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 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 Coupled Model Intercomparison 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 hydrological response to external forcings and also to study inter-model differences or biases.
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 (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 and Floter, 2011).
Rainfall is generated by a multitude of different systems (e.g. midlatitude
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 cycle (i.e. high precipitation in the Intertropical Convergence Zone; ITCZ) seen in complex CGCMs can be found in models
with intermediate complexity such as the CLIMBER-2 (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, idealised models such as the
The simple Globally Resolved Energy Balance (GREB) model was originally
developed to simulate the globally resolved surface temperature and in
particular its response to a
This paper introduces a simple hydrological cycle model for the GREB model. 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. We improve three separate parameterisations in the model: precipitation, evaporation and the circulation of water vapour. The model is 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).
The following section presents the data sets used, the original GREB model and the methods. In Sect. 3, the new parameterisations of the hydrological cycle model in the GREB model are described. Section 4 presents three different sensitivity experiments to test the new hydrological cycle model. Finally, we give a discussion and summary of the results.
The GREB model is a three-layer (land and ocean surface, atmosphere and deep
ocean) global climate model on a
Thus, the GREB model is conceptually very different from the CGCM simulations in the Coupled Model Intercomparison Project phase 5 (CMIP5), as atmospheric circulations, cloud cover and changes to soil moisture are not simulated but prescribed as external boundary conditions in the model. This leads to some parts of the hydrological cycle not being simulated in the GREB hydrological cycle model (i.e. runoff). The effect of ocean circulation on the atmosphere is represented only through the sea surface temperature but is not explicitly simulated. Additionally, the GREB 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 a single year.
The original GREB model used climatological fields from the National
Centers for Environmental Prediction (NCEP) reanalysis
data from 1950 to 2008 (Kalnay et al., 1996) for surface temperature,
GREB mean state boundary conditions and reference climatologies:
topography
The observed hydrological cycle in terms of the annual mean and its seasonal cycle (DJF minus JJA) for precipitation, evaporation and moisture circulation are shown in Figs. 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 (Figs. 2c and 3c) is dominated by large-scale convergence and divergence zones over the oceans and their seasonal shift.
The decomposition of the hydrological cycle into its parts:
precipitation in mm day
As Fig. 2 but for the seasonal cycle (DJF–JJA). The decomposition
of the hydrological cycle into its parts: precipitation in
mm day
Model simulations, pre-industrial (pi-Control) and Representative
Concentration Pathways 8.5 (RCP8.5) from the CMIP5 database are used for
comparison (Taylor et al., 2012). All data sets are regridded to a horizontal
resolution of
List of CMIP5 models.
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,
Variables of the GREB model.
The saturation water vapour pressure is calculated after (Dommenget and
Floter, 2011; James, 1995)
The seasonally varying flux correction term,
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 outlines the development of each of the three models and discusses how the change in the reference climatologies from NCEP to ERA-Interim has affected the model. All variables are summarised in Table 2.
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 (Figs. 2
and 3). It has, however, substantial differences from the observed
precipitation, as it cannot capture the high rainfall in the ITCZ and the
enhanced precipitation over the midlatitude storm track regions, and misses
many aspects of the seasonal cycle. The root mean square 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
Precipitation
Annual mean precipitation for four development steps of the GREB
precipitation parameterisation
Relative humidity (rq) is widely used in climate models as a predictor for precipitation (Petoukhov et al., 1999, 2005; Wang and Myask, 2000; Weaver et al., 2001). In the GREB model, it increases precipitation mainly over humid regions such as the Amazon Basin (Fig. 5c) and amplifies the seasonal cycle (Fig. 5d). The overall pattern of rainfall with high precipitation in the tropics and decreasing towards higher latitudes is not changed. Including rq gives some moderate improvement relative to the original GREB model (Fig. 4a comparing marker “0” to marker “b”).
The mean vertical air motion (
The GREB precipitation model without
In summary, the new GREB precipitation model is significantly better than the
original model. The RMSE is reduced by 0.65 to 0.81 mm day
Annual mean flux
corrections of specific humidity for the original GREB model
As Fig. 6 but for the seasonal cycle (DJF minus JJA). Flux
corrections of specific humidity for the original GREB model
In the original GREB model, evaporation is calculated using a widely used bulk formula approach (see Eq. 1 in Richter and 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 (Fig. 2e). The seasonal cycle (Fig. 3e) is, however, very different from observed, and the land–sea differences are too strong.
For the new evaporation model, we retained the original bulk formula approach
and included a few minor changes by considering land–sea differences,
revised wind (
The skin temperature difference approximated by
The wind magnitudes (
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 Figs. 4b, e and 8.
Annual mean evaporation for three development steps of the GREB
evaporation parameterisation
Fitting the evaporation efficiency
The original GREB model was evaporating too much on the annual mean (see Fig. 2e) especially over the equatorial Pacific and Atlantic. The new hydrological cycle model parameterisation largely decreases evaporation over these regions and the flux corrections are reduced over the globe in the annual mean (Fig. 6e, f). The correlation of the annual mean experiences the largest changes from changing the reference climatology (Fig. 4b).
In the seasonal cycle, each included variable improves the simulation of evaporation in the GREB model (Fig. 4e). The seasonal cycle of flux corrections caused by evaporation in the original GREB model is 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 Equator (Fig. 7e). The improved evaporation seasonal cycle mainly removes this distinct pattern over the oceans and reduces flux corrections over most land areas. (Fig. 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 (Figs. 2h, 3h).
The original GREB model transport of moisture was very weak and had little agreement with observations (Figs. 2f and 3f). Atmospheric transport of moisture in GREB (Eq. 4) is controlled by diffusion and advection with mean winds. This model considered a divergence free two-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
This new model has now fairly realistic transport in the annual mean and the seasonal cycle (Figs. 2i and 3i), with clear moisture transport out of regions with diverging flow (e.g. in the subtropics off the coast of Peru) and into converging zones (e.g. ITCZ). The new parameterisation of convergence also reduces the flux corrections in the annual mean and the seasonal cycle (Figs. 6g, h and 7g, h).
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 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
We estimate the effect that the change in reference climatologies will 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 does not lead to major improvements in the representation of the hydrological cycle in the GREB model, but it increases the correlation of precipitation, evaporation and circulation and reduces the RMSE (Fig. S1 in the Supplement). 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).
We now test the new hydrological model in a series of three different sensitivity experiments. The discussion focuses 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.
The response of the hydrological cycle to seasonal changes is a good test for evaluating the skill of the hydrological cycle 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 is identical to the observations; see Fig. 9a.
Annual cycle of specific humidity with seasonal varying flux
corrections
The El Niño response of the hydrological cycle in observations
for precipitation
To illustrate that the seasonal cycle is not a feature of the seasonally varying flux corrections, we changed the flux corrections to an annual mean value for the original GREB model (Fig. 9b, e) and for the new GREB model (Fig. 9c, f). 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 (Fig. 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 (Fig. 9b). For 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 (Fig. 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.
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
The new GREB response in precipitation shows a strong similarity with the
observed changes (Fig. 10g). There is a shift of rainfall from the Maritime
Continent towards the NINO3.4 region (5
The observed evaporation response to ENSO events in the tropical Pacific somewhat counteracts the precipitation response, as we observe mostly decreased evaporation over regions with enhanced precipitation and increased evaporation over regions with reduced precipitation (Fig. 10a and b). These evaporation changes are mostly caused by changes in winds, with decreased evaporation over regions where 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 simulations have only a weak spatial correlation (0.3) with the observed evaporation changes overall.
The observed strong changes in the circulation of atmospheric humidity
(Fig. 10c) is mostly due to changes in the convergence of moisture (e.g.
In summary, the new GREB model does simulate the precipitation and circulation response to ENSO conditions fairly well, whereas the original GREB model has very little skill, illustrating the significant improvement of the new GREB model over the original GREB model. However, the evaporation response in both models is not as well simulated as the precipitation and circulation responses.
Response of the hydrological cycle to an RCP8.5 forcing in the
CMIP5 ensemble mean for precipitation
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 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 Fig. 11a. This pattern is normally referred to as the wet-get-wetter paradigm (Held and Soden, 2006). Although this approach has been questioned by more recent studies (Chadwick et al., 2013), it is still a good first-order approach to the changes in the global hydrological cycle, although changes over land might be muted or even reversed (He and Soden, 2016).
To evaluate the GREB hydrological cycle model independent of the other GREB
model components, such as the
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 Fig. 11d). This is mainly due to an increase in the saturation water vapour pressure of about 7 % per degree of warming (Clausius–Clapeyron). The original GREB precipitation response pattern is not correlated to the CMIP5 ensemble mean response pattern (Fig. 12a), suggesting that local differences in the precipitation response are very different from those in the CMIP simulations.
RCP8.5 response of CMIP5 models (blue), original GREB (0) and
improved GREB (red
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 (Fig. 12a and c). This is strongly related to the moisture 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 Fig. 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 and Xie, 2008).
In this study, we introduced the newly developed 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 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 evaporation model is still a limiting factor in the GREB model.
We applied the new hydrological cycle model to a number of sensitivity studies, which 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, due to the much-improved transport of moisture. Finally, the response to global warming now shows a precipitation response 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 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 affect the hydrological cycle. The new GREB hydrological cycle model is therefore a good tool in helping to conceptually understand the hydrological cycle and its response to global warming or other external forcings. It will further help in understanding CMIP model biases in the simulation of the hydrological cycle.
The GREB model source code used in this paper as well as
the data used to run the model are available on GitHub:
The supplement related to this article is available online at:
CS developed the new hydrological cycle model code and together with DD designed the sensitivity experiments. DD provided the original GREB model code and NL performed preliminary tests with precipitation.
The authors declare that they have no conflict of interest.
This study was supported by the Australian Research Council (ARC), with additional support coming via the ARC Centre of Excellence in Climate System Science and the ARC Centre of Excellence in Climate Extremes.
We would like to thank the three anonymous referees for their constructive and helpful comments which led to a substantial improvement in the manuscript. Edited by: Min-Hui Lo Reviewed by: three anonymous referees