HESS Opinions: The need for process-based evaluation of large-domain hyper-resolution models

Abstract

A meta-analysis on 192 peer-reviewed articles reporting on applications of the variable infiltration capacity (VIC) model in a distributed way reveals that the spatial resolution at which the model is applied has increased over the years, while the calibration and validation time interval has remained unchanged. We argue that the calibration and validation time interval should keep pace with the increase in spatial resolution in order to resolve the processes that are relevant at the applied spatial resolution. We identified six time concepts in hydrological models, which all impact the model results and conclusions. Process-based model evaluation is particularly relevant when models are applied at hyper-resolution, where stakeholders expect credible results both at a high spatial and temporal resolution.

Hydrol. Earth Syst. Sci., 20, 10691079, 2016 www.hydrol-earth-syst-sci.net/20/1069/2016/ doi:10.5194/hess-20-1069-2016 Author(s) 2016. CC Attribution 3.0 License.

HESS Opinions: The need for process-based evaluation of large-domain hyper-resolution models

Lieke A. Melsen1, Adriaan J. Teuling1, Paul J. J. F. Torfs1, Remko Uijlenhoet1, Naoki Mizukami2, and

Martyn P. Clark2

1Hydrology and Quantitative Water Management Group, Wageningen University, Droevendaalsesteeg 3a, 6708 PB Wageningen, the Netherlands

2National Center for Atmospheric Research (NCAR), Boulder, CO, USA

Correspondence to: Lieke A. Melsen ([email protected])

Received: 25 November 2015 Published in Hydrol. Earth Syst. Sci. Discuss.: 21 December 2015 Revised: 24 February 2016 Accepted: 26 February 2016 Published: 9 March 2016

Abstract. A meta-analysis on 192 peer-reviewed articles reporting on applications of the variable inltration capacity (VIC) model in a distributed way reveals that the spatial resolution at which the model is applied has increased over the years, while the calibration and validation time interval has remained unchanged. We argue that the calibration and validation time interval should keep pace with the increase in spatial resolution in order to resolve the processes that are relevant at the applied spatial resolution. We identied six time concepts in hydrological models, which all impact the model results and conclusions. Process-based model evaluation is particularly relevant when models are applied at hyper-resolution, where stakeholders expect credible results both at a high spatial and temporal resolution.

In hydrology, it is essential to understand and predict the motion of water within the Earth system, which implies that both space and time have to be considered. In hydrological models space can be accounted for by using distributed (spatially explicit) models, where space is cut in small pieces, to paraphrase Zeno. Different types of distributed hydrological models exist; Todini (1988) distinguished roughly two different classes. The rst class consists of distributed differential models. These models explicitly simulate lateral uxes by means of differential equations. The second class are the distributed integral models, which consist of one-dimensional columns and ignore lateral uxes between the columns (lateral uxes can be accounted for with an extra routing scheme, although this does not allow for lateral redistribution). These models have a wide application in land surface modelling (Clark et al., 2015). In this discussion we focus on the latter.

The constant development in computational power, the increased understanding of physical processes, and the increased availability of high spatial resolution hydrological information stimulated the development of increasingly complex and distributed hydrological models (Boyle et al., 2001;Liu and Gupta, 2007). Increasing the spatial resolution of global hydrological models (GHMs) has been labelled as one of the current grand challenges in hydrology by Wood et al. (2011) and Bierkens et al. (2014), who call for global modelling at the so-called spatial hyper-resolution ( 1 km and

smaller). Arguably, there is a growing societal need for hydrological information at the (sub-)kilometre scale. Whereas model products at the 1 or 0.5 resolution may provide rel-

Published by Copernicus Publications on behalf of the European Geosciences Union.

1 Introduction

One of the famous paradoxes of the Greek philosopher Zeno of Elea ( 450 BC) concerns a shot arrow (Fearn, 2001): If

one shoots an arrow, and cuts its motion into such small time steps that at every step the arrow is standing still, the arrow is motionless, because a concatenation of non-moving pieces cannot create motion. Only ages later, this reasoning could be refuted by the invention of integral and differential calculus by Newton and Leibniz (Stillwell, 1989), accepting innitely small rates of change. Motion is a change of location over time, thus motion links time and space.

the temporal resolution should decrease accordingly to meet these needs. This should be reected in the calibration and validation time interval of the model, in order to guarantee model credibility at the required temporal and spatial resolution.

2 Timescales

A short review of scientic literature about scaling issues provides the impression that the focus has mostly been on the spatial scale and/or resolution rather than on its temporal counterpart (Kleme, 1983; Dooge, 1986; Gupta et al., 1986; Dooge, 1988; Feddes, 1995; Kalma and Sivapalan, 1995; Sposito, 1998; Beven, 1995; Bierkens et al., 2000;Gentine et al., 2012). Many concepts have been developed to describe representative areas and volumes (Gray et al., 1993). In soil physics, the representative elementary volume (REV) is an often used concept, which describes the volume for which a measurement can be considered representative (Whitaker, 1999). Wood et al. (1988) explored a similar concept with applications in hydrology, namely the representative elementary area (REA), the critical area at which the pattern of small-scale heterogeneity becomes unimportant. Reggiani et al. (1998) proposed the representative elementary watershed (REW), allowing for closure of the balance equations averaged over time and space. Similar concepts, which statistically integrate temporal variations, have not been reported in the literature. The lack of attention for the temporal scale, however, is remarkable because hydro-logical states and uxes are mostly studied as a function of time. As an illustration of the lack of attention for the aspects of temporal scale, it should be noted that in the recent papers by Wood et al. (2011) and Bierkens et al. (2014) on spatial hyper-resolution modelling, the temporal resolution of these models is referred to only once. One of the reasons why the development of a representative elementary time step (RET) is more complex is that several different time concepts play a role in hydrological modelling.

As a guideline and rst step for the discussion on time dimensions in hydrological models, we identify six time concepts, which in practice are often mixed up and misinterpreted. A distinction is made between scale, which is dened as a continuous variable, resolution, dened as discrete variable being a model property, and time interval, which is a discrete variable independent of the used model. The six concepts are

1. the process timescale

2. the input resolution

3. the numerical resolution (time step)

4. the output resolution (temporal resolution)

5. the calibration/validation time interval

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1070 L. A. Melsen et al.: Process-based evaluation of hyper-resolution models

evant information for policy makers at the (inter)national level, hyper-resolution results will become relevant for local water managers or even individual farmers (see e.g. Bastiaanssen et al., 2007). The scientic challenge is not to simply provide information based on a model with default parameters, but to provide credible information that matches the actual situation in the eld at a temporal resolution, which is consistent with the spatial resolution of the model. The temporal and spatial scales are linked through the characteristic speed (including both velocity and celerity; see McDonnell and Beven (2014)) of the involved hydrological processes (Blschl and Sivapalan, 1995), the so-called process scale; see Fig. 1. The Figure shows that there is a general tendency for the temporal process scale to decrease with the spatial process scale, although there is quite a broad bandwidth and local changes might occur stepwise. Policy makers might be able to deal with model products at a monthly resolution, whereas resource managers and farmers expect, at the spatial hyper-resolution, credible model products with a daily or hourly resolution.

Although increasing the spatial resolution of hydrological models is claimed to provide the opportunity to improve physical process representation (Bierkens et al., 2014;Bierkens, 2015), almost every hydrological model requires calibration of the model parameters (Beven, 2012). Models can contain conceptual parameters, which have no directly measurable physical meaning and thus need calibration. In addition, the measurement scale of parameters which do have a physical meaning often differs from the model scale, making calibration necessary to determine the effective parameter values to account for sub-grid variability (Kim and Stricker, 1996). Beven and Cloke (2012) responded to the hyper-resolution challenge by emphasizing that the focus of hydrologic modelling should be on determining and accounting for epistemic uncertainty and appropriate parameterizations at different spatial resolutions, rather than on maximizing the spatial resolution. Increasing the spatial resolution of the model (towards hyper-resolution) is not a solution to sub-grid variability, since many of the relevant processes take place on even smaller scales (Wood et al., 1992; Kim and Stricker, 1996; Arora et al., 2001; Montaldo and Albertson, 2003; Beven and Cloke, 2012; Clark et al., 2015). Hence, de-spite their increasing spatial resolution, also GHMs require calibration in order to obtain effective parameters, and validation to determine model credibility. Even if a correct physical representation of hydrological processes is impossible, the goal of the model should be to mimic realism and hydro-logical processes as closely as possible (Wagener and Gupta, 2005; Kirchner, 2006; McDonnell et al., 2007). This implies that the models should be subject to a process-based calibration and validation procedure (Gupta et al., 1998, 2008; Clark et al., 2011). Since different hydrological processes dominate at different scales (Fig. 1), the temporal and spatial scales are linked. Because the spatial resolution of GHMs is currently being increased to meet societal needs (Wood et al., 2011),

L. A. Melsen et al.: Process-based evaluation of hyper-resolution models 1071

Figure 1. The timescales and space scales of several hydrometeorological processes. Adapted from Brutsaert (2005) and Blschl and Siva-palan (1995), who based it on Orlanski (1975), Dunne (1978), Fortak (1982), and Anderson and Burt (1990). The blue areas indicate the temporal and spatial resolution at which the VIC model has been applied, when it was initially developed (A) and presently (B). The dashed arrow pointing downwards shows the ambitions of spatial hyper-resolution modelling, whereas the dashed arrow pointing towards (C) shows the temporal and spatial resolution of hyper-resolution modelling if it follows the direction of characteristic velocity of hydrometeorological processes.

6. the interpretation time interval.

First, the process timescale is dened, as the characteristic timescale of the hydrological process considered. This is the typical time period over which the process takes place. Inltration excess overland ow, for instance, has a relatively short timescale, whereas regional groundwater ow has a longer timescale. The end user determines which process is most relevant in the modelling procedure.

Second, the temporal resolution of the input data or input resolution is relevant for the modelled process. The input resolution of the forcing data can differ from the output resolution of the model, and this can impact the results of the model. An example is given in the upper panels of Fig. 2, showing an application of the GreenAmpt (Green and Ampt, 1911) inltration model.

The numerical resolution (or the time step) of the model is the time interval over which the model calculates the states and the uxes internally. A model can only deterministically resolve a process if the numerical resolution is higher than the characteristic timescale of the process. The panels in the

second row of Fig. 2 show how the numerical resolution impacts model output for the process of ponding, which leads to different conclusions about ponding, based on the model output.

The output resolution (often referred to as simply temporal resolution) is the time interval at which the model output yields the states and uxes. This time interval can be equal to the numerical resolution of the model, or aggregated from the numerical resolution. The modelled process can only be identied if the output time interval is shorter than the characteristic timescale of the process, which is shown in the lower panels of Fig. 2.

The calibration and validation time interval of the model is dened here as the time interval at which the model output is being confronted with observations. Calibration and validation of the model output can be conducted at another time interval than the output resolution, by aggregating the model output. Calibration and validation should be performed at a time interval smaller than or equal to the timescale of the process that is relevant for the end user.

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1072 L. A. Melsen et al.: Process-based evaluation of hyper-resolution models

Input resolution

0 0 1 2 3 4

8

Input res. = 5 min

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"The whole day no ponding occured."

4

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"There was no more ponding after 2 h."

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"Ponding lasted longer than

4 h."

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"Ponding reached a depth of 1.78 cm."

8

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Num. res. = 5 min

Outp. res. = 0.5 h

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Input res. = 5 min

Num. res. = 5 min

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"Ponding reached a depth of 1.07 cm."

Depth (cm) or rate (cm/h)

6

6

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4

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2

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0 0 1 2 3 4

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Time (h)

Time (h)

Pond depth (cm) Infilt. rate (cm/h) Prec. rate (cm/h)

Figure 2. Application of the GreenAmpt inltration scheme for different input resolutions (upper row), different numerical resolutions (middle row), and different output resolutions (lower row). For each set-up, the model was fed with the same extreme precipitation event of 32 mm of rain in 30 min (4 mm in rst 5 min, 5 mm in 510 min, 7 mm in 1020 min, 5 mm in 2025 min and 4 mm in 2530 min). The model parameters have been kept constant; saturated hydrologic conductivity Ks = 0.044 cm h

1, initial soil moisture i = 0.1, saturated

soil moisture s = 0.5, matric pressure at wetting front [Psi1] = 22.4 cm. Each of the three time concepts impacts the conclusions that are drawn

from the model results, which shows that calibration and validation at the appropriate time interval is essential to resolve the processes taking place.

Finally, the interpretation time interval is dened as the time interval at which the model output is eventually analysed or interpreted. This can be equal to the calibration time interval, or the model output can be further aggregated resulting in a larger interpretation time interval (e.g. from daily to monthly). Since the model has not been validated or calibrated on time intervals smaller than the calibration time interval, the credibility of the results will be unknown for time interval smaller than the calibration time interval.

It is critical to note that some of these time concepts are necessarily equal to or larger than related time concepts, sometimes for logical reasons (the output resolution cannot be higher than the numerical resolution) and sometimes

for model credibility reasons (the interpretation time interval should not be smaller than the calibration time interval). It is also important to note that the rst time concept, the process scale, explicitly links the temporal and the spatial scale (Stommel, 1963; Blschl and Sivapalan, 1995; Brutsaert, 2005). Conversely, the spatial resolution of a model will set a minimum temporal resolution determining which processes need to be resolved.

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3 Example for VIC model studies

To illustrate the development of calibration/validation time interval and spatial resolution in large-domain hydrological modelling, we carried out a meta-analysis on the use of GHMs. The variable inltration capacity (VIC) model (Liang et al., 1994) was chosen for this analysis because it is widely used and therefore enough studies were available for a meta-analysis. The VIC model is mentioned explicitly in Bierkens et al. (2014) as a type of model being run at the spatial hyper-resolution. Sub-grid variability is parameterized as a distribution of responses without explicit treatment of the pattern.We believe this model is representative of the much larger class of global hydrological models.

The VIC model was initially constructed to couple climate model output to hydrological processes: it is capable of solving both the energy and the water balance. Lohmann et al. (1996) developed a horizontal routing model to couple the individual grid cells of the VIC model. This facilitated the distributed application of VIC for rainfallrunoff processes at large domains. No explicit denition of a spatial derivative or scale appears in the equations of the VIC model, the spatial resolution of the model only appears in the routing scheme through the horizontal ow velocity (see Kampf and Burges (2007) for a description of spacetime representation in other distributed hydrologic models).

In our analysis we assembled 242 peer-reviewed studies that used the VIC model. Of these, 192 studies used the model in a distributed way and performed a calibration or validation on the model output (see Table A1 in Appendix A). Figure 3 presents a spacetime perspective on the application of the VIC model during the past 2 decades.As expected, the spatial resolution at which the model is applied has increased steadily over the years (Fig. 3a). While the model was initially constructed for spatial resolutions of the order of 0.5 to 2 , it is now mostly applied at 1/8 and smaller. The main driver for the increase in spatial resolution is the availability of high-resolution spatial data sets, such as that presented by Maurer et al. (2002). The increase in resolution, however, does not apply to the employed calibration and validation time interval. Figure 3b shows that the time interval at which the model has been calibrated and validated has remained steady over the years. Therefore, while the spatial resolution of the model has increased, the model output is still calibrated and validated at the original coarse time interval. Processes with a short timescale, which become more important when the spatial resolution increases, will likely be overlooked during the calibration and validation of the model if the time interval is too coarse. Several studies have already shown that calibration on a coarser time interval does not guarantee credible results for shorter time intervals (Melsen et al., 2015; Kavetski et al., 2011; Littlewood and Croke, 2013). There are, however, examples of studies where the interpretation time interval is smaller than the calibration time interval, e.g. Liu et al. (2013) and Costa-Cabral et al. (2013).

Figure 1 indicates the initial development scale of the VIC model (A), the scale where it is heading to right now (B), and the direction where it should go in order to resolve relevant hydrometeorological processes (C). Therefore, the VIC model with a high spatial resolution should be calibrated and/or validated at a time interval short enough to catch the processes relevant at those particular spatial scales.

Two causes for the discrepancy in the joint development of spatial resolutions and calibration time intervals come to mind: lack of computational power, or a lack of (using) observations with a high temporal frequency. Figure 3c shows that the total number of grid cells that was used in the studies has on average increased over time. This is as expected: computational power has increased signicantly over the years. According to Moores law (Moore, 1965), computational power roughly doubles every 2 years. The grey lines in Fig. 3c indicate the corresponding slope in computational power on a loglog scale. The largest numbers of grid cells per year likely indicate the limit of technical capability. Overall, the trend in the studies, even in the higher quantiles, is much lower than the computational limit, suggesting that computational power is not a constraint for most studies. This implies that, presently, the main constraint for calibration and validation of distributed hydrological models at a certain time interval (Fig. 3b) is not the computational power, but the lack of (using) observations with a high temporal frequency. A possible explanation for this may be that many (global) studies rely on data from the Global Runoff Data Centre (GRDC), which are often available only at the monthly time interval. Also important is that for large basins, the typical application scale of VIC and other GHMs, ow is often regulated by dams for hydropower and ood control.Naturalized ows for these basins are often estimated at the monthly time interval. Our results reinforce the conclusion of Kirchner (2006) that eld observations should account for the spatial and temporal heterogeneity of hydrometeorological processes, and the statement from Kavetski et al. (2011) that in most cases, temporal resolution is xed by the data collection procedure.

4 Problem statement and outlook

The meta-anlysis on VIC studies showed that the spatial resolution at which the model is applied has increased over the years, while the calibration time interval has remained steady (Fig. 3). The examples are shown for the VIC model only, but we have the impression that the obtained trends apply for all GHMs. There is a general tendency to move towards higher spatial resolution in large-domain hydrological models (induced by e.g. Wood et al., 2011; Bierkens et al., 2014), whereas the available data for calibration and validation are model independent.

Although coarse temporal resolution data can be used to constrain model uncertainty, the ambition to move towards

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1074 L. A. Melsen et al.: Process-based evaluation of hyper-resolution models

2

Spatial resolution of VIC model grid

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1998 2002 2006 2010 2014Year of publication

1998 2002 2006 2010 2014

1998 2002 2006 2010 2014

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Figure 3. The year of publication versus the highest spatial resolution of the VIC model that was used in the study (a), the smallest time interval on which the calibration and/or validation of the VIC model was performed (b), and the total number of grid cells in the study (c) based on 192 peer-reviewed studies. The grey lines in (c) show the slope of computational power increase according to Moores law (Moore, 1965). The point size is proportional to the number of studies that were published in a certain year with a certain spatial or temporal resolution. If the spatial resolution was given in kilometres, it was assumed that 1 = 100 km. For the total number of grid cells, catchment size was

divided by cell size, assuming that 1 = 100 km, unless the number of grid cells was explicitly given. Statistics (the mean and the standard

deviation) have been obtained per year on logarithmically transformed data. With linear regression a line was tted through the mean and the standard deviation.

spatial hyper-resolution hydrological models with predictive capabilities should keep pace with the data that are required to run, calibrate, and validate the models. Increasing the spatial resolution of the model implies modelling different relevant hydrometeorological processes (there are some interesting developments concerning parameter transferability over spatial resolutions; see e.g. Samaniego et al., 2010, Kumar et al., 2013, and Rakovec et al., 2015), which in turn requires calibration and validation to be performed on a smaller time interval. It requires a community effort to increase the availability of high temporal resolution data for calibration and validation of large-domain hydrological models. Especially for large-domain studies, where data collection from all the separate basins at different institutes and countries is very time consuming (explaining the success of the GRDC), the data need to be gathered at and accessible from one point. It should also be recognized that discharge data only, especially at a monthly timescale, do not provide sufcient information for a process-based model evaluation at the spatial hyper-resolution scale. Possible paths forward are the use of tracer data to identify different ow paths (Tetzlaff et al., 2015), the use of multiple objectives (Gupta et al., 1998), and the use of satellite and remote sensing data (Pan et al., 2008), all at a representative spatial and temporal resolution.

We acknowledge that calibration and validation at the appropriate time interval is only one of the many challenges of spatial hyper-resolution hydrological modelling. Even with enough observations available for calibration and validation, disinformative data (Beven and Westerberg, 2011), correct subgrid parameterizations (Beven et al., 2015), and model structural uncertainty (Clark et al., 2015) remain outstanding challenges. However, we believe that all these challenges can only be tackled if the models are subject to critical and

process-based evaluation and validation (Gupta et al., 2008; Clark et al., 2011). In the end, the goal is to model hydrological processes in an appropriate way (Beven, 2006; McDonnell et al., 2007).

Along with an increased spatial resolution of the model products, there will be a shift in users expectations of those products. Whereas coarse-scale (0.5 to 1 ) products may provide relevant information for policy makers at the national or state level, products at the spatial hyper-resolution (0.1 to 1 km) are potentially of interest to a much wider range of users, including for instance farmers that want to schedule their irrigation. At the sub-kilometre scale, new processes such as inltration excess overland ow and ponding can (and should) be resolved, but at the same time these processes cannot be explicitly resolved at a daily or monthly time interval. Thus, the recent call for increasing the spatial resolution of distributed hydrological models (Wood et al., 2011; Bierkens et al., 2014) should not focus solely on the spatial resolution, but should aim to increase the evaluation time interval simultaneously, at a balanced rate consistent with the characteristic timescales and space scales of the relevant hydrological processes (Fig. 1). We believe that such a balanced approach will serve societal needs best.

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Appendix A: Articles in the meta-analysis

Table A1. All articles used to create Fig. 3, with their highest spatial resolution (Spat.; in degrees) and the time interval (Temp) used for calibration and validation.

Authors Journal Year Title Spat. Temp.

Abdullah, F. A. and D. P. Lettenmaier J. Hydrol. 1997 Application of regional parameter ... 1.000 monthly Acharya, A., et al. J. Hydrol. 2011 Modeled streamow response ... 0.125 monthly Adam, J. C., et al. J. Geophys. Res. 2007 Simulation of reservoir inuences ... 1.000 monthly Agboma, C. O., et al. J. Hydrol. 2009 Intercomparison of the total storage ... 0.300 monthly Ahmad, S., et al. Adv. Water Resour. 2010 Estimating soil moisture ... 0.125 daily Andreadis, K. M. and D. P. Lettenmaier Adv. Water Resour. 2006 Assimilating remotely sensed ... 0.125 daily Arora, V. K. and G. J. Boer J. Climate 2006 The temporal variability of ... 2.000 monthly Ashfaq, M., et al. J. Geophys. Res. 2010 Inuence of climate model ... 0.125 daily Bao, Z., et al. J. Hydrol. 2012 Comparison of regionalization ... 0.250 monthly Bao, Z., et al. J. Hydrol. 2012 Attribution for decreasing ... 0.250 monthly Bao, Z., et al. Hydrol. Process. 2012 Sensitivity of hydrological ... 0.250 monthly Bohn, T. J., et al. Environ. Res. Lett. 2007 Methane emissions from ... 1.000 daily Bohn, T. J., et al. J. Hydrometeorol. 2010 Seasonal Hydrologic Forecasting ... 0.125 monthly Bowling, L. C., and D. P. Lettenmaier J. Hydrometeorol. 2010 Modeling the Effects of ... 0.125 hourly Chang, J., et al. Quaternary Int. 2014 Impact of climate change ... 0.500 daily Cherkauer, K. A., and D. P. Lettenmaier J. Geophys. Res. 1999 Hydrologic effects of frozen soils ... 0.500 daily Christensen, N. S., et al. Climatic Change 2004 The effect of climate change on ... 0.125 daily Christensen, N. S., and D. P. Lettenmaier Hydrol. Earth Syst. Sci. 2007 A multimodel ensemble approach ... 0.125 daily Costa-Cabral, M., et al. Climatic Change 2013 Snowpack and runoff response ... 0.125 monthly Crow, W. T., et al. J. Geophys. Res. 2003 Multiobjective calibration of ... 0.125 hourly Cuo, L., et al. J. Hydrol. 2013 The impacts of climate change ... 0.250 daily Demaria, E. M. C. , et al. J. Hydrol. 2013 Climate change impacts on ... 0.250 daily Demaria, E. M. C., et al. Int. J. River Bas. Manag. 2014 Satellite precipitation in ... 0.125 monthly Daza, A., et al. Int. J. River Bas. Manag. 2013 Multi-annual variability of ... 0.125 daily Drusch, M., et al. Geophys. Res. Lett. 2005 Observation operators for the ... 0.125 daily Eum, H., et al. Hydrol. Process. 2014 Uncertainty in modelling the ... 0.063 daily Fan, Y. et al. J. Hydrometeorol. 2011 Verication and Intercomparison ... 0.125 monthly Feng, X., et al. J. Hydrometeorol. 2008 The Impact of Snow Model ... 0.125 daily Ferguson, C. R., et al. Int. J. Remote Sens. 2010 Quantifying uncertainty in ... 0.125 monthly Ferguson, C. R., et al. J. Hydrometeorol. 2012 A Global Intercomparison of ... 0.250 daily Gao, H., et al. J. Hydrometeorol. 2004 Using a Microwave Emission ... 0.125 daily Gao, H., et al. J. Hydrometeorol. 2006 Using TRMM/TMI to Retrieve ... 0.125 daily Gao, H., et al. J. Hydrometeorol. 2007 Copula-Derived Observation ... 0.125 daily Gao, H., et al. Int. J. Remote Sens. 2010 Estimating the water budget ... 0.500 monthly Gao, Y., et al. J. Geophys. Res. 2011 Evaluating climate change ... 0.125 monthly Garg, V., et al. J. Hydr. Eng. 2013 Hypothetical scenario?based ... 0.250 yearly Gebregiorgis, A. and F. Hossain J. Hydrometeorol. 2011 How Much Can A Priori Hydrologic ... 0.125 daily Gebregiorgis, A. S., et al. Water Resour. Res. 2012 Tracing hydrologic model ... 0.125 daily Gu, H., et al. Stoch. Environ. Res. Risk Ass. 2014 Impact of climate change ... 0.125 daily Guerrero, M., et al. Int. J. River Bas. Manag. 2013 Parana River morphodynamics ... 0.125 monthly Guo, J., et al. J. Hydrol. 2004 Impacts of different precipitation ... 0.125 daily Guo, J., et al. Proc. Env. Sci. 2011 Daily runoff simulation in ... 0.042 daily Haddeland, I., et al. Gephys. Res. Lett. 2006 Anthropogenic impacts on ... 0.500 monthly Haddeland, I., et al. J. Hydrometeorol. 2006 Reconciling Simulated Moisture ... 0.125 hourly Haddeland, I., et al. J. Hydrol. 2006 Effects of irrigation on the ... 0.500 daily Hamlet, A. F., et al. J. Climate 2005 Effects of Temperature and ... 0.125 monthly Hamlet, A. F. and D. P. Lettenmaier Water Resour. Res. 2007 Effects of 20th century warming ... 0.125 monthly Hidalgo, H. G., et al. J. Hydrol. 2013 Hydrological climate change ... 0.500 monthly Hillarda, Y., et al. Remote Sens. Environ. 2003 Assessing snowmelt dynamics ... 0.125 daily Huang, M., et al. J. Geophys. Res. 2003 A transferability study of model ... 0.130 daily Hurkmans, R. T. W. L., et al. Water Resour. Res. 2008 Water balance versus land ... 0.088 daily Hurkmans, R. T. W. L., et al. Water Resour. Res. 2009 Effects of land use changes ... 0.050 daily Hurkmans, R., et al. J. Climate 2010 Changes in Streamow Dynamics ... 0.088 daily Jayawardena, A. W., et al. J. Hydrolog. Eng. 2002 Meso-Scale Hydrological ... 1.000 daily Kam, J., et al. J. Climate 2013 The Inuence of Atlantic ... 0.125 daily Lakshmi, V., et al. Gephys. Res. Lett. 2004 Soil moisture as an ... 0.125 monthly Li, J., et al. J. Hydrometeorol. 2007 Modeling and Analysis ... 0.042 daily Li, H., et al. J. Hydrometeorol. 2013 A Physically Based Runoff ... 0.063 monthly Liang, X. and Z. Xie Adv. Water Resour. 2001 A new surface runoff ... 0.125 daily Liang, X. and Z. Xie Global Planet. Change 2003 Important factors in land? ... 0.125 daily Liang, X., et al. J. Geophys. Res. 2003 A new parameterization ... 0.125 daily

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Authors Journal Year Title Spat. Temp.

Liang, X., et al. J. Hydrol. 2004 Assessment of the effects ... 0.031 daily Liu, Z., et al. Hydrol. Process. 2010 Impacts of climate change on ... 0.500 daily Liu, L., et al. J. of Flood Risk Manag. 2013 Hydrological analysis for water ... 0.010 daily Liu, H., et al. Hydrol. Earth Syst. Sci. 2013 Soil moisture controls on ... 0.500 monthly Liu, X., et al. Hydrol. Earth Syst. Sci. 2014 Effects of surface wind speed ... 0.250 monthly Livneh, B., et al. J. Climate 2013 A Long-Term Hydrologically ... 0.063 monthly Lohmann, D., et al. Hydrolog. Sci. J. 1998 Regional scale hydrology: ... 0.167 daily Lu, X., and Q. Zhuang J. Geophys. Res. 2012 Modeling methane emissions ... 0.333 daily Lucas-Picher, P., et al. Atmosphere-Ocean 2003 Implementation of a ... 0.405 monthly Luo, Y., et al. J. Hydrometeorol. 2005 The Operational Eta Model ... 0.125 monthly Luo, L. and E. F. Wood Gephys. Res. Lett. 2007 Monitoring and predicting ... 0.125 monthly Luo, L. and E. F. Wood J. Hydrometeorol. 2008 Use of Bayesian Merging ... 0.125 monthly Lutz, E. R., et al. Water Resour. Res. 2012 Paleoreconstruction of cool ... 0.063 monthly Mao, D. and K. A. Cherkauer J. Hydrol. 2009 Impacts of land-use change ... 0.125 monthly Mao, D., et al. Water Resour. Res. 2010 Development of a coupled ... 0.125 daily Marshall, M., et al. Climate Dynamics 2012 Examining evapotranspiration ... 1.000 monthly Matheussen, B., et al. Hydrol. Process. 2000 Effects of land cover change ... 0.250 monthly Maurer, E. P., et al. J. Geophys. Res. 2001 Evaluation of the land ... 0.125 monthly Maurer, E. P., et al. J. Climate 2002 A Long-Term Hydrologically ... 0.125 monthly McGuire, M., et al. J. Water Resour. Plan. Manage. 2006 Use of Satellite Data for ... 0.125 monthly Meng, L. and S. M. Quiring Int. J. Climatol. 2010 Observational relationship of ... 0.500 monthly Miguez-Macho, G., et al. B. Am. Meterol. Soc. 2008 Simulated water table ... 0.008 monthly Miller, W. P., et al. J. Water Res. Pl. Manag. 2012 Water Management Decisions ... 0.125 monthly Minihane, M. R. Phys. Chem. Earth 2012 Evaluation of streamow ... 0.250 monthly Mishra, V., et al. J. Hydrometeorol. 2010 Parameterization of Lakes ... 0.125 daily Mishra, V. and K. A. Cherkaue Agric. For. Meteorol. 2010 Retrospective droughts in ... 0.125 monthly Mishra, V., et al. J. Hydrometeorol. 2010 Assessment of Drought due ... 0.125 monthly Mishra, V., et al. Int. J. Clim. 2010 A regional scale assessment ... 0.125 monthly Mishra, V., et al. Global Planet. Change 2011 Lake Ice phenology of ... 0.125 daily Mishra, V., et al. Global Planet. Change 2011 Changing thermal dynamics ... 0.125 daily Mishra, V. and K. A. Cherkauer J. Geophys. Res. 2011 Inuence of cold season ... 0.125 daily Mo, K. C. J. Hydrometeorol. 2008 Model-Based Drought Indices ... 0.500 monthly Mo, K. C., et al. J. Hydrometeorol. 2012 Uncertainties in North American ... 0.500 monthly Munoz-Arriola, F., et al. Water Resour. Res. 2009 Sensitivity of the water resources ... 0.125 monthly Nijssen, B., et al. Water Resour. Res. 1997 Streamow simulation for ... 0.500 monthly Nijssen, B., et al. J. Climate 2001 Global Retrospective Estimation ... 2.000 monthly Nijssen, B., et al. Climatic Change 2001 Hydrologic sensitivity of global ... 1.000 monthly Niu, J., et al. J. Hydrol. 2013 Impacts of increased CO2 ... 1.000 monthly

Niu, J. and J. Chen Hydrological Sciences Journal 2014 Terrestrial hydrological responses ... 1.000 daily Niu, J. and B. Sivakumar Stoch Environ Res Risk Assess 2014 Study of runoff response to ... 1.000 monthly Niu, J., et al. Hydrol. Earth Syst. Sci. 2014 Teleconnection analysis of ... 1.000 monthly Null, S. E. and J. H. Viers Water Resour. Res. 2013 In bad waters: Water year ... 0.125 monthly ODonnell, G. M., et al. J. Geophys. Res. 2000 Macroscale hydrological modeling ... 0.500 monthly Oubeidillah, A. A., et al. Hydrol. Earth Syst. Sci. 2014 A large-scale, high-resolution ... 0.042 monthly Ozdogan, M. Hydrol. Earth Syst. Sci. 2011 Climate change impacts on ... 0.125 monthly Pan, M. and E. F. Wood J. Hydrometeorol. 2006 Data Assimilation for ... 0.500 daily Parada, L. M. and X. Liang J. Geophys. Res. 2004 Optimal multiscale Kalman ... 0.125 daily Parada, L. M. and X. Liang J. Geophys. Res. 2008 Impacts of spatial resolutions ... 0.125 daily Park, D. and M. Markus J. Hydrol. 2014 Analysis of a changing ... 0.125 daily Parr, D. and G. Wang Global Planet. Change 2014 Hydrological changes in the ... 0.030 daily Qiao, L., et al. Water Resour. Manag. 2014 Climate Change and ... 0.125 daily Qin, S., et al. Int. J. Remote Sens. 2013 Development of a hierarchical ... 0.030 daily Raje, D. and R. Krishnan Water Resour. Res. 2012 Bayesian parameter uncertainty ... 1.000 monthly Raje, D., et al. Hydrol. Process. 2014 Macroscale hydrological modelling ... 1.000 monthly Ray, R. L., et al. Remote Sens. Environ. 2010 Landslide susceptibility mapping ... 0.010 daily Rhoads, J., et al. J. Geophys. Res. 2001 Validation of land surface models ... 1.000 daily Rosenberg, E. A., et al. Water Resour. Res. 2011 Statistical applications of... 0.063 monthly Rosenberg, E. A., et al. Hydrol. Earth Syst. Sci. 2013 On the contribution of ... 0.125 daily Saurral, R. I. J. Hydrometeorol. 2010 The Hydrologic Cycle of the ... 0.125 monthly Schaller, M. F. and Y. Fan J. Geophys. Res. 2009 River basins as groundwater ... 0.125 monthly Schumann, G. J.-P., et al. Water Resour. Res. 2013 A rst large-scale ood ... 0.250 monthly Shefeld, J., et al. J. Geophys. Res. 2003 Snow process modeling ... 0.125 daily Shefeld, J., et al. J. Hydrometeorol. 2012 Representation of Terrestrial ... 0.500 monthly Shi, X., et al. Environ. Res. Lett. 2011 The role of surface energy ... 1.000 weekly Shi, X., et al. J. Climate 2013 Relationships between Recent ... 1.000 monthly

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Authors Journal Year Title Spat. Temp.

Shrestha, R. R., et al. Hydrol. Process. 2012 Modelling spatial and ... 0.063 monthly Shrestha, K. Y., et al. J. Hydrometeorol. 2014 An Atmospheric-Hydrologic ... 0.250 daily Shrestha, R. R., et al. J. Hydrometeorol. 2014 Evaluating Hydroclimatic ... 0.063 daily Shrestha, R. R., et al. Hydrol. Process. 2014 Evaluating the ability of a ... 0.063 monthly Shukla, S., et al. Hydrol. Earth Syst. Sci. 2012 Value of medium range ... 0.500 2-weeks Shukla, S., et al. Hydrol. Earth Syst. Sci. 2012 On the sources of global land ... 0.500 monthly Sinha, T., et al. J. Hydrometeorol. 2010 Impacts of Historic Climate ... 0.125 weekly Sinha, T. and K. A. Cherkauer J. Geophys. Res. 2010 Impacts of future climate ... 0.125 weekly Sinha, T. and A. Sankarasubramanian Hydrol. Earth Syst. Sci. 2013 Role of climate forecasts and ... 0.125 monthly Slater, A. G., et al. J. Geophys. Res. 2007 A multimodel simulation of ... 1.000 monthly Sridhar, V., et al. Climate Dynamics 2013 Explaining the hydroclimatic ... 0.125 monthly Stephen, H., et al. Hydrol. Earth Syst. Sci. 2010 Relating surface backscatter ... 0.125 daily Su, F., et al. J. Geophys. Res. 2005 Streamow simulations of ... 1.000 monthly Su, F., et al. J. Geophys. Res. 2006 Evaluation of surface water ... 1.000 monthly Su, F., et al. J. Hydrometeorol. 2008 Evaluation of TRMM Multisatellite ... 0.125 daily Su, F. and D. P. Lettenmaier J. Hydrometeorol. 2009 Estimation of the Surface ... 0.125 monthly Tang, C. and T. C. Piechota J. Hydrol. 2009 Spatial and temporal soil ... 0.125 monthly Tang, Q. and D. P. Lettenmaier Int. J. Remote Sens. 2010 Use of satellite snow-cover ... 0.063 monthly Tang, C., et al. J. Hydrol. 2011 Relationships between ... 0.125 monthly Tang, Q., et al. J. Hydrometeorol. 2012 Predictability of Evapotranspiration ... 0.063 daily Tang, C., et al. Global Planet. Change 2012 Assessing streamow sensitivity ... 0.063 monthly Tang, C. and R. L. Dennis Global Planet. Change 2014 How reliable is the ofine ... 0.125 monthly Vano, J. A. et al. J. Hydrometeorol. 2012 Hydrologic Sensitivities of ... 0.125 monthly VanShaar, J. R. et al. Hydrol. Process. 2012 Effects of land-cover changes ... 0.125 monthly Vicuna, S. et al. J. Am. Water Resour. As. 2007 The sensitivity of California ... 0.125 monthly Voisin, N., et al. J. Hydrometeorol. 2008 Evaluation of Precipitation ... 0.500 monthly Voisin, N.,et al. Weather Forecast. 2011 Application of a Medium-Range ... 0.250 daily Wang, A., et al. J. Geophys. Res. 2008 Integration of the variable ... 0.125 monthly Wang, J., et al. Int. J. Clim. 2010 Quantitative assessment of climate ... 0.125 monthly Wang, G .Q, et al. Hydrol. Earth Syst. Sc. 2012 Assessing water resources in ... 0.500 daily Werner, A. T., et al. Atmosphere-Ocean 2013 Spatial and Temporal Change ... 0.063 daily Wen, Z., et al. Water Resour. Res. 2012 A new multiscale routing ... 0.031 daily Wenger, S. J., et al. Water Resour. Res. 2010 Macroscale hydrologic ... 0.063 daily Wojcik, R., et al. J. Hydrometeorol. 2008 Multimodel Estimation of ... 0.125 hourly Wood, A. W., et al. J. Geophys. Res. 2002 Long-range experimental ... 0.125 monthly Wood, A. W., et al. J. Geophys. Res. 2005 A retrospective assessment ... 0.125 monthly Wu, Z., et al. Atmosphere-Ocean 2007 Thirty-Five Year (19712005) ... 0.300 daily Wu, Z. Y., et al. Hydrol. Earth Syst. Sci. 2011 Reconstructing and analyzing ... 0.300 daily Wu, H., et al. Water Resour. Res. 2014 Real-time global ood ... 0.125 daily Xia, Y., et al. J. Geophys. Res. 2012 Continental-scale water ... 0.125 daily Xia, Y., et al. Hydrol. Process. 2012 Comparative analysis of ... 0.125 monthly Xia, Y., et al. Hydrol. Process. 2014 Evaluation of NLDAS-2 ... 0.125 daily Xie, Z., et al. J. Hydrometeorol. 2007 Regional Parameter Estimation ... 0.500 monthly Yang, G., et al. J. Hydrometeorol. 2010 Hydroclimatic Response of ... 0.125 daily Yang, G., et al. Landscape Urban Plan. 2011 The impact of urban development ... 0.125 daily Yang, G. and L. C. Bowling Water Resour. Res. 2014 Detection of changes in ... 0.125 daily Yearsley, J. Water Resour. Res. 2012 A grid-based approach for ... 0.063 daily Yong, B., et al. Water Resour. Res. 2010 Hydrologic evaluation of ... 0.063 daily Yong, B., e al. J. Hydrometeorol. 2013 Spatial-Temporal Changes of ... 0.063 daily Yuan, F., et al. Can. J. Remote Sens. 2004 An application of the VIC-3L ... 0.250 daily Yuan, X., et al. Hydr. Sci. J. 2009 Sensitivity of regionalized ... 0.500 monthly Yuan, X., et al. J. Hydrometeorol. 2013 Probabilistic Seasonal ... 0.250 monthly Zeng, X., et al. J. Hydrometeorol. 2010 Comparison of Land?Precipitation ... 0.125 monthly Zhang, X., et al. Phys. Chem. Earth 2012 Modeling and assessing ... 0.031 monthly Zhang, B., et al. Agr. Water Manage. 2012 Drought variation trends in ... 0.500 yearly Zhang, B., et al. Theor. Appl. Climatol. 2013 A drought hazard assessment ... 0.500 yearly Zhang, B., et al. Hydrol. Process. 2014 Assessing the spatial and ... 0.500 yearly Zhang, X., et al. J. Hydrometeorol. 2014 A Long-Term Land Surface ... 0.250 monthly Zhang, B., et al. Hydrol. Process. 2014 Spatiotemporal analysis of climate ... 0.500 yearly Zhao, F., et al. J. Hydrometeorol. 2012 Application of a Macroscale ... 0.050 daily Zhao, X. and P. Wu Natural Hazards 2013 Meteorological drought over ... 0.500 yearly Zhao, Q., et al. Env. Earth Sci. 2013 Coupling a glacier melt model ... 0.083 daily Zhao, F., et al. J. Hydrol. 2013 The effect of spatial rainfall ... 0.050 daily Zhu, C. and D. P. Lettenmaier J. Climate 2007 Long-Term Climate and ... 0.125 monthly Ziegler, A. D., et al. J. Climate 2003 Detection of Intensication in ... 2.000 monthly Ziegler, A. D., et al. Climatic Change 2005 Detection of time for plausible ... 0.125 monthly

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1078 L. A. Melsen et al.: Process-based evaluation of hyper-resolution models

Acknowledgements. The authors would like to thank Claudia Brauer and Massimiliano Zappa for their useful suggestions concerning a draft version of this paper.

Edited by: E. Zehe

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