simulated well by the original GREB model.
The seasonally varying flux correction term, !" &<$$%&7 , is calculated as the residual between the tendencies without flux corrections and observed tendencies: This effectively corrects the GREB model to have a climatological specific humidity as observed. The flux correction term 20 !" &<$$%&7 can help to evaluate the improvements in the hydrological cycle model. The better the model the smaller the correction term should be in Eq. (4). We can therefore split the flux correction into three diagnostic terms With each term on the RHS representing the fraction of the flux corrections attributed to precipitation, evaporation and circulation biases, respectively. Each term is estimated as the difference between the observed and the GREB model 25 tendencies of the humidity resulting from precipitation, evaporation and circulation biases: with the GREB model tendencies of the humidity resulting from circulation, ∆" &'$&8=Mlmnj , defined as: 30 The observed humidity tendencies resulting from circulation, ∆" &'$&8=Mlmnj , are defined by the residual of the total humidity tendency minus the precipitation and evaporation tendencies. By construction, all three flux correction terms (evaporation, precipitation and circulation) sum up to the total flux correction term.

Hydrological Cycle Model Development 5
The development of the new hydrological cycle model of the GREB model is based on the existing zero-order hydrological cycle model of the GREB model. The following section will outline the development of each of the three models and discuss how the change in the reference climatologies from NCEP to ERA-interim has affected the model. All variables are summarised in Table 2. 10

Precipitation
The original GREB precipitation model captures some large-scale aspects of the mean and seasonal cycle of observed precipitation, such as more precipitation in the tropics and during warm seasons over land (Figures 2 and 3). It has however, substantial differences from the observed precipitation, as it cannot capture the high rainfall in the ITCZ, the enhanced precipitation over the midlatitudes storm track regions and misses many aspects of the seasonal cycle. The root-mean-square 15 error for the annual mean of the original GREB model precipitation parameterisation is 1.46 mm/day.
The new parameterisation of precipitation in the GREB model is assumed to be proportional to q air , as in the original GREB model. We further assume that relative humidity, )", and upward air motion, u, increase rainfall. The latter is assumed to be a function of the mean and the standard deviation of the daily mean variation, u v%+w and u ;7q , respectively. The new precipitation parameterisation is: 20 Δ" #$%&'# = ) #$%&'# • " +'$ • 2 $? • )" + 2 y • u v%+w + 2 y;7q • u ;7q 11 The model parameters, ) #$%&'# , 2 $? , 2 y and 2 y;7q are fitted to minimise the RMSE between observations and GREB Relative humidity ()") is widely used in climate models as a predictor for precipitation (Petoukhov et al., 2005;Petoukhov et al., 1999;Wang & Myask, 2000;Weaver et al., 2001). In the GREB model it increases precipitation mainly over humid 30 regions like the Amazons basin (Figure 5c and amplifies the seasonal cycle (Figure 5d). The overall pattern of rainfall with high precipitation in the tropics and decreasing towards higher latitudes is not changed. Including )" gives some moderate improvement relative to the original GREB model (Figure 4a comparing marker '0' to marker 'b').
The mean vertical air motion (u v%+w ) provides a substantial improvement of the precipitation model (Figures 4a and d comparing marker '0' to 'c'). Ascending air masses in the ITCZ lead to increased precipitation, whereas descending air masses (i.e. in the subtropics) supress precipitation. It creates a sharper and more realistic gradient in precipitation than the 5 original GREB model (compare Figures 3d & 5e). With adding u v%+w , GREB is in the range of uncertainty of more complex CMIP5 models in the annual mean and the seasonal cycle (Figures 4a and d).
The GREB precipitation model without u ;7q has still fairly weak mean precipitation in the midlatitudes storm track regions (compare Figures 5g and 2g) and has a weak seasonal cycle with the wrong sign in these regions as well (compare Figures   5h and 3g). The transient pressure systems in these regions lead to large vertical motions (u) on shorter, daily time scales 10 that result into large precipitation, but have a near zero u v%+w . Thus, to capture the precipitation in regions with strong variability in u, but weak u v%+w , we include u ;7q . This mainly enhances rainfall in the mid-and high latitudes (Figures 2g   and 3g).
In summary, the new GREB precipitation model is significantly better than the original model. The RMSE is reduced by 0.65 mm/day to 0.81 mm/day in the annual mean and by 1 mm/day in the seasonal cycle. GREB precipitation now has a 15 comparable skill to more complex CGCMs and lies within the range of uncertainty of CMIP5 modelled precipitation.

Evaporation
In the original GREB model evaporation is calculated using a widely used bulk formula approach (see Eq. (1) in Richter and 25 Xie (2008). This model does capture the main aspects of the regional differences in the annual mean evaporation in GREB, with enhanced evaporation over subtropical oceans and weaker evaporation over land (Figure 2e). The seasonal cycle ( Figure 3e) is, however, very different from observed and the land-sea differences are too strong.
The skin temperature difference approximated by 2 %/+M7%v# is larger over land. It reflects that the GREB model does not simulate the daily cycle and the larger daily cycle over land leads to an effectively larger difference between the simulated 15 Ç ;8$É and the skin temperature. The offset of 1 o C over oceans is also found by Feng et al. (2018).
The wind magnitudes (4 * ) in the original GREB model were estimated on the basis of the monthly mean climatologies of the zonal and meridional wind components. This, however, is not an accurate estimate of the monthly mean wind magnitudes, as it neglects the turbulent term due to high frequent variability. In the new GREB model we estimate the monthly mean 4 * climatology based on the original 6 hourly ERA-Interim time steps. 20 We can estimate how much each of these changes improved the evaporation model by including only one of these changes and fitting the parameters of these models individually, see  (Figures 6e & f). The correlation of the annual mean experiences the largest changes from changing the reference climatology (Figure 4b).
In the seasonal cycle, each included variable improves the simulation of evaporation in the GREB model (Figure 4e). The seasonal cycle of flux corrections caused by evaporation in the original GREB model are large over land and large over oceans. There are positive flux corrections around the equator and negative flux corrections over the oceans north of the 5 equator ( Figure 7e). The improved evaporation seasonal cycle mainly removes this distinct pattern over the oceans and reduces flux corrections over most land areas. (Figures 7e & f). Overall, the new evaporation model is slightly better than in the original GREB model, but it still has substantial limitation in simulating the seasonal cycle correctly (Figures 2h & 3h).

Transport
The original GREB model transport of moisture was very weak and had little agreement with observations ( Figs. 2f and 3f). 10 Atmospheric transport of moisture in GREB (Eq. (4)) is controlled by diffusion and advection with mean winds. This model considered a divergence free 2-dimensional flow.
However, moisture convergence, as it occurs for example in the ITCZ, is important for the transport of moisture in these regions. The mean convergence by advection including the moisture convergence term is: The second term on the RHS was not considered in the original GREB model, but is now considered in the new model. The moisture convergence term can be approximated by knowing the vertical air flow assuming continuity and hydrostatic balance: with the known parameters scaling height of water vapour, å /+#<8$ , density of air, 1 +'$ , gravitational acceleration, g, and the

Boundary Conditions and Input Data
The original GREB model used the NCEP reanalysis as boundary conditions and as references for estimating the parameterisation of the model. New generations of reanalysis products have improved, because of the use of better models, better input data and better assimilation products (Dee et al., 2011). This is shown by Chen (2016) who investigated the variability and trends of the vertically integrated water vapour and found that ECMWF's ERA-Interim reanalysis has a 5 higher accuracy than NCEP and a better agreement with observations over oceans and in the tropics. NCEP underestimates water vapour in troposphere (Kishore et al., 2011). We therefore changed the reference climatology of specific humidity in the GREB model from NCEP to ERA-Interim. To get a consistent model we also take surface temperature, horizontal winds the climatology of omega and standard deviation of omega from ERA-Interim. The effect of changing the mean climatology from the years 1950-2008 to 1979-2015 is small compared to the differences between NCEP and ERA-Interim. The 10 parameters of our new GREB hydrological cycle model are then fitted against the new reference climatologies.
We estimate the effect that the change in reference climatologies have on the new GREB hydrological cycle model by fitting the parameters of the new model as described above to both the NCEP and ERA-interim reanalysis. The resulting hydrological cycle models are evaluated against observations (GPCP and ERA-interim) in Taylor diagrams for the annual mean. Changing the reference climatology doesn't lead to major improvements in the representation of the hydrological 15 cycle in the GREB model but, it increases the correlation of precipitation, evaporation and circulation and reduces the RMSE ( Figure S1 in the supplementary plots). The main improvement is in the tropics and might be related to the underestimated value of specific humidity in the tropics found by Chen (2016) and Kishore et al. (2011).

Model Verification
We now test the new hydrological model in a series of three different sensitivity experiments. The focus in the discussion 20 will be on evaluating the new model. The three examples test the hydrological cycle model response to changes in the boundary conditions. These changes are beyond those used to fit the model parameterisation and can therefore be a test of the model's skill. We will leave more in-depth analysis of some of these experiments to future studies.

Seasonal Cycle
The response of the hydrological cycle to seasonal changes is a good test for evaluating the skill of the hydrological cycle 25 model. The GREB model applies monthly flux correction terms to maintain a mean atmospheric humidity as observed. Thus, by construction the specific humidity in each calendar month in the GREB model will be identical to the observations, see  Figure 9). This annual mean flux correction value is added on every time step to the tendency equation of specific humidity (Eq. (4)).
With the new parameterisations for precipitation, evaporation and circulation the new GREB model resolves the seasonal cycle better than the original GREB model (Figure 9). The seasonal cycle of the original GREB model was too weak in the northern hemisphere when compared to observations and throughout the year the GREB model was too dry (Figure 9b). For 5 the southern hemisphere, the original GREB model was too wet. The new GREB model captures the high humidity in northern hemispheric summer and the low values in winter (Figure 9c). This makes the seasonal cycle stronger in the new GREB model and it is closer to the reference climatology. In summary, the new GREB hydrological cycle model simulates the seasonal evolution of the atmospheric humidity very well and significantly better than the original GREB model.

El Niño Southern Oscillation 10
Strong El Niño and La Niña events lead to significant changes in the tropical precipitation and associated hydrological cycle changes. Since these natural modes of climate variability are well documented they present a good test case for the GREB model.
We therefore conducted a set of sensitivity experiments with the GREB model forced by the mean conditions for strong El Niño and La Niña events. The GREB model was forced with mean composites of T surf , horizontal winds and omega from 15 observations for four El Niño (1982/83, 87/88, 91/92, 97/98) and La Niña (1988/89, 99/00, 07/08, 10/11) events. The anomalies are calculated around El Niño/La Niña from May before the peak in December to April in the following year and against the climatological mean. In the GREB model simulation they are added on top of the reference climatology. The observed anomalies in the hydrological cycle during these El Niño events are shown in Figures 10a-c. La Niña events are qualitatively the same, but with opposite signs. We clearly note strong regional changes in the precipitation in the tropical 20 Pacific that match changes in moisture transport (Figure 10c), illustrating that ENSO events mark strong regional changes in the hydrological cycle related to changes in the circulation.
The new GREB response in precipitation shows a strong similarity with the observed changes ( Figure 10g). There is a shift of rainfall from the Maritime Continent towards the NINO3.4 region (5°N to 5°S & 170°W to 120°W) over the Pacific.
However, the overall amplitude in the precipitation response is in general weaker than observed. In contrast, the original 25 GREB model has nearly no precipitation response to the ENSO forcings. This is consistent with the weak response in the circulation in the original GREB model (Figure 10f). The correlation between the GREB simulated El Niño response increases from 0.0 for the original GREB model to 0.9 with the new GREB model.
The observed evaporation response to ENSO events in the tropical Pacific is somewhat counteracting the precipitation response, as we observe mostly decreased evaporation over regions with enhanced precipitation and increased evaporation 30 over regions with reduced precipitation (Figures 10a and b). These evaporation changes are mostly caused by changes in winds, with decreased evaporation over regions were the winds have weakened (e.g. NINO3.4 region). The new GREB model somewhat captures this pattern, but shows a stronger evaporation response, which partly explains the weaker precipitation response. However, both the original and the new GREB model evaporation have only a weak spatial correlation (0.3) with the observed evaporation changes overall.
The observed strong changes in the circulation of atmospheric humidity (Figure 10c) is mostly due to changes in the convergence of moisture (e.g. omega). Since, convergence of moisture was not considered in the original GREB model, the simulated changes in the circulation are very weak in the original GREB model (Figure 10f). The new GREB model does 5 consider convergence of moisture and simulates the changes in the circulation of atmospheric humidity very similar to the observed (Figure 10i). The new circulation parameterisation in the new GREB model improves the correlation between the observed and the simulated circulation tendency from 0.3 (original GREB) to 0.95.
In summary, the new GREB model does simulate the precipitation and circulation response to ENSO conditions fairly well, whereas the original GREB model had very little skill, illustrating the significant improvement of the new GREB model over 10 the original GREB model. However, the evaporation response in both models is not as well simulated as the precipitation and circulation response.

Global Warming
The response of the hydrological cycle to global warming is one of the potential applications of the GREB model and a comparison of the GREB model with the CMIP model simulations response to global warming provides a good test. The 15 CMIP5 ensemble mean response of precipitation shows a distinct increase of rainfall in the equatorial pacific, decreases of mean rainfall in some subtropical regions (i.e. east pacific) and increases in some areas of the midlatitudes, see Figure 11a.
This pattern is normally referred to as wet-get-wetter paradigm (Held & Soden, 2006). Although this approach has been questioned by more recent studies (Chadwick et al., 2013) it still gives a good first order approach of the changes in the global hydrological cycle, although changes over land might be muted or even reversed (He & Soden, 2016). 20 To evaluate the GREB hydrological cycle model independent of the other GREB model components, such as the T surf tendencies, we force the original and new GREB model with RCP8.5 equivalent CO 2 concentrations and all other input variables for the hydrological cycle model taken from CMIP model simulations. That is, we add T surf , horizontal winds and vertical velocity RCP8.5 CMIP5 ensemble mean anomalies from the models described in Table 1 on top of the GREB control reference climatologies. In the control run the reference boundary conditions of T surf , horizontal winds and omega are 25 taken.
The precipitation response in the original GREB model is positive in all locations and it closely follows the pattern of specific humidity in the control simulation (see Eq. (1) and Figure 11d). This is mainly due to an increase in the saturation water vapour pressure of about 7% per degree of warming (Clausius-Calpeyron). The original GREB precipitation response pattern is not correlated to the CMIP5 ensemble mean response pattern (Figure 12a), suggesting that local differences in the 30 precipitation response are very different from those in the CMIP simulations. The improved GREB model response pattern is similar to the CMIP models with enhanced and reduced response roughly at similar locations, which leads to a much improved correlation (Figures 12a and c). This is strongly related to the moisture  Table 1 Deleted: . transport changes. However, the overall global mean precipitation response in the new GREB model is shifted upwards compared to the CMIP5 ensemble mean, which is related to the much stronger response in evaporation (compare Figures   11b and h). In CMIP5 models, we see a muted response of evaporation mainly due to changes in surface relative humidity and surface stability (Richter & Xie, 2008).

Summary and Discussion 5
In this study, we introduced the newly develop hydrological cycle model for the GREB model. It consists of three parts: precipitation, evaporation and transport. The development of these models started from the existing zero order hydrological cycle model of the GREB model and used physical reasoning and observations for fitting parameters.
The simulation of precipitation and transport of moisture in the new hydrological cycle model is now comparable in skill to CMIP models in terms of annual mean and the seasonal cycle of rainfall. The simulation of precipitation in the GREB model 10 is closer to the observed precipitation pattern than any CMIP5 model in both, the annual mean and the seasonal cycle. This is directly related to the fact that the GREB mode has a prescribed atmospheric circulation, which is the main driver of the global precipitation pattern.
The evaporation has only improved slightly, but does simulate the annual mean values fairly well. However, it is still different from the observed seasonal cycle and the skill is much lower than that of the CMIP model. This suggests that the 15 evaporation model is still a limiting factor in the GREB model.
We applied the new hydrological cycle model to a number of sensitivity studies, that illustrated that the new hydrological cycle model is much improved over the original GREB model. The annual cycle simulation without any correction terms is very realistic with the new model and the precipitation response to ENSO events is now very similar to the observed, owing to the much-improved transport of moisture. Finally, the response to global warming now shows a precipitation response 20 pattern that is comparable to that of the CMIP models. Again, a limiting factor in this sensitivity experiment was the evaporation response of the GREB model in comparison to that of CMIP models.
An interesting aspect of the GREB model is that it has the atmospheric circulation (vertical and horizontal winds), humidity and surface temperatures as boundary conditions. This allows the GREB model to be used as a diagnostic tool to understand how different boundary conditions affect aspects of the climate system, such as the hydrological cycle's response to global 25 warming. It may also help to study how biases in the hydrological cycle in CMIP models related to different boundary conditions from the atmosphere, such as biases in the vertical winds. A recent study by (Yang et al., 2018) links circulation biases in CMIP models to biases in precipitation and moisture. Forcing GREB with the circulation of CMIP models could shed light on how discrepancies in circulation between CMIP models effect the hydrological cycle. The new GREB hydrological cycle model is therefore a good tool in helping to conceptually understand the hydrological cycle and its 30 response to global warming or other external forcings. It will further help in understanding CMIP model biases in the simulation of the hydrological cycle.