Global hydrological models: a review

Abstract

Global hydrological models (GHMs) have effectively become a separate research field in the last two decades. The paper reviews and compares 12 known global modelling efforts since 1989, the year the first GHM was published. Structure, strengths and weaknesses of individual models are examined, and the objectives of model development and their initial applications are documented. Issues such as model uncertainty, data scarcity, integration with remote sensing data and spatial resolution are discussed.

Editor D. Koutsoyiannis

Résumé

Les modèles hydrologiques globaux (MHG) sont en fait devenus un domaine de recherche distinct au cours des deux dernières décennies. Cet article examine et compare 12 démarches de modélisation globale connues depuis 1989, année de publication du premier MHG. La structure, les forces et faiblesses de chaque modèle ont été examinées et les objectifs de développement des modèles et leurs premières applications ont été décrits. Des questions telles que l’incertitude du modèle, la rareté des données, l’intégration des données de télédétection et la résolution spatiale ont été discutées.

Key words:

• global hydrological models
• grids
• remote sensing
• hydrology

Mots clefs:

• modèles hydrologiques globaux
• maillages
• télédétection
• hydrologie

INTRODUCTION

The continuing debate on climate change (e.g. Kundzewicz and Stakhiv 2010, Huard 2011) and other global drivers of change highlights the interdependence of various earth systems and the need for integration of those systems into global simulation models (Wilby 2010). There is an impact on regional and, hence, global climate, from changes in soil moisture and terrestrial evapotranspiration (Munro et al. 1998, Koster et al. 2003, Koster et al. 2004, Seneviratne et al. 2010, Dirmeyer 2011), and hence river discharge which in turn impacts on sea characteristics (Milly et al. 2010). Land-use changes upstream affect the hydrology and water quality thousands of miles downstream (Freeman et al. 2007). Global hydrology is closely linked with the nutrient cycle (cause of eutrophication of coastal zones) (Foley et al. 2005, Rabalais et al. 2009, Fekete et al. 2010) and the carbon cycle (impacting on the climate). The changes in these global cycles eventually have social and economic implications. Due to globalization, virtual water trade, for example, has become an important factor of both the global water cycle and food security (Islam et al. 2006). While the scientific community has long been aware of, and has dealt with, impacts of climate on hydrology, the feedback has only recently started to receive attention. All this leads to the notion of the ‘global water system’ (Alcamo et al. 2008, Alcamo 2009), in which the global water flow is connected to other systems through physical relationships, economics and institutions. This system is further complicated by the interference from humans through water storage and withdrawals (Rost et al. 2008b).

Models that attempt to simulate global hydrology and associated processes are similar to numerous stand-alone hydrological models and to hydrological components of the general circulation models (GCMs). However, they differ in the detail of description of processes, parameter estimation approaches, time scales, and spatial resolution of input data and simulations (Haddeland et al. 2011). The stand-alone models are usually applied at the basin scale, or a smaller catchment scale, and have many parameters that need to be calibrated or estimated regionally. Examples of such models include the Soil and Water Assessment Tool (SWAT; Neitsch et al. 2002), the Hydrological Simulation Program-Fortran (HSPF; Bicknell et al. 1997) and the Hydrologiska Byråns Vattenbalansavdelning (HBV; Lindström et al. 1997). Some of these models can, in principle, be applied at the global scale, but, due to severe information constraints, this never happens in practice. The hydrological models that are a part of GCMs are usually land surface schemes (LSSs) that simulate the energy balance at soil, atmosphere and vegetation interfaces at finer time scales (often hours), and do not have a flow routing component. Examples of such models include the Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1986), the Simple Biosphere Model (SiB; Sellers et al. 1986) and the Joint UK Land Environment Simulator (JULES; http://www.jchmr.org/jules/index.html).

The actual global hydrological models (GHMs) have few calibratable parameters and are calibrated either at eco-region, climatic-region or large river basin scales (Vörösmarty et al. 1989, Döll et al. 2003, Widén-Nilsson et al. 2007). Some models, such as the Water Balance Model – Water Transport Model (WBM-WTM; Vörösmarty et al. 1998), are not calibrated per se but have an adjustment factor to tune them. The model Water – Global Analysis and Prognosis (WaterGAP; Alcamo et al. 2003, Döll et al. 2003) is a combination of calibration and tuning. It is first calibrated with a single parameter against streamflow. The basins that underestimate or overestimate flows are then tuned by two adjustment factors, runoff and discharge correction (Döll et al. 2003). The spatial resolution of GHMs is defined by the resolution of available global climate input data. GHMs are relatively new and have emerged in the last two decades. Lately, there has been increasing activity in this field and a concerted effort is evolving (Lawford et al. 2004, Döll et al. 2008). Also, GHMs are becoming more complex and resolute as more functionality is added to them and finer global spatial datasets are becoming available. Issues of the sensitivity of models to varying spatial and temporal scales of input and output data, measuring modelling uncertainty and coupling GHMs with other models have become prominent (Döll et al. 2008, Voß et al. 2008).

The explosion of global data availability from satellites in the last two decades (Tang et al. 2009) has had an influence on the development of GHMs. Although some GHMs have been applied at a range of scales, they are, as a rule, built for global-scale studies. They would not be the preferred choice in basin-scale applications, due to the coarser resolution of GHMs at present, and the fact that there is a large family of hydrological models that have been designed for this purpose. However, GHMs may provide valuable spatial and temporal estimates of global water resources, and help to analyse possible projections/scenarios of changes of those estimates; GHMs have been built effectively for this purpose. Global estimates obtained through GHMs could be an improvement over those simply based on the statistical analysis of ground-based observed data, which, at a global scale, remain limited and, hence, contain a lot of uncertainty (Rodda 1995). An even greater use of GHMs is revealed when they are linked with other models, i.e. describing global economy, ecology, trade, biodiversity, energy balance, land-use change, climate change, crop growth and other development issues/components related to water (Vörösmarty et al. 2000, Islam et al. 2006, Alcamo 2009). The requirements from the GHMs depend upon the demands of such associated models.

To the best of the authors’ knowledge, a single source/compilation of GHMs does not exist. Recently, Trambauer et al. (2013) examined GHMs in the context of drought forecasting in Africa. This paper extends the discussion to the broader context of developing simulation tools for global food trade, agriculture and economy, and examines constraints and development trends of GHMs, including those of uncertainties, input data quality and integration with remote sensing data.

EXISTING GLOBAL HYDROLOGICAL MODELS—DESCRIPTION

Over the last few decades, many isolated efforts were made to simulate the global hydrological cycle. A review of the existing literature suggests that there are at least 12 GHMs (or tools that can be interpreted as such) at present. Table 1 lists these GHMs in chronological order of their development and includes details of the main developers, their objectives for developing the model and some example applications. Table 2 summarizes the technical details of these models.

Table 1 Origin and known applications of existing global hydrological models.

No.	Model	Developed/maintained by	Year	Objective(s)	Applications
1	HDTM 1.0 (HydroDynamic Model) / WBMplus / WBM-WTM (Water Balance Model - Water Transport Model)	University of New Hampshire, USA	1989	To study global biogeochemical cycles. Linked to Terrestrial Ecosystem Model and Trace Gas Model through soil moisture and evapotranspiration	Comparison of PET methods on US watersheds—WBM (Vörösmarty et al. 1998) Using GHM in an application of isotope tracers at continental scale in hydrological modelling (Fekete et al. 2006) Calculation of variability and uncertainty in the global irrigation water demand—WBMplus (Wisser et al. 2008) Analysis of the effect of climate and hydrological alteration in hydrological cycle to study nutrient transport (Fekete et al. 2010) Using GHM to calibrate remote sensing signal to discharge (Brakenridge et al. 2012)
2	Macro-PDM (Macro Probability Distribution Model)	University of Reading, UK	1998	To build a macro-scale global model. Among the initial efforts, only one model existed before: WBM. This uses the VIC principle on a global scale	Measurement of uncertainty in an ensemble with 21 GCMs at global scale using a campus-wide computer grid (Gosling et al. 2010) Study of the impact of climate change on river flow regimes (Arnell and Gosling 2013)
3	MPI-HM (Max Planck Institute – Hydrology Model)	Max-Planck-Institut für Meteorologie (Max Planck Institute for Meteorology), Germany	1998	To define lateral flow of water from continents to oceans and to link with a GCM (ECHAM)	Validation of the weather forecasting models, European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA) and National Center for Environmental Prediction Re-Analysis (NRA) (Hagemann and Dümenil 2001)
4	GWAVA (Global Water Availability Assessment model)	Centre for Ecology & Hydrology (formerly Institute of Hydrology), UK	1999	To study progression of global water scarcity due to population increase and climate change	Estimation of water scarcity for eastern and southern Africa (Meigh et al. 1999) Measurement of the impact of climate and land-use change (Meigh and Tate 2002)
5	VIC (Variable Infiltration Capacity model)	University of Washington, Seattle, USA	2001	To improve on the previous model by incorporating two layers in soils and introducing sub-grid heterogeneity for vegetation, soil moisture storage capacity and precipitation	Estimation of global soil moisture content (Nijssen et al. 2001b) Prediction of discharge of the world’s rivers (Nijssen et al. 2001a) Evaluation of the Atmospheric Model Intercomparison Project (AMIP II) (Irannejad and Henderson-Sellers 2007)
6	LAD (Land Dynamic model)	National Oceanic and Atmospheric Administration (NOAA) / Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA	2002	To improve the energy and water balance of the older model	Illustrating an approach of land model evaluation with precipitation uncertainty (Milly and Shmakin 2002) Measurement of the inter-annual variation in river discharges (Shmakin et al. 2002)
7	WaterGAP (Water – Global Analysis and Prognosis model)	University of Kassel; University of Frankfurt, Germany	2003	To combine water availability and water use based on structural and technological changes at global scale	Identification of regions in which water resources have higher sensitivity to global change—critical regions (Alcamo and Henrichs 2002) Global modelling of irrigation water requirements (Döll and Siebert 2002) Calculation of water availability indicators (Döll et al. 2003) Integration of Gravity Recovery and Climate Experiment (GRACE) data into global hydrological models (Werth et al. 2009) Analysis of river flow alterations due to water withdrawals and reservoirs (Döll et al. 2009) Simulation of continental water storage variation at the global scale (Werth and Güntner 2010) Computing the water mass variations to calculate load-induced deformation of the Earth’s crust (Fritsche et al. 2012) Studying the impact of groundwater and surface water withdrawals on water storage (Döll et al. 2012) Studying large-scale variation characteristics of global groundwater (Jin and Feng 2013) Calculating seasonal water storage variations as impacted by water abstractions (Döll et al. 2014)
8	PCR-GLOBWB (PCRaster GLOBal Water Balance model)	Utrecht University, The Netherlands	2004	To add advance routine for grid heterogeneity for surface runoff, inter-flow and groundwater; also added routine for lateral transport of heat by water	Measurement of the skill of seasonal predictability of river discharge for different European rivers (Bierkens and van Beek 2009) Analysis of the depletion of global groundwater resources (Wada et al. 2010) Modelling methane (CH4) emissions of boreal and arctic wetlands (Petrescu et al. 2010) Analysis of future global runoff changes (Sperna Weilanda et al. 2011) Calculation of global water stress (van Beek et al. 2011, Wada et al. 2011) Study of the impact of human abstraction of surface water and groundwater on streamflow (de Graaf et al. 2014)
9	LPJmL (Lund-Potsdam-Jena managed Land model)	Potsdam Institute for Climate Impact Research (PIK), Germany	2007	To simulate the spatial and temporal dynamics of global vegetation, and study its impact on global hydrological and carbon cycles.	Calculation of green water flows—LPJ (Gerten et al. 2005) Measurement of global carbon fluxes and pools (Bondeau et al. 2007) Checking the uncertainty of the terrestrial carbon and water cycle at different spatial resolutions using the LPJ-Dynamic Global Vegetation Model (LPJ-DGVM) (Müller and Lucht 2007) Studying human alteration of the terrestrial water cycle through land management (Rost et al. 2008b) Calculation of agricultural green and blue water consumption (Rost et al. 2008a) Calculation of global-scale water withdrawal, allocations and consumptive use for surface water and groundwater (Wada et al. 2014)
10	WASMOD-M (Water And Snow balance MODeling system)	Department of Earth Sciences, Air, Water and Landscape Sciences, Uppsala University, Sweden	2007	To complement existing global models and to come up with a set of minimum parameters for gauged and ungauged river basins	Comparison of two flow network-response functions to evaluate the improvement in runoff routing (Gong et al. 2009) Comparison of two precipitation datasets (TRMM and WATCH Forcing Data) in southern Africa (Li et al. 2013)
11	H08 (H07)	National Institute of Environmental Studies, University of Tokyo, Japan	2008	To assess global water availability at a sub-annual time-scale	Calculation of national agriculture water withdrawals and locating water-stressed regions (Hanasaki et al. 2008b) Estimation of global virtual water flows (Hanasaki et al. 2010) Analysis of scenarios for different socio-economic conditions to calculate water availability and scarcity (Hanasaki et al. 2013)
12	ISBA-TRIP (Interactions between Soil, Biosphere, and Atmosphere – Total Runoff Integrating Pathways)	Centre National de Recherchés Météorologiques, France	2010	To measure continent-level terrestrial water storage and to use GRACE data to validate it.	Measurement of terrestrial water storage and its seasonal and inter-annual variability (Alkama et al. 2010)

Table 2 Technical features of existing global hydrological models.

No.	Model	Spatial resolution	Temporal resolution / simulation time step^1	PET	Reservoirs	Irrigation	Crop/vegetation model	Soil layers	Number of parameters
1	HDTM 1.0	0.5°	Monthly / month	PET, Korzoun et al. (1977)	Yes	Yes	Three vegetation types: forest, grassland and shrubland	Single layer till rooting depth considered	>4
2	Macro-PDM	0.5°	Daily / day	Penman, Penman-Monteith and Priestley-Taylor	No	No	Forest and grassland only	1	8
3	MPI-HM	0.5°	Daily / day	Thornthwaite formula	No	No	None	1	3
4	GWAVA	0.5° / 0.1°	Monthly / day		Yes	Yes	Trees, bushes, grass and bare soil
5	VIC	2°	Daily / day	Penman-Monteith	No	No	13 land cover + water	2–3	Original VIC (not global) (Liang et al. 1994): 22 parameters
6	LaD	1°	Daily / hour	Custom equation as part of energy balance	No	No	32 vegetation types of Matthews (1983) reduced to 10 and put into a 1° resolution global map	5
7	WaterGAP	0.5°	Monthly / day	Priestley-Taylor	Yes	Yes	16 land cover types	1	36
8	PCR-GLOBWB	0.5°	Daily / day	Penman-Monteith	Yes	No	Three categories: natural vegetation, rainfed crops and irrigated crops; these are further subdivided into tall and short vegetation	3 layers: 2 upper soil layers and one groundwater layer
9	LPJmL	0.5°	Daily / day	Priestley-Taylor	Yes	Yes	Natural vegetation: nine plant functional types; agricultural vegetation: 12 crop functional types	2
10	WASMOD-M	0.5°	Monthly / month	Custom equation based on air temperature and relative humidity	No	No	None	1	4–6 (based on presence of snow)
11	H08 (H07)	1° / 0.5°	Daily / 3-h	Custom equation based on energy balance	Yes	Yes	Crop growth model used similar to SWIM	1
12	ISBA-TRIP	1°	Daily / ISBA: 20 min, TRIP: 1 h	Custom equation based on water balance in the soil layer	No	No	Coordination of Information on the Environment (CORINE)	3	2 (primary) and 14 secondary that can be derived from primary

Note: Empty boxes imply missing information.

¹Simulation time step is the smallest time unit at which the model operates, whereas temporal resolution is the time interval at which the output is provided.

An initial effort in the development of GHMs was made by Vörösmarty et al. (1989), who developed the Water Balance Model (WBM) and linked it with the Water Transport Model (WTM). The WBM predicts soil moisture (SM), evapotranspiration (ET) and surface runoff at grid level, and the WTM routes the discharge generated in the grid cell through the channel using a linear reservoir model (Vörösmarty et al. 1989). The field capacity (FC) and, hence, water availability are linked to the vegetation type and soil at grid-level resolution. The WBM-WTM model relies on a narrow range of parameters based on those published in the literature and then iterates annually until a dynamic steady state is achieved (i.e. soil moisture, ET, runoff and snowmelt come within an acceptable level of difference for successive runs). It has been modified over the years to include irrigation and reservoirs, accounting for the irrigated and non-irrigated fraction, reservoir operations (WBM_plus class), effect of permafrost (Pan-Arctic Water Balance Model (PWBM) and HydroDynamic Model (HDTM 1.0), along with the multi-layer soil moisture routine (HDTM 1.0; http://www.wsag.unh.edu/wbm.html). The parameter values in the WBM are assigned a priori and are not calibrated. In the Macro Probability Distribution Model (Macro-PDM; Arnell 1999), developed in 1998, streamflow is simulated as direct runoff and delayed runoff. A similar vegetation classification as in WBM is used, but the soil moisture FC is statistically distributed within a grid to account for sub-grid variations. The ratio between ET and potential evapotranspiration (PET) is described by a linear function of average soil moisture in a grid cell. In this model, the values of parameters are set from a literature review or previous model applications. Six out of 13 parameters are globally uniform. Around the same time, the Max-Planck Institute (MPI) in Germany developed a model that coupled the European Centre Hamburg Model (ECHAM) GCM with a hydrological discharge (HD) model (Hagemann and Dümenil 1997). This model is known as the Max Planck Institute-Hydrology Model (MPI-HM). In this model, vegetation in each grid cell is partitioned based on vegetation maps, as developed by Matthews (1983), and the fraction of such vegetation dependent on the available water content in the root zone (decreases below 40% of FC). The streamflow and surface runoff are simulated as a cascade of linear reservoirs, whereas the baseflow is described by a single reservoir. The Global Water Availability Assessment model (GWAVA; Meigh et al. 1999), developed to examine issues of water scarcity, also used a probability distribution to simulate soil moisture storage. This model includes water demand based on population, livestock, irrigation schemes and industrial water use. It uses four simplified land cover categories (trees, bushes, grass and bare soil). Groundwater is first explicitly calculated by using potential yield from a well and estimating borehole density in each grid. It is then compared to groundwater recharge calculated through the surface flow model and a conservative value of the two, based on aquifer classification, is used.

All the above models treat soil as a single layer. The Variable Infiltration Capacity model (VIC; Nijssen et al. 2001b), developed in 2001, considers two layers of soil and includes sub-grid variability in land surface vegetation, soil moisture storage capacity and precipitation. The VIC model can run either as an energy and water balance model or just as a water balance model. Multiple land covers (13) including bare soil are considered in the VIC model. It also accounts for the top vegetation cover. The second layer is modelled as a nonlinear storage. Snow is simulated by a single layer energy and mass balance model. A separate river routing model is used. The Land Dynamics model (LaD; Milly and Shmakin 2002) was developed to improve an older water and energy balance model by Manabe (1969) by adding sensible heat storage on land, groundwater storage and stomata resistance. Grid cells are treated as either glaciated or non-glaciated. Water storage is considered in snow, glacier ice, root zone and groundwater. Runoff is generated after the soil reaches its water-holding capacity, and is then passed through a groundwater reservoir (with some residence time) before becoming streamflow. The PCRaster GLOBal Water Balance model (PCR-GLOBWB; van Beek and Bierkens 2008), developed in 2004, broke up the soil layers into three storage ‘buckets’, each contributing to the streamflow in the form of surface runoff, interflow and baseflow, respectively. The surface vegetation is simplified into three categories—natural, rainfed and irrigated—which are further classified as short (retrieving moisture from the top soil layer) or tall vegetation (retrieving moisture from the bottom layer). Evapotranspiration is broken up into transpiration by vegetation and evaporation from bare soil.

The Water – Global Analysis and Prognosis model (WaterGAP; Alcamo et al. 2003, Döll et al. 2003) and the Lund-Potsdam-Jena managed Land model (LPJmL; Bondeau et al. 2007) are two GHMs that were developed in Germany during the past decade. While the WaterGAP model puts more emphasis, at least at present, on water demand simulation, the LPJmL model is more detailed in vegetation and crop simulations. The WaterGAP model is made up of two modules—the GHM per se and the global water use model. The latter incorporates human water consumption (in the form of domestic, manufacturing, thermal power production, livestock and irrigation use). The GHM model considers soil as a single layer and calculates the vertical and lateral water balance within each grid. Surface and subsurface runoff are transported as a fast response, and the baseflow (i.e. contribution from groundwater) is transported as a slow response. The lateral movement of runoff is described through multiple storages representing local and global lakes, reservoirs, wetlands and streams. The LPJmL model was developed by adding a hydrology component to an existing dynamic global vegetation model (DGVM). The vegetation routine of the model simulates photosynthesis, evapotranspiration, plant respiration and the carbon cycle. It allows for nine natural plant types and 12 crop types (both rainfed and irrigated). There can be one stand of natural vegetation and multiple stands of crop types within each grid. Some of the inputs for the vegetation are dynamically generated within the model. The hydrological routine calculates water balance for each stand of the grid and each grid flows into another via a river routing module (Rost et al. 2008a). The evapotranspiration is broken up into productive water consumption (plant transpiration) and non-productive consumption (interception loss and evaporation). Soil storage is represented by two ‘buckets’.

The Water And Snow balance MODeling system (WASMOD-M; Widén-Nilsson et al. 2007), originating from WASMOD (Xu 2002), uses a minimum number (4–6) of calibrating parameters. WASMOD-M runs at monthly time steps and separates runoff into fast and slow components for each grid. It considers rain, snowmelt, snow accumulation and evapotranspiration for each grid within its routine. The parameters in the model are regionalized to simplify model application. It has six parameters, of which five can be calibrated and one is fixed (Widén-Nilsson 2007). The H08 model (Hanasaki et al. 2008a, 2008b) is a more detailed and integrated system, made up of six modules—land surface hydrology, river routing, crop growth, reservoir operation, environmental flow requirements and anthropogenic water withdrawal. The land-surface hydrological module calculates both the hydrology balance and energy balance. It uses the ‘leaky-bucket’ concept to model soil moisture (Hanasaki et al. 2008a). The river routing module uses the Total Runoff Integrating Pathways model (TRIP; (Oki and Sud 1998). The TRIP model is a network of integrated pathways providing information on lateral water movement over land. The crop routine uses heat unit theory (Barnard 1948, Phillips 1950) and is based on the Soil and Water Integrated Model (SWIM; Krysanova et al. 1998). The basis of the heat unit theory is that each plant has its own range of temperature within which it grows. SWIM is a river basin model developed by the Potsdam Institute for Climate Impact Research (PIK), Germany, to simulate hydrology, sediments, nutrients and carbon movement, along with plant growth and yield. Nineteen crop types are used and large reservoirs (with a storage capacity greater than 10⁹ m³) are incorporated.

The ISBA-TRIP model (Alkama et al. 2010) was developed by combining two models—the modified land surface model by Noilhan and Planton (1989) and the surface runoff pathway network from TRIP, by Oki and Sud (1998). The heterogeneity within a grid is described by using a tile approach that divides a grid into a series of sub-grid patches based on land use and soil properties; partial grid saturation is also accounted for. The model calculates the surface energy and water budget for each grid with the soil represented by three layers. TRIP routes the daily discharge simulated by ISBA into streamflow.

COMPARISION OF MODEL FEATURES

All GHMs run in a grid format. In most GHMs, the spatial resolution is 0.5 degrees (just over 3100 km² per grid cell at the Equator). The grid format and resolution are dictated by the availability of global meteorological data and computational resources. The gridded format makes it convenient to manipulate other available input data, which are also usually available in grid format (e.g. originating from remote sensing (RS) data). With faster computational devices and availability of finer resolution input data, higher resolution GHMs are being developed, such as a 5-min version of WaterGAP (http://www.massentransporte.de/index.php?id=303), 6-min version of PCR-GLOBWB (called PCR-GLOBWB 2.0: http://www.globalhydrology.nl/models/pcr-globwb-2-0/) and the latest version of WBM_plus that can run at a range of resolutions dictated by the underlying gridded network (45″, 90″, 3′, 5′, 6′, 15′ – B. Fekete, City University of New York (CUNY), pers. comm.).

Most of the GHMs have a temporal resolution of 1 day despite the fact that the available input data normally have a monthly time step. Historical data covering the full 20th century, for example, are only available at a monthly temporal resolution, which necessitates statistical downscaling into a daily temporal scale. With improvement of meteorological reanalysis data, the models have started using more of these as inputs. The fourth generation of ECMWF reanalysis (ERA) daily datasets (from 1979 to date) are being developed; ERA data have already been used in some GHMs (Wada et al. 2010) and in model intercomparison studies (Weedon et al. 2011).

Only five models—WBM_plus, WaterGAP, PCR-GLOBWB, LPJmL and H08—explicitly consider reservoir storage. Out of these, PCR-GLOBWB does not simulate irrigation. Some models consider soil layers as a single storage unit (Macro-PDM, MPI-HM, WASMOD-M, H08 and WaterGAP), whereas others consider multiple storage layers (PCR-GLOBWB: two layers, VIC: two layers, LPJmL: two layers, ISBA-TRIP: three layers, and LaD: five layers).

Only H08 and LPJmL have an explicit crop growth model. Although all the models can handle changes in meteorological data due to climate change (such as precipitation and ET due to changes in temperature), only the models that have crop growth and/or vegetation models can deal with the impact on plant physiology due to changes in carbon dioxide concentration and increase in temperature. From that perspective, LPJmL and H08 may be well suited to evaluate the impact of climate change scenarios on crop yield (and hence on hydrology). The LPJmL modle simulates natural vegetation (along with agriculture), and the proportion of different vegetation classes in each grid is based on relative advantage in terms of light, water, space and other environmental factors (Gerten 2013).

A few models, such as VIC, LaD, WaterGAP and LPJmL, have a detailed land-use classification. Other models have used a simplified classification, for example, WBM-WTM uses only three categories (i.e. forest, grassland and shrubland); and the newer version, WBM_plus, accounts for multiple categories (e.g. Wisser et al. 2010 handle four categories). The model can simulate up to 32 of the vegetation classes of the Terrestrial Ecosystem model (Melillo et al. 1993). The current version of WBM can read the parameters related to the vegetation directly as input from an external source and, hence, the model can simulate as many classes as formed by the different parameter combinations (B. Fekete, pers. comm.). Macro-PDM uses only forest and grassland categories for land use, whereas PCR-GLOBWB uses three categories: natural vegetation, rainfed crops and irrigated crops, which are further divided into short and tall vegetation (to simulate ET from different layers of the soil profile).

Models also differ in terms of how they account for energy balance, sub-grid effects and soil stratification. About half of the models reviewed (MPI-HM, PCR-GLOBWB, VIC, LaD, H08 and ISBA-TRIP) have their own energy balance module. Some models treat a grid as homogenous with respect to infiltration, climate data and vegetation, while others account for sub-grid effects to describe heterogeneity within a grid cell (VIC, ISBA-TRIP). Some consider root-zone depth as the height of one of the soil layers (such as ISBA-TRIP), whereas others have a fixed depth of the first layer (PCR-GLOBWB: 0.3 m, LPJmL: 0.5 m).

The main output of all the models is streamflow, which is derived from partitioning precipitation into evapotranspiration, soil moisture, fast and slow flow (although the terms used may be different, e.g. surface runoff, lateral flow and baseflow). The VIC, WaterGAP, LPJmL and H08 models also look at crop water requirements. These are the models that also have a detailed land-use classification (Table 2). All models provide output at grid level (mostly at 0.5° resolution at present). These grid-level outputs are aggregated to river basin scale, based on the number of grids that fall within a river basin boundary. None of the models uses an incremental drainage sub-basin discretization directly.

Global hydrological models are often developed to support simulation of certain phenomena which are not always hydrology per se (Table 1). Consequently, they have certain areas of preference. For example, LPJmL has a vegetation model along with the hydrological model. The LaD, ISBA-TRIP and VIC models include hydrology, but also focus on energy balance, and the H08 model focuses on crop growth and energy balance. WaterGAP, WBM_plus (irrigation only) and GWAVA also consider water use. Although the use of any PET equation in a hydrological model may be seen as an energy balance, in this study, unless the model has an energy balance built into its framework, it is not considered. None of the models reviewed incorporates land-use change models, i.e. that simulate changes in land use due to development (for a review of land-use change models, see Agarwal et al. 2002). Also, the GHMs do not consider the impact of market forces or economics (in terms of human interventions) on hydrology.

ISSUES AND TRENDS IN GHM DEVELOPMENT

Attempts are being made to coordinate the development of GHMs. The Global Water System Project (GWSP), along with the Integrated Project Water and Global Change (WATCH) (http://www.eu-watch.org/templates/dispatcher.asp?page_id=25222705), invited teams developing GHMs to participate in a model intercomparison project (http://www.eu-watch.org/nl/25222736-Global_Modelling.html). Seven different GHMs were forced with the same set of climatic inputs, and their results were compared at both a continental scale and the scale of major river basins. The study concluded that there was limited agreement between models on global water projections. For example, the range of predicted global runoff from different models was about 45% of the mean simulated runoff (Haddeland 2011). Similarly, Gudmundsson et al. (2012) applied an ensemble of nine large-scale hydrological models in Europe and found a large spread in model accuracy including high variation in the low runoff percentile.

Another 4-year initiative, the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP; http://www.pik-potsdam.de/research/climate-impacts-and-vulnerabilities/research/rd2-cross-cutting-activities/isi-mip) is currently underway. Several GHMs, including VIC, H08, WaterGAP, MacPDM, WBM, MPI-HM and PCR-GLOBWB, along with other global impact models, are included in this project, where new climatic and socio-economic scenarios developed as part of the Fifth Assessment Report of the IPCC (Intergovernmental Panel on Climate Change) are used as forcing, and their possible impact on different sectors (such as agriculture, water, ecosystems, infrastructure and health) are being evaluated.

Focusing on uncertainties

In the WATCH study, although, at the global level, the deviation between the models of the simulated total annual flow was not very large—a coefficient of variation (CV) of about 0.09 (Voß et al. 2008), there were larger deviations in colder (polar, without Antarctica: CV ≈ 1.0) and drier regions (Africa and Australia: CV ≈ 0.41). Also, despite the fact that there was a closer match in the total flow, there was a very wide variation in the soil moisture (CV ≈ 0.33) and evaporation products (CV ≈ 0.27) suggesting the importance of looking into structural differences in the models. While some models simulated an increase in total global freshwater flow for the period 2071–2100, others showed a reduction (Voß et al. 2008), the range being from −40 to +30%. The study showed high uncertainty in the intermediate processes. Wada et al. (2013) used seven GHMs to assess the impact of climate change on future irrigation water demand. They concluded that high uncertainty, until at least mid-century, is due to GHMs rather than to GCMs.

Uncertainties in GHMs have still not been sufficiently analysed or emphasized. Most of the time the validity of model outputs of GHMs is asserted by comparing the results with the output of other GHMs. Sometimes the assessment is made based on anecdotal terms, for example, “... on the whole the selected parameters produce a reasonably good representation of monthly hydrological regimes across Europe.” (Arnell 1999); or “… we see that WBM runoff is ‘well behaved’ in relation to the precipitation data used ...” (Fekete et al. 2002). There are four types of uncertainties in hydrological modelling: those associated with model inputs, model structure, parameter values and observed data. Palmer et al. (2008) analysed the uncertainties associated with WaterGAP. Based on this and other analyses (such as Kaspar 2004), it is concluded that the uncertainties due to inputs are higher than the parameter uncertainties. Using ‘goodness’ of the model calibration as an indicator, they found total uncertainty in streamflow to be medium in 43% of large river basins, lower in 32% and higher in 25%. Widén-Nilsson (2007) compared WASMOD-M and five other global models and found a high volume error (i.e. error in the river runoff) in all the models, although the regions of high error were not consistent. The volume error mostly ranged from −65 to 50%. Biemans et al. (2009) found a multiplier effect of precipitation uncertainty in predicting streamflow at the global scale. An average of 30% uncertainty in the precipitation data, when used as an input with LPJmL, resulted in an average 90% uncertainty in streamflow.

One of the reasons for high uncertainty in model inputs is data scarcity, or inconsistency in the input data (Arnell 1999, Döll and Siebert 2002, McMillan et al. 2012, Kauffeldt et al. 2013, Mulligan 2013, Müller Schmied et al. 2014). Data scarcity is greater in developing regions (Schuol and Abbaspour 2006), and is due to well-known problems of weak observational infrastructure, gaps due to missing data, and unwillingness to share data. Also, low quality ‘disinformative data’ (Kauffeldt et al. 2013) often provide a false sense of data richness, effectively being responsible for a large part of model uncertainty.

Integrating with remote sensing

Continuously progressing remote sensing (RS) technologies can help reduce uncertainties associated with inputs and observations. The future of GHMs is to a large degree associated with the development of RS technologies and public availability of RS data. Most of the GHMs are already using some satellite products, such as solar radiation, digital elevation models (DEMs), land use, etc., as their input data. Although (at least at present) ground-based measurements are assumed or perceived to be more accurate than satellite-based measurements, it is obviously impossible to cover the entire world with the former. All GHMs (other than WaterGAP) are tuned by first converting flow from the grids into streamflow and then validating against the observed data from, generally, large gauged rivers. For example, Macro-PDM uses 31 large river basins for validation, MPI-HM uses 35, and PCR-GLOBWB uses annual streamflow time series from 99 large river basins. VIC, LaD, WaterGAP (which is also calibrated), GWAVA, WASMOD-M, H08 and ISBA-TRIP use 26, 82, 724, 96, 663, 37 and 33 river basins, respectively. However, the number of basins used for validation/calibration for the same model may vary based on the study, e.g. Döll et al. (2003) use 724 calibration stations for WaterGAP, whereas Hunger and Döll (2008) use 1235 stations for the same model. Clearly, such limited tuning/calibration introduces uncertainty in model outputs. There are also inaccuracies inherent in the land-based streamflow measurements. Also, as most of the large rivers have been highly modified (Döll et al. 2009), it is imperative for future GHM modelling activities to include river alterations and water withdrawals (van Beek et al. 2011). In addition, there has been a significant decrease in the number of river gauging stations worldwide since the early 1990s, and the existing gauging network monitors streamflow from only approximately 50% of the land mass (Fekete and Vörösmarty 2007).

The future of hydrological modelling also rests in using satellite data (directly or derived) for calibration. Significant progress has been made in satellite-based data acquisition in the last decade. With the launch of the European Space Agency’s (ESA) Soil Moisture and Ocean Salinity (SMOS) satellite in November 2009, the first global soil moisture maps have become available. The satellite uses large microwaves (L-band) to measure ‘brightness temperature’ through which surface soil moisture is calculated every three days. The data are being validated by a network of ground-based measurements (International Soil Moisture Network), coordinated by the Global Energy and Water Cycle Experiment (GEWEX) in cooperation with the Group on Earth Observations (GEO) and the Committee on Earth Observation Satellites (CEOS) and ESA (http://www.esa.int/esaLP/LPsmos.html). There is a lot of promise in composite systems comprising active and passive microwave technologies (Das et al. 2011). The US National Aeronautics and Space Administration (NASA) launched a combined radiometer and synthetic aperture radar operating at L-band (1.20–1.41 GHz) in January 2015 (SMAP; http://smap.jpl.nasa.gov/mission/). Although there are still limitations in terms of measuring soil moisture beyond a certain depth from the surface, RS soil moisture can still be used as a boundary condition for equations of soil moisture dynamics within a model. Satellite-derived evapotranspiration products are also becoming easily available (such as the MODerate-resolution Imaging Spectro-radiometer (MODIS) product, MOD 16 – (http://modis.gsfc.nasa.gov/data/dataprod/dataproducts.php?MOD_NUMBER=16). An algorithm based on a modified Penman-Monteith equation was used to develop MOD16 (Mu et al. 2007). There are known attempts to use satellite-based data to derive ET and calibrate a model against it (although not a GHM) for a 46 000-km²catchment in southern India (Immerzeel and Droogers 2008). The authors used the Surface Energy Balance Algorithm for Land (SEBAL) to calculate ET from satellite data. Such satellite-derived ET estimates are in themselves quite complex and parameter-intensive, and may hardly be regarded as observations. However, such attempts point to possible alternatives for calibration of GHMs in the future, when and if satellite-based ET estimates become more accurate and direct. Similarly, satellite-based leaf area index (LAI) products are now available. They include MOD15 from MODIS, ECOCLIMAP (http://www.cnrm.meteo.fr/gmme/PROJETS/ECOCLIMAP/page_ecoclimap.htm), GLOBCARBON (http://www.fao.org/gtos/tcopjs4.html) and CYCLOPES (http://postel.obs-mip.fr/?CYCLOPES-Project,82; Garrigues et al. 2008).

Since the launch of the GRACE satellite, research has focused on measuring terrestrial storage (Strassberg et al. 2009, Syed et al. 2009, Alkama et al. 2010, Tang et al. 2010, Döll et al. 2014) and to incorporate it into hydrology (Werth et al. 2009). GRACE, however, has a very coarse spatial and temporal resolution combined with the uncertainties in partitioning the GRACE signal. GRACE observes the combined mass changes in the atmosphere, surface waters (rivers, lakes, reservoirs, floodplains and wetlands), soil and the groundwater. Hence, the only way to measure any of the above independently requires some estimates of all the other components. Also, GRACE only provides infrequent (approx. 10 days) snapshots of changes in continental water storage, where the actual storage conditions have to be known at the time of the satellite’s pass over. Its spatial resolution is approx. 200 km (i.e. 2 × 2° at the Equator). Overall, at present, the uncertainties associated with the GRACE data are on a par with, or even higher than, the uncertainties in GHMs for small to medium size river basins, which GRACE measurement can aim to reduce (Alkama et al. 2010). However, it may be possible that further development of GRACE or related technologies would reduce such uncertainties. The handicap of coarser resolution is being resolved, to some extent, with the Gravity field and steady-state Ocean Circulation Explorer (GOCE) mission (2009–2013), which provides data related to Earth’s gravity at 100-km resolution (http://www.esa.int/SPECIALS/GOCE/index.html).

Improving precipitation inputs

The performance of any hydrological model depends on the quality and scale of available input data, especially precipitation. Traditional (raingauge) precipitation data remain limited worldwide. Radar technology, although an improvement over raingauge data, still has limitations due to obstructions and range. Satellites can provide uninterrupted, global meteorological data collection and hence help, in principle, to improve the primary input to hydrological models. Both the geostationary satellites, observing visible (VIS) and infrared (IR) radiation, and the low Earth Orbiting (LEO) satellites using microwave (MW) technology (along with VIS and IR), provide precipitation information. They have their distinct strengths and weaknesses (Kidd et al. 2009). While VIS and IR data are available at higher resolution, the precipitation derived from it is dependent on the relationship between cloud top temperature and rainfall, i.e. ‘cold-cloud duration’ methods (Kidd et al. 2009), but the precipitation estimates are indirect measurements and prone to errors. Passive MW technology addresses these issues, but their existing spatial and temporal resolution is still a hindrance to effective use in hydrological modelling. Precipitation data derived from passive MW techniques still need to be calibrated. Various efforts are being made to combine the strengths of the LEO and geostationary satellites to develop more reliable precipitation datasets (Kuligowski 2002). The use of satellite-based precipitation data in hydrological modelling is overall still in its early stages and has not yet led to significant improvements in the outputs of GHMs as compared to radar- or ground-based precipitation data (Tobin and Bennett 2009). Meteorological reanalysis data can help fill the gap for missing long-term historical rainfall data. Li et al. (2013) compared hydrological output in southern African river basins by forcing a regional hydrological model with rainfall derived from two different sources—satellite-based Tropical Rainfall Measuring Mission (TRMM) and reanalysis of ERA-40. According to their analysis, streamflow simulations were better when the model was forced with rainfall (after bias correction) from reanalysis compared to satellite-based rainfall.

Improving spatial resolution

Wood et al. (2011) argue that the uncertainties associated with existing GHMs are too high and their current usual spatial resolution at the scale of 50-km grids (considering 0.5° grids) is too coarse to simulate “water cycle science questions” effectively (Wood et al. 2011). The authors make a case for developing future GHMs at “hyper-resolution” scale, i.e. at the scale of 1 km globally and 100 m at the continental level. They believe that the computational constraints that prevented such studies earlier no longer exist due to easy access to parallel-clustered computing resources. Gosling et al. (2010) used Campus Grid to run multiple GCMs with climate change data. They were able to reduce the computation time from 750 h to 9 h on a single-processer personal computer. Also, high resolution RS data are becoming common. Such high-resolution models would capture heterogeneity and would better represent surface–subsurface and land–atmosphere interactions. Although the idea of increasing the resolution of GHMs is feasible with increasing computer power, it is important to also consider that many local issues may be better addressed by using basin-specific models rather than GHMs. Increasing complexity and resolution of GHMs may require more spatially diverse observational data at the ground level (which is already a big problem). One question that can be raised is that of the scope of application of GHMs: with increasing spatial resolution, is it the ultimate intention to address local water resources problems by means of GHMs?

Modelling at a finer spatial resolution opens yet another possibility for running GHMs at the small basin scale (instead of grids). Some countries have a very detailed system of basin delineation. For example, South Africa evaluates and monitors its water resources on a so-called ‘quaternary’ sub-basin scale. Quaternary sub-basins are incremental drainage subdivisions, ‘flowing’ one into another and covering the entire country. There are almost 2000 of these sub-basins with an area ranging from some 60 km² (in more humid regions of the country) to some 2000 km² (in arid areas). The recent trend is to address water management problems at the scale of even finer subdivisions, the ‘quineries’. Countries like India, have not yet established such detailed drainage subdivisions and for many large-scale assessments only 19 major drainage areas are used. These drainage areas range from 22 000 km² (Sabarmati River basin) to 860 000 km² (Ganga River basin) (Amarasinghe et al. 2005). In the United States, watershed delineation is carried out in detail, with the entire country delineated to six levels. This is publicly available as the Watershed Boundary Dataset (http://www.ncgc.nrcs.usda.gov/products/datasets/watershed/index.html). The six levels are classified as regions (level 0), sub-regions (level 1), basins (level 2), sub-basins (level 3), watersheds (level 4) and sub-watersheds (level 5). The sixth-level drainage delineation has a drainage area of up to 160 km². Such fine-resolution river basin delineations are still restricted to a few countries, but the recent trend is to address water management problems at the scale of even finer subdivisions. The advantage of this could be closer integration of such models with the country-specific national drainage divisions.

CONCLUSIONS

The last two decades have seen substantial effort in the development of GHMs. The models are based on either energy balance or hydrological balance, or both. The complexities of the models vary based on their objectives and applications. Structural issues, such as the number of soil layers, number of land-use classifications, crop growth models, irrigation water applications and reservoir storage, are dealt with differently in the various models. A comparative study of seven models has shown structural differences in the models and little agreement in the projections made by them. The structural differences also relate to inclusion of anthropogenic disturbances, inclusion of vegetation growth models and the type of bucket model used (leaky bucket versus non-leaky bucket).

Most of the models use satellite-based or Climatic Research Unit (CRU) weather input data, available in a 0.5-degree gridded format. This also defines the spatial resolution of the models. Most of the GHMs run on a daily temporal scale. However, for the long-term assessment of the impacts of climate change and impact on global water and food trade, a monthly temporal scale is sufficient and may simplify the calibration process.

The models also need to move to finer spatial resolution to address some of the global societal issues, but they should not aim to replace more locally focused modelling efforts. Progress in GHMs is also dependent on improved access to observed hydrometeorological data, particularly in developing countries. Access to more observed data could expand the ‘calibrated area’ of the globe, thus also improving the overall accuracy of global hydrological modelling efforts and providing more accurate, although simulated, time series of various components of the hydrological cycle. This may be seen as a possible interim (or even long-term) solution for ground-based ‘data-poor’ areas, where ground observations will probably never materialize to required levels, while RS data still require decades to ensure that time series are of a reasonable length. Hence, simulations will always be needed in such areas. Therefore, improving the accuracy of GHMs by all possible means, may be effectively seen as a form of international cooperation and economic/humanitarian assistance. However, countries have to be prepared to cooperate by allowing better access to national archives of observed hydro-meteorological data.

It is suggested that, to improve the GHMs, there should be a closer integration of satellite-based products and models that would help reduce the internal uncertainties within the models.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Acknowledgements

The authors gratefully acknowledge comments provided by Robyn Johnston (IWMI, Colombo) in reviewing the manuscript. Comments provided by two anonymous reviewers are also acknowledged.

Additional information

Funding

This study was funded by the CGIAR Research Program on Water, Land and Ecosystems (WLE).