Toward computationally efficient large-scale hydrologic predictions with a multiscale regionalization scheme



[1] We present an assessment of a framework to reduce computational expense required for hydrologic prediction over new domains. A common problem in computational hydrology arises when a hydrologist seeks to model a new domain and is subsequently required to estimate representative model parameters for that domain. Our focus is to extend previous development of the Multiscale Parameter Regionalization (MPR) technique, to a broader set of climatic regimes and spatial scales to demonstrate the utility of this approach. We hypothesize that this technique will be applicable for (1) improving predictions in ungauged basins, and (2) as a tool for upscaling high-fidelity hydrologic simulations closer to a general circulation model (GCM) scales, while appreciably reducing computational expense in parameter estimation. We transfer hydrologic model parameters from a single central European basin, to 80 candidate basins within the United States. The regionalization is further tested across a range of climatic and land-cover conditions to identify potential biases in transferability. The results indicate a high degree of success in transferring parameters from central Europe to North America. Parameter scaling from 1/8° up to 1° confirms that MPR can produce a set of quasi-scale independent parameters, with only modest differences in model performance across scales (<3%). Model skill generally decreases approximately 10–20% when transferring parameters toward alternate climatic and land-cover conditions. Finally, we show that the success of model parameter transfer is contingent upon soil, land-cover, and climatic regimes relative to those used during calibration, particularly going from high-to-low clay content and from dense-to-sparse forest.

1. Introduction

[2] Recent increases in computational capabilities have allowed hydrologists to model large areas of the earth surface. Particularly, important has been the ability to define a representative set of hydrologic parameters for a region of interest, via automatic search procedures that seek to minimize errors between observed and simulated quantities of interest. Despite the gains in computational power, and the boom in parallel computing [Jin et al., 2011], it remains impractical to calibrate a model at every new region of interest. This is due either to the effort required to set up the numerical framework for a search procedure, or the more arduous task of setting up an observation station (in data scarce regions), or both [Sivapalan, 2003].

[3] Several alternatives have been proposed to avoid the need for site-specific calibration. These can be grouped into two general methodologies for transferring model parameter information. The first set of methods seek to group transfer domains via hydrologic similarity [e.g., Vandewiele and Elias, 1995; Koren et al., 2000; Nijssen et al., 2001; Merz and Blöschl, 2004; Oudin et al., 2008; Zhang and Chiew, 2009; Samaniego et al., 2010a], or by applying multiple diagnostic signatures [e.g., Yadav et al., 2007; Yilmaz et al., 2008; Clark et al., 2008; Winsemius et al., 2009]. These methods first classify basins or regions based on physiographic metrics (e.g., terrain characteristics, land-cover, hydrologic response time, climatology, etc.), or through low-dimensional parameter inference (categorizing basin according to strengths or inadequacies of model response to different performance measures [Clark et al., 2008]). Thus, a new region of interest is classified according to these metrics and assigned a set of representative parameters, hence drastically reducing computation effort required for calibration. A major difficulty with similarity approaches is reconciling the scale of the physiographic data with the scale of model parameters, where spatial averaging reduces physical representativeness, information content, and explanatory skill of the physiographic data.

[4] The second set of methods include regional calibration [e.g., Fernandez et al., 2000; Hundecha and Bárdossy, 2004; Zhang et al., 2008; Samaniego et al., 2010b], regression-based approaches [e.g., Abdulla and Lettenmaier, 1997; Seibert, 1999; Hundecha and Bárdossy, 2004; Wagener and Wheater, 2006; Gan and Burges, 2006; Götzinger and Bárdossy, 2007; Pokhrel et al., 2008; Viviroli et al., 2009; Singh et al., 2012; Livneh and Lettenmaier, 2013], and through spatial interpolation [e.g., Abdulla et al., 1996; Merz and Blöschl, 2004; Parajka et al., 2005, 2007; Hundecha et al., 2008; Troy et al., 2008]. The distinction between these methods is whether parameter calibration is performed simultaneously on multiple catchments (i.e., regional calibration), on whether is done on individual catchments (i.e., regression and interpolation). The former method is advantageous in that it avoids overfitting parameters to individual catchments. Studies employing this method have succeeded in maintaining much of the model predictive skill, albeit requiring a comparatively large computational effort [Fernandez et al., 2000; Hundecha and Bárdossy, 2004]. Conversely, the latter methods (i.e., regression and interpolation) may face highly complex spatial parametric fields, such that suitable regional parameters may not be obtainable, due to overfitting of parameters to specific calibration settings (basins). A recent study conducted by Parajka et al. [2013] provides a comprehensive overview on different methods and their performances in parameter transferability from gauged to ungauged basins.

[5] In many cases, some degree of model calibration is required to reduce errors between observed and simulated quantities (e.g., streamflow) with the aim of improving simulations of hydrologic processes. However, calibrating a hydrologic, or land surface model over large river basins (greater than 105 km2) poses a significant computational challenge, particularly when model simulations seek to capture processes at fine spatial scales (e.g., 1–5 km). Two alternative approaches could be pursued to deal with this problem. The first approach involves estimating (via calibration) a set of representative parameters in a relatively small part of the domain (or subbasins), and then directly using those calibrated parameters for simulations in large river basins [e.g., Troy et al., 2008]. This approach is analogous to one used for the predictions in ungauged basin (PUB) [Sivapalan, 2003], as discussed above in detail. The second approach would be to simply calibrate model parameters at a coarser spatial resolution (e.g., 50–100 km grid cell size) to reduce the computational load during calibration [Troy et al., 2008]. However, this approach requires a robust parameterization technique in order to capture fine scale processes (e.g., at 1–5 km) while using parameters estimated at a coarser resolution. In other words, the selected technique should allow the transferability of calibration parameters across scales, without inducing a significant loss of model performance [Troy et al., 2008; Samaniego et al., 2010b; Beven and Cloke, 2012; Kumar et al., 2013].

[6] In this study, we present a modeling procedure that has the objective of both: (1) maintaining a high degree of model skill, while (2) significantly reducing computational effort in making model simulations of new spatial domains or scales. The essence of this procedure lies in the Multiscale Parameter Regionalization technique (MPR) [Samaniego et al., 2010b] and the concept that a set of representative model parameters can remain stable across a range of spatial resolutions. We subsequently hypothesize that a parameter search at a coarse resolution (e.g., 1° ≈ 100 km) with a small number of grid cells should be directly applicable to finer spatial resolutions (e.g., 1/8° ≈ 12.5 km), hence limiting the computational cost of model calibration. We extend the previous efforts of Samaniego et al. [2010b] and Kumar et al. [2013] to test this hypothesis across two continents (Europe and North America) that provide a significant range of spatial scaling as well as a diversity of climate and land-cover conditions to assess the degree of spatial independence of transferred parameters. It is anticipated that the results from this proof-of-concept experiment be widely relevant to a range of land surface modeling applications. Applications range from (1) coupled modeling i.e., reconciling differences in spatial resolution between finer resolution land surface models with coarser resolution GCMs, while preserving land surface model performance, to (2) extending calibrated hydrologic performance to ungauged basins with differing climate, terrain, soil, and land-cover conditions. In both of these applications, the goal with this method is to obviate the need for computationally intensive model calibrations. In this way, we focus the presentation of this work to address the call for Innovative Methods for Reducing Computational Time and Expense.

2. Experimental Setup

[7] The objective here is to present a simple experiment that demonstrates an appreciable reduction in computational effort for the task of estimating hydrologic model parameters over new domains and scales of interest. We predicate the reduction in computational expense on the degree to which model performance is preserved. From the end-user perspective, it follows that computational savings are secondary to the fidelity of ensuing hydrologic simulations. The efficiency of this method is presented in the context of gradients in (1) scale, in terms of upscaling or downscaling parameters, which is often needed when reconciling hydrologic simulations with companion data, such as GCM or RCM outputs, and (2) basin physical characteristics, such as climate (i.e., aridity index), soil (clay content), land cover (vegetation types), and topography, to assess how well parameter information is transferred across gradients of these. In this study, MPR is applied to the mesoscale Hydrologic Model (mHM) [Samaniego et al., 2010b]; however, the concepts presented here are applicable to a wide range of hydrologic and land-surface models.

2.1. Mesocale Hydrologic Model (mHM) and Multiscale Parameter Regionalization (MPR) Technique

[8] The mHM is a spatially distributed, mesoscale hydrologic model that uses grid cells as the primary hydrologic unit. It accounts for the following hydrologic processes: canopy interception, snow accumulation and melt, soil moisture and evapotranspiration, surface and subsurface runoff generations, deep percolation and base flow, and flood routing. The model uses a degree-day method to account for snow accumulation and melting processes [Hundecha and Bárdossy, 2004]. Root-zone soil moisture dynamics and runoff generation processes within mHM are conceptualized similar to those of the HBV model [Bergström, 1995]. Actual evapotranspiration from soil layers is estimated as a fraction of potential evapotranspiration (PET) depending on the soil moisture stress and fraction of vegetation roots. The total runoff (interflows and base flow) produced at every grid cell is routed to its neighboring downstream cell using the Muskingum routing algorithm. For full details regarding model physics, the reader is referred to Samaniego et al. [2010b]. To date, the mHM model has been successfully applied to several river basins in Germany, ranging in size from 4 to 47,000 km2 [Samaniego et al., 2010a, 2010b; Kumar et al., 2010; Samaniego et al., 2013; Kumar et al., 2013].

[9] In contrast with most hydrologic models, mHM explicitly takes into account the subgrid variability of input data into model parameters. It uses three levels of gridded information to better represent the spatial variability of basin physical characteristics, modeled state variables, and meteorological forcing data [Samaniego et al., 2010b]. The level most relevant to this experiment is the lowest (i.e., finest scale) level, referred to level-0, which contains information on morphological variables (e.g., terrain elevation, slope, soil textural properties and geological characteristics, etc.) and land cover states and related characteristics (e.g., leaf area index). The cell size at this level varies from 100 to 1000 m. The second level, referred to level-1, is used to model the dominant hydrological processes mentioned above. The cell size at this level varies from 2 to 100 km. The third level, referred to level-2, is used to describe the variability of the meteorological forcing variables (e.g., precipitation, temperature, etc.). The cell size at this level is greater than or equal to 2 km.

[10] The key to the efficacy of the mHM framework is through coupling with the multiscale parameter regionalization (MPR) technique [Samaniego et al., 2010b; Kumar et al., 2013]. MPR first estimates about 20 model soil parameters (β0) at the finest scale (i.e., level-0) via a series of pedo-transfer functions, wherein a set of regional transfer coefficients (or global calibration parameters, γ = 52) links model parameters (β0) to basin physical characteristics (e.g., terrain slope, sand and clay contents, bulk density, etc.). The term “global parameters” here refers to a set of regional coefficients applicable to all grid cells over the entire modeling domain, and, hereafter, this term is used in this study to be consistent with earlier works on MPR [Samaniego et al., 2010a, 2010b; Kumar et al., 2010; Samaniego et al., 2013; Kumar et al., 2013]. Global parameters (γ) in hydrologic literature are also referred as “transfer function parameters” [Hundecha and Bárdossy, 2004; Götzinger and Bárdossy, 2007; Singh et al., 2012] or “super-parameters” [Pokhrel et al., 2008]. In the subsequent step, the effective fields of required model parameters at level-1 (β1) are generated by upscaling their corresponding level-0 parameters (β0) using operators such as the arithmetic mean, the harmonic mean, among others. The two step MPR technique allows the model to not only account for the subgrid variability of input data but also to generate the effective fields of model parameter (β1) at several spatial resolutions using a same set of global parameters (γ), pedo-transfer (or regionalization) functions, and upscaling operators. Figure 1 shows a schematic representation of MPR for deriving the gridded estimates of effective parameter (i.e., porosity of top soil layer) at four spatial resolutions. For further details on MPR, the reader is referred to Samaniego et al. [2010b] and Kumar et al. [2013]. Their detailed studies were restricted to river basins in southern Germany. However, within that limited spatial domain, it was shown that it is possible to transfer global parameters with MPR to nearby catchments and to spatial scales other than those used during calibration, without a significant loss in model performance.

Figure 1.

Schematic representation of the MPR technique for generating the effective field of model parameter (porosity of top 20 cm soil layer) at coarser modeling scales (level-1, inline image) based on its fine scale estimate (level-0, inline image). Gridded estimate of inline image is obtained through pedo-transfer function (f) of Zacharias and Wessolek [2007] which links soil textural and land-cover properties (u) with a set of global parameters (γ calibrated in the Neckar basin, Germany). The coupling between inline image and inline image is established with an upscaling operator O which in this case is the harmonic mean [Zhu and Mohanty, 2002]. Spatial fields of inline image at four spatial resolutions (level-1) in the Ohio river basin (US) is used for this illustration.

2.2. Study Domain and Computational Savings Experiment

[11] The study domain is entirely composed of basins in the United States (Figure 2), with the exception of a central European Neckar river basin, located in south Germany, in which global parameters of MPR were initially estimated [Kumar et al., 2013]. The selected 80 US basins are located within the Ohio, Arkansas, and Red river basins and represent a wide range of physiographic and hydro-meteorological properties, with drainage area ranging from approximately 1000–525,800 km2. A short summary of major basin characteristics and model input data are provided in Tables 1 and 2, respectively.

Figure 2.

Location and relative size of study basins overlain upon a digital elevation model. Location of (left) 80 US river basins, and (right) the Neckar river basin (Germany).

Table 1. Summary Statistics for Selected Physiographical and Hydrometeorological Characteristics for 80 US River Basins (21 Located Within the Arkansas and Red River Basins, 59 in the Ohio River Basin)a
Basin CharacteristicsNeckarArkansas and RedOhio
  1. a

    Additionally, the basin characteristics for the Neckar river basin (Germany) are also provided. Hydrometeorological characteristics are compiled with data sets corresponding to the period 1979–2008. Percentage of land covers, with respect to the basin area, is based on data of year 1993 and 2001 for the Neckar and US river basins, respectively.

Drainage area (km2)12,70010305190409,60010403535525,800
Mean slope (%)
Mean aspect (%)175145165210130190240
Forest cover (%)372127306198
Permeable cover (%)542849423499
Mean sand content (%)
Mean clay content (%)46.525.031.542.017.025.540.0
Mean annual runoff (mm)36044188536321459759
Mean annual precipitation (mm)910569873134796011101412
Mean annual temperature (°C)8.812.714.817.17.311.315.2
Runoff coefficient0.
Aridity index1.
Table 2. Description of Input Data Required to Set Up mHM
  1. a

    Potential evapotranspiration is estimated with the Hargreaves and Samani [1985] method.

  2. b

    BGR: Federal Institute for Geosciences and Natural Resources, Germany.

  3. c

    BUEK: Bodenbersichtskarte der Bundesrepublik Deutschland.

  4. d

    CGIAR-CSI: Consortium for Spatial Information.

  5. e

    DEM: Digital Elevation Model.

  6. f

    DWD: German Weather Service.

  7. g

    LUBW: State Institute for Environmental Protection Baden-Württemberg, Germany.

  8. h

    MRLC: Multiresolution Land Characterization.

  9. i

    iNLDAS-2: North American Land Data Assimilation System Phase 2.

  10. j

    jNRCS: Natural Resources Conservation Service.

  11. k

    kSRTM: Shuttle Radar Topography Mission.

  12. l

    lSTATSGO2: Digital General Soil Map of the United States—State Soil Geographic data set.

  13. m

    mUSDA: United States Department of Agriculture.

  14. n

    nUSGS: US Geological Survey.

Meteorological forcing inputs (precipitation, air temperature, and potential evapotranspiration)aUSHourly NLDAS-2 data at 1/8° resolutionXia et al. [2012b], NLDAS,i
 NeckarDaily DWDf data (905 rain-gauges and 302 weather stations), interpolated at 8 km resolutionKumar et al. [2013]
Terrain characteristics (e.g., elevation, slope, aspect, flow direction, and flow accumulation)USSRTMk 90 m DEMe data, resampled to 1/128° (≈°800 m) resolutionCGIAR-CSId,
 NeckarDEM data at 50 m resolution, resampled to 100 m resolutionLUBWg,
Soil data set (e.g., sand and clay content, bulk density, and depth of different soil horizons)USSTATSGO2l at a scale of 1:250,000, resampled to 1/128° (≈°800 m) resolutionUSDA-NRCSm, j ssurgo/description_statsgo2.html/
 NeckarBUEKc at a scale of 1:1000,000, resampled to 100 m resolutionBGRb,
Land cover (e.g., major class: forest, permeable, and impervious cover)US30 m National Land Cover Database (2001), resampled to 1/128° (≈°800 m) resolutionMRLCh,
 Neckar30 m LANDSAT-TM5 satellite image (1993), classified and resampled to 100 m resolutionSamaniego et al. [2008]
Geological formationsUSGround Water Atlas of the United States compiled by USGSl at a scale of 1:2,500,000, resampled to 1/128° (≈°800 m) resolutionNational Atlas of the United States, http://www.national
 NeckarGeological map at a scale of 1:600,000, resampled to 100 m resolutionLUBW
Discharge dataUSDaily observed streamflow from USGS. For some gauging stations in Arkansas and Red river basins, naturalized flows are provided by the US Army Corps of Engineers, Tulsa OK officeUSGS
 NeckarDaily observed streamflowLUBW

[12] The Neckar River basin (Figure 2) was used to estimate an initial set of global parameters since it was central to development of mHM and MPR [Samaniego et al., 2010b; Kumar et al., 2013]. Further, it possesses diverse and high quality meteorological data and other necessary physical characteristics such as soil textural and land cover properties that are essential for the estimation of global parameters (Table 2) (see Samaniego et al. [2010b] and Kumar et al. [2013] for more details).

[13] The goal here is to evaluate model performance with an a priori set of (pedo-) transfer functions and global parameters over a broad range of US river basins and spatial resolutions. We specifically sought conditions different from those used during the initial parameter estimation procedure, as well as any other conditions previously tested, i.e., over southern German river basins, 2–32 km spatial resolution [Samaniego et al., 2010b; Kumar et al., 2013]. It is worth noting that during the evaluation procedure, only the set of global parameters (or regional transfer coefficients) is transferred to a new modeling domain, rather than the gridded estimates of effective model parameters. The latter are generated by the two-step MPR procedure using a series of transfer functions, basin physical characteristics, and global parameters, as described above in section 2.1. (see also Figure 1 for more details). Furthermore, the transfer functions which link the model parameters to basin physical characteristics implicitly account for an implicit similarity measure which is essential for transferring information from a known condition to those only partially known. In our case, this implies that by using functional relationships defined a priori, any grid cells that share similar land surface properties (e.g., terrain, soil, and land cover characteristics) would correspondingly share similar model parameters by construct.

[14] The computational savings are subsequently computed by applying the global parameters to several new US basins that would ordinarily each require a separate calibration. The success of this parameter transfer is first assessed relative to spatial scale, through comparing simulated flows with observations after upscaling (to 1° ≈ 100° km pixel size) and downscaling (to 1/8° ≈ 12.5° km pixel size) model spatial resolution. The computational savings of the scaling exercise are evaluated at this stage. The required meteorological forcing inputs at coarser spatial resolutions (e.g., at 1°) were estimated by aggregation of the available 1/8° data (Table 2) such that mass is conserved across spatial resolutions. We note that the aggregation scheme used here is consistent with previous studies assessing the impact of changes in spatial resolution on model simulations [Koren et al.,1999; Haddeland et al., 2002; Boone et al., 2004; Liang et al., 2004; Stöckli et al., 2007; Troy et al., 2008; Samaniego et al., 2010b]. One implicit disadvantage of this aggregation scheme is the loss of spatial variability at coarser resolutions (e.g., 1°), which may influence the simulated water fluxes and states (as described latter in the results part in detail).

[15] Next, the parameter transfer is analyzed with respect to climate and land cover features (i.e., soil, vegetation, and topography) by applying the global parameters to a series of smaller tributary catchments (Figure 2), which are a subset of the model parameter estimation experiment (MOPEX) data set [Schaake et al., 2006], screened for adequate precipitation gauge density and minimal anthropogenic impacts such as upstream regulation, like irrigation and other consumptive uses. These catchments span a range of climate and land cover conditions (Table 1) that allow for an examination into the success of parameter transfer relative to gradients of basin climatic and physical features (e.g., runoff coefficient, terrain slope, % clay content, and % forest cover). In this case, model simulations were conducted at 1/8° spatial resolution, consistent with the scale of meteorological data sets (Table 2). Model skill scores are presented via the Nash-Sutcliffe coefficient (NSE) [Nash and Sutcliffe, 1970] metric,

display math(1)

where Qo(t) and Qs(t) are the observed and simulated values at each time step (t), inline image is the observed mean, and n is the total number of time steps. NSE is useful in comparing interbasin performance, since it normalizes the mean squared error, MSE, by the observed variance, inline image, of each basin. An NSE value of 1 corresponds to a perfect model fit to observations, while any value less than 0 describes a model simulation that performs worse than simply using inline image as the predictor.

[16] In all analyses, the internal mHM runs were carried out at 3 hourly time step for the period 1979–2008 (consistent with the availability of meteorological inputs), while streamflow observations and model skill scores were computed at monthly, weekly, and daily time steps. These time steps are consistent with those used in the recent study by Xia et al. [2012a] for reporting the performance of different models participating in the second phase of the North American Land Data Assimilation System project (NLDAS-2); the meteorological forcing data set used in this study (Table 2).

3. Results and Discussion

3.1. Impacts of Spatial Resolutions on Streamflow

[17] A comparison of observed and simulated hydrographs is shown in Figure 3 for three large US basins corresponding to the Ohio river at Metropolis, the Arkansas river at Little Rock, and the Red river at Index gauging station. The simulations were made using global parameters that were estimated over the Neckar river basin at 8 km (≈ 1/12°) spatial resolution, and were then transferred to each basin and scaled to a range of spatial resolutions (1/8°, 1/4° 1/2°, and 1°) to test the robustness of the parameter transfer. Model performance for each scale is listed in Table 3, revealing only modest differences in NSE skill (less than 3%) across scales, despite scaling more than 10 times the original calibration resolution (from 1/12° to 1°). The comparable performance of the model across spatial resolutions further corroborates that semidistributed parameterizations of hydrologic models are capable of producing discharge estimation efficiency that is comparable with distributed models [Smith et al., 2004, 2012]. The problem with the semidistributed or lumped parameterizations stems from the fact that they do not readily allow the transferability of effective parameters calibrated in a given sub-basin to others. This is the reason why practitioners need frequent recalibration of their models when they are applied to different spatial domains. The MPR technique, on the contrary, allows to make reliable predictions on any sub-basin or scale of interest with a minimal effort because the required effective model parameters (at level-1) are always estimated based on the underlining subgrid information (level-0) using the same set of global parameters, upscaling operators, and regionalization functions (see Figure 1 for details). It is worthwhile mentioning that even distributed hydrologic models that do not account for the subgrid variability would perform poorly when applied at spatial resolutions other than those used during calibration of global parameters, and thus require a computationally extensive recalibration [Samaniego et al., 2010b; Kumar et al., 2013].

Figure 3.

Comparison of observed and simulated monthly flows using a consistent set of global parameters (derived in the Neckar basin) applied at four spatial resolutions (1/8°, 1/4°, 1/2°, and 1°) for the (a) Ohio, (b) Arkansas, and (c) Red river basins.

Table 3. Model Performance (NSE) for the Monthly, Weekly, and Daily Simulated Streamflows at Four Spatial Resolutions Over Three Large US River Basinsa
Spatial ResolutionRedbeArkansasceOhiod
  1. a

    The number of grid cells corresponding to the selected spatial resolution is also shown, as a reference global parameters estimated in the Neckar river basin at 8 km (≈ 1/12°) used 248 grid cells.

  2. b

    Red river basin at Index (124,320 km2) with naturalized flows.

  3. c

    Arkansas river basin at Little Rock (409,600 km2) with naturalized flows.

  4. d

    Ohio river basin at Meteropolis (525,800 km2) with observed flow (USGS).

  5. e

    Naturalized streamflow data from the US Army Corps of Engineers, Tulsa OK office.

Monthly Flows
(1/8 × 1/8)°9030.8628600.8236880.89
(1/4 × 1/4)°2530.867640.839730.89
(1/2 × 1/2)°730.852150.842630.88
(1 × 1)°240.85630.84740.88
Weekly Flows
(1/8 × 1/8)°9030.7828600.8136880.85
(1/4 × 1/4)°2530.787640.819730.85
(1/2 × 1/2)°730.782150.812630.85
(1 × 1)°240.77630.82740.85
Daily Flows
(1/8 × 1/8)°9030.6628600.8036880.83
(1/4 × 1/4)°2530.667640.809730.83
(1/2 × 1/2)°730.652150.812630.82
(1 × 1)°240.65630.81740.82

[18] The performance of mHM is satisfactory at all four spatial resolutions; however, its skill (NSE) deteriorated when moving from the monthly (0.82–0.89) to the weekly (0.77–0.85) to daily time scales (0.65–0.83), with an average NSE score of approximately 0.86, 0.81, and 0.76, respectively. Other performance metrics such as the relative bias with respect to observed mean discharge are within ±10% of one another, while the correlation coefficients are on average, greater than 0.89 at three time scales, which are in agreement with the recent findings of Xia et al. [2012a]. The overall performance of mHM with transferred parameters could be rated as “very good,” or “good,” according to the criteria given by Moriasi et al. [2007], or by Martinez and Gupta [2010], respectively. Furthermore, the results obtained here are comparable to those achieved in previous studies conducted over a common study domain [e.g., Abdulla et al., 1996; Lohmann et al., 1998; Maurer et al., 2002; Haddeland et al., 2002; Lohmann et al., 2004; Wang et al., 2008; Troy et al., 2008; Santhi et al., 2008; Livneh and Lettenmaier, 2012; Xia et al., 2012a]. An important benefit of the MPR method is that no additional calibrations were required for any of the simulations.

[19] The simulated streamflows in the Ohio basin are shown to be slightly less sensitive to scaling than the Arkansas and the Red river basins (Figure 3). The transferred parameters tend to overestimate the warm-season flows in the arid basins (Arkansas and Red, respectively), and underestimate the cold-season flows in humid Ohio basin, irrespective of spatial resolution. These errors could be due to several factors, such as errors in meteorological forcing inputs (e.g., precipitation, temperature), model structure, and parameterization, i.e., base flow recession constants controlling the mHM linear reservoir were not calibrated, that could result in either too rapid or too slow a flow recession.

[20] The method used for estimating PET will also have a considerable influence on the model performance. For example in the Ohio river basin, changing the PET estimate from the Hargreaves and Samani method [Hargreaves and Samani, 1985] to the monthly climatology-based, vegetation adjusted, pan evaporation (PE) data set from NOAA-NWS [Farnsworth and Thompson, 1982; V. Koren et al., unpublished report, 1998] improves streamflow performance from a NSE value of 0.88–0.93, respectively. Santhi et al. [2008] noticed an improvement in the streamflow simulations (with the SWAT model) by calibrating the empirical coefficient of the Hargreaves and Samani method in the Ohio river basin. Also, in second phase of the North American Land Data Assimilation System project (NLDAS-2), Xia et al. [2012a, 2012b] reported a considerable improvement in performance of the SAC-SMA model, which, in part, was related to the changes in PET estimates from the NOAH model-based PE to monthly climatologically based PE data sets from NOAA-NWS. Despite the lower model performance obtained with the Hargreaves and Samani method, it was still used in this study so to maintain a consistent estimate of PET across all basins, including the Neckar river basin where the global parameters were initially estimated.

[21] The computational savings associated with using MPR for running the model at four spatial resolutions are illustrated in Figure 4 for the Ohio river basin. This reduction in computational expense is based on the quasi-scale independence of model performance for simulated streamflows. Therefore, it follows that if one were to use MPR to calibrate global parameters at a new basin of interest, they could conceivably calibrate the model at the coarsest resolution (i.e., 1°), while obtaining performance comparable to the finest resolution (i.e., 1/8°). The reduction in computational time for this case of approximately 64% is not equal to the ratio of spatial resolutions (1/64, or a reduction of roughly 98%) because MPR references and upscales parameters from the finest grid mesh (i.e., STATSGO2 data at 1/128°) to the required modeling resolution (e.g., 1°) for each simulation, which requires additional processing time.

Figure 4.

Illustration of the relative computation time required to run mHM at several spatial resolutions for the Ohio river basin, normalized by the time required for the 1/8° simulation. The number of grid cells for each spatial resolution is also shown. The lack of a geometrical relationship is due to MPR referencing fine resolution data (level-0 at 1/128°) needed to compute model parameters for each coarser spatial resolution.

[22] It is important to reiterate the key to the efficacy of the MPR scaling method, namely that required soil or vegetation parameters (e.g., porosity, maximum interception storage capacity) are derived by first referencing the finest available data (level-0), which, for example, in this study is based on the STATSGO2 soil or MRLC land-cover databases at 1/128° (≈ 800 m) spatial resolution (Table 2). In this way, effective parameters at each modeling scale (e.g., 1°) are always derived from a consistent level-0 data field (see, e.g., Figure 1 for estimating the effective porosity fields at four modeling scales using MPR). Upscaling is done only after parameter fields are derived at the finest scale (i.e., using global parameters and transfer functions), rather than the more conventional method of first computing a dominant or average data field at the coarser scale of interest.

3.2. Impacts of Spatial Resolutions on Distributed Water Fluxes and States

[23] Figure 5 illustrates the impact of changing spatial resolutions on five distributed water fluxes and states, namely, evapotranspiration, root-zone soil moisture, snow melt, groundwater recharge, and total runoff, over the Ohio, Arkansas, and Red river basins. The sensitivity of the simulated variables to spatial aggregation is quantified as the deviation in their overall estimate at coarser resolutions (e.g., 1°) from their corresponding estimates at finer resolution (1/8°) considered here as the reference value. In general, simulated water fluxes and states over the more arid Arkansas and Red river basins appear more sensitive to spatial aggregation than those over the more humid Ohio river basin (Figure 5). For example, the total runoff and groundwater recharge rates simulated at 1° resolution in the Arkansas-Red river basins are approximately 7 and 5% lower than at 1/8° resolution, whereas the same scaling over the Ohio basin results in changes of approximately 2.5 and 1.1%, respectively. Evapotranspiration in all three basins, on the contrary, exhibited an increase of nearly 1.8% at 1° resolution, compared to its finer 1/8° estimate; the absolute value of this increase compensates for decreasing total runoff at coarser resolution.

Figure 5.

Percent changes in simulated water fluxes and state variable at coarser scales (e.g., 1°) with respect to their corresponding estimates at finer scales (e.g., 1/8°) over the (a) Ohio, (b) Arkansas, and (c) Red basins using the global parameters calibrated in the Neckar river basin. (d) The long-term averages of daily water fluxes and soil moisture simulated at 1/8° spatial resolution over the entire modeling period (1980–2008).

[24] Most of these changes at coarser scales are mainly due to the smoothness of the meteorological forcing fields. This implies that spatially aggregated precipitation resulted in reduced variability of distributed precipitation fields, thus reducing simulated runoff at coarser scales. It follows that the more uniform precipitation fields along with the aggregated soil and vegetation parameters lead to reduced soil moisture variability at coarser resolutions, which may subsequently enhance evapotranspiration due to better accesses of vegetation to soil water content (i.e., soil water remains longer in the top-soil layers). More arid regions like the Arkansas and Red river basins where evapotranspiration is limited by soil water availability, subsequently exhibited greater sensitivity to spatial aggregation than more humid areas where evapotranspiration is predominantly energy limited. On the other hand, the smooth topography and ensuing temperatures at coarse scales which serves to reduce the snowpack near the snow-line, lead to altered snowpack evolution during the cold season. This reduction is directly attributed to the lack of subgrid terrain variation (or elevation bands) at coarser resolutions in the present model version. We found the sensitivity of the mHM simulated water fluxes and states to changes in spatial resolutions, qualitatively similar to those reported in previous scaling studies with different hydrologic and land-surface models [Koren et al., 1999; Haddeland et al., 2002; Boone et al., 2004; Liang et al., 2004; Stöckli et al., 2007; Troy et al., 2008; Zhao et al., 2013]. Although, one-to-one comparison of results is not possible due to the differences in study area, data sets, time period, and model structure, among other experimental settings and goals of each study, our modeling results using the MPR scheme indicated a significantly reduced sensitivity of simulated variables to spatial aggregation (almost by half) compared to previous studies, for example, over the Arkansas-Red river basin with the VIC model by Haddeland et al. [2002].

[25] To further analyze the relative contribution of the spatial aggregation of meteorological forcings and soil and vegetation parameters for the study domain, additional model simulations were carried out with identical settings for which mHM was run at 1/8° resolution with meteorological forcing data at this resolution, but with uniformly disaggregated parameter fields from coarser resolutions (i.e., e.g., all grid cells (up to 64) at 1/8° covering a 1° cell were allocated with same parameters). Results of this analysis (not shown here) confirmed that aggregating meteorological forcings, had greater influence over simulated variables at coarser resolutions, as compared with aggregating parameter fields. The total runoff, for instance, simulated with the disaggregated parameter fields of 1° resolution over the Ohio and the Arkansas-Red river basins was around 1 and 3% lower than that obtained with the 1/8° parameter fields, respectively. Other simulated variables such as evapotranspiration, snow melt, and soil water content also exhibited a reduced sensitivity (≈ 1–2% changes) to spatial aggregation, compared to a baseline analysis shown in Figure 5. In conclusion, nearly two thirds of the scale sensitivity of simulated variables at coarser resolutions is due to smearing of precipitation and temperature fields, whereas the remaining sensitivity can be attributed to the subgrid variability of soil and vegetation parameters. Arid regions like the Arkansas-Red river basins exhibit larger sensitivity than humid ones like the Ohio basin.

3.3. Parameter Transfer Across Climatic and Land-Cover Gradients

[26] The runoff coefficient, Rc, is a useful measure of basin response, associated with climate [Wagener et al., 2007], and given as the ratio of total discharge with incident precipitation. Basins are further classified based on soil characteristics (% clay content), vegetation type (% forest cover), and topography (average terrain slope). Figure 6 illustrates the success of parameter transfer (i.e., from the Neckar) to US basins in terms of model performance (NSE) versus basin characteristics. Performance is expectedly worse for basins with transferred parameters, compared to what would be attainable through local calibration; however, appreciable computational savings are obtained by avoiding an intensive parameter search. On average, the NSE values for monthly, weekly, and daily streamflows were approximately 0.79, 0.74, and 0.64, respectively. Other statistical criteria such as the correlation coefficient for these time scales was on average greater than 0.88, and the relative bias was within ±20% for 90% of the basins. Overall these results imply that the simulations with transferred parameters capture the temporal dynamics of the observed flows reasonably well, albeit the skill of the model improves with coarser temporal resolution. Considering the NSE criterion of greater than 0.40, according to Xia et al. [2012a], the model simulations can be considered useful in all basins for monthly and weekly streamflow, and in 77 basins out of 80 basins for daily streamflow.

Figure 6.

Model performance in terms of NSE for 80 US basins using global parameters received from the Neckar R. (shown in black filled circle). (top) Monthly streamflow. (middle and bottom) Weekly and daily streamflows. Dashed lines denote the average skill scores for 4 bins, each consisting of 20 ensemble members (i.e., basins) sorted by the selected basin physical characteristics.

[27] In general, model performance deteriorated when moving away from the climatic and physiographical conditions under which calibration was performed as shown in Figure 6. Performance appears relatively stable with respect to climate. Rc values ranging between 0.08 and 0.43 (i.e., from more arid to more humid regions), corresponding with average NSE scores of 0.82, 0.75, and 0.66 for monthly, weekly, and daily streamflows, respectively. Model skill declined by approximately 10–15% in most humid basins (Rc greater than 0.5), which are predominantly high elevation, headwater basins (of the Ohio river) within the Appalachian Mountain range. Performance for these cases may suffer due to the lack of a detailed snow parameterization (i.e., mHM uses a simple degree-day snow model, without consideration for subgrid elevation bands), as well as potential errors in the meteorological forcing data that includes both precipitation and potential evapotranspiration estimates. A recent study conducted by Martinez and Gupta [2010] over the CONUS found comparatively higher errors in modeled flow for basins on the western slope of the Appalachian Mountains, relative to those of the nearby basins.

[28] In terms of basin physical characteristics, increasing clay content corresponds to increasing model performance, while the opposite is true for increasing terrain slope and forest cover (Figure 6). Land cover exhibits a clear relationship with parameter transferability, such that basins approaching 100% forest coverage tend to perform worse than areas that with less forest coverage. This result is consistent with the lack of calibration of vegetation parameters, such that basins where vegetation dominates hydrologic response receive least benefit from transferred global parameters. Coincidentally, the poorest performing basins have among the highest Rc values and lowest clay contents, making their hydrologic response considerably different from the conditions under which parameters were calibrated (i.e., in the Neckar river basin).

[29] To further analyze the relationship between model performance and selected climatic and physical characteristics, average NSEs were computed via binning all available basins in four equally sized classes (i.e., 20 basins per class) for each characteristic separately. The resulting bins are displayed in Figure 6 as dashed lines. The average range in NSE is on the order of (0.71–0.83), (0.67–0.77), and (0.60–0.68) for monthly, weekly, and daily streamflows, respectively. On average over the three time scales, forest cover exhibited a largest control on NSE scores corresponding to their maximum and minimum classes (0.14), followed by the terrain slope (0.12), and finally runoff coefficient and clay content; both with differences in their NSE scores of 0.11. It should be noted that most of the basin characteristics are cross correlated with each other. For instance, forest cover is highly correlated with both terrain slope (r = 0.82) and runoff coefficient (r = 0.67).

3.4. Model Performance Using Global Parameters Calibrated in a US Basin

[30] A final experiment was made to assert whether the quality of parameter transfer is biased toward the conditions under which the global parameters were initially estimated (i.e., calibrated). To this end, an additional calibration was performed over the Red river basin (at the Index gauging station). Using a 1/4° spatial resolution, the Red river has roughly the same number of model grid cells (at level-1 with ≈250 grid cells) as the Neckar river basin (i.e., approximately the same computational load), while being considerably more arid. These new global parameters were subsequently transferred to all US basins and the fidelity of model simulations were evaluated in the same manner as the Neckar river parameter transfer experiment (sections 3.1. and 3.3.).

[31] Figure 7 and Table 4 summarize the results obtained for the scaling experiment similar to Figure 3 and Table 3, respectively. As expected, model performance improved over the Red river and in the nearby Arkansas river basin due to greater optimality of the new global parameters to local conditions (relative to those of the remote Neckar river). Particularly, low-flow errors during the warm season in both basins are reduced, and the model captures observed flow dynamics more closely. An interesting feature is that model performance in the more humid Ohio river basin was nearly unaffected by the new global parameters (derived over arid regions) relative to the previous global parameters. Differences in NSE scores for this basin with either set of global parameters (i.e., from the Neckar or the Red river basins) are less than 2.2%, with average NSE scores of approximately 0.90 and 0.82 for monthly and daily streamflow, respectively. The quasi-scale invariance performance of MPR is confirmed by the results presented in Table 4. At most, NSE scores differ by 2.3% (for the Arkansas river) across the range of spatial resolutions tested. Given that differences are nearly equal to those obtained with Neckar river parameters, it is reasonable to assert that the quasi-scale independence property of MPR global parameters for streamflow simulations is not biased to the calibration location.

Figure 7.

Same as Figure 3, except with global parameters derived over the Red river basin (versus the Neckar in Figure 3).

Table 4. Same as Table 3, Except With Global Parameters Calibrated Over the Red River Basin (Versus the Neckar River in Table 3).
Spatial ResolutionRedArkansasOhio
Monthly Flows
(1/8 × 1/8)°9030.9028600.8736880.90
(1/4 × 1/4)°2530.907640.889730.90
(1/2 × 1/2)°730.892150.892630.90
(1 × 1)°240.88630.89740.89
Weekly Flows
(1/8 × 1/8)°9030.8728600.8236880.85
(1/4 × 1/4)°2530.867640.829730.85
(1/2 × 1/2)°730.862150.812630.85
(1 × 1)°240.85630.82740.84
Daily Flows
(1/8 × 1/8)°9030.8128600.7836880.83
(1/4 × 1/4)°2530.817640.779730.82
(1/2 × 1/2)°730.802150.772630.82
(1 × 1)°240.79630.77740.82

[32] The effects of spatial aggregation on other distributed water fluxes and state variables with a new set of global parameters over three selected basins is shown in Figure 8. In general, the model exhibits similar deviations in simulated variables at coarser scales, as those obtained with the Neckar parameters (i.e., Figure 5). There is general tendency toward reduction in total runoff, snow melt, and groundwater recharge rates with increasing spatial resolution as a consequence of aggregation of the meteorological forcing data set. The more arid regions like the Arkansas and Red river basins once again display higher sensitivity to spatial aggregation as compared to the more humid Ohio basin. From the analysis presented above and shown in Figure 5 (with Neckar parameters) and Figure 8 (with Red parameters), it appears that the global MPR parameters, calibrated at different locations, have negligible impacts on the spatial aggregation of distributed water fluxes and state variables.

Figure 8.

Same as Figure 5, except with global parameters derived over the Red river basin (versus the Neckar in Figure 5).

[33] The new set of global parameters estimated in the Red river basin were further transferred to all US basins to investigate the impact of climatic and land cover gradients on model performance, similar to the analysis presented in section 3.3. Figure 9 generally shows similar relationships between the NSE scores and the selected basin characteristics as those of obtained with the Neckar parameters (i.e., Figure 6). Basins located in more humid regions with higher forest coverage and lower clay content exhibited, on average, a lower NSE values as compared to those of the other basins. Land cover (% forest cover) again appeared as the most dominant link with model performance, followed by terrain slope, runoff coefficient and finally clay content.

Figure 9.

Same as Figure 6, except with global parameters derived over the Red river basin (versus the Neckar in Figure 6).

[34] A slight improvement in model performance was observed using the global parameters calibrated over the Red river basin as compared to those obtained with the Neckar basin. For example, the NSE score for monthly streamflows with the Red river parameters was, on average, approximately 0.81, which is nearly 2.5% higher than those obtained with the Neckar parameters. The increase in NSE is largely due attributable to model performance improvements in the Arkansas and the Red river basins. Figure 10 shows a scatter plot contrasting model performance when using global parameters calibrated in either the Neckar or the Red river basin. Beyond the aforementioned improvements in model simulations using the new global parameters, an interesting feature of Figure 10 is that Ohio river basin simulations remained largely unaffected by the choice of global parameters, as they closely follow the 1:1 line particularly at the monthly and weekly time scale. On daily time scale, there is a slightly higher scatter of NSE values about the 1:1 line, although the general tendency of the model is to follow this equality. The resulting correlation coefficient (r) between the NSE pairs was, on average, greater than 0.90, which generally indicates a stable relationship, and further confirms the global parameter transfer for MPR, and the realization of meaningful computational savings.

Figure 10.

Direct comparison of model performance (NSE) obtained using global parameters derived over the more-humid Neckar river basin (horizontal axis) against those derived over the considerably more-arid Red river basin (vertical axis). Scatter plots correspond to the (a) monthly, (b) weekly, and (c) daily streamflow simulations.

4. Conclusions

[35] In this study, a set of parameter transfer experiments were conducted to investigate the fidelity of model performance at different spatial resolutions and over differing hydroclimatic conditions. Based on the results obtained for 80 US river basins with the mHM model parameterized with the MPR technique, the most notable findings are summarized as follows:

[36] 1. Global parameters of MPR estimated in a central European Neckar river basin are transferrable to remote large river basins (e.g., located in the United States) with modest loss in fidelity. Upscaling parameters to more than 10 times their estimated spatial resolution (i.e., from 1/12° to 1°) confirms that they are quasi-scale independent. However, the spatial aggregation of meteorological fields, bears notable influence on simulations of water fluxes and state variables at coarser resolutions, and the effects are more pronounced in arid regions (Arkansas and Red river basins) versus the humid regions (Ohio basin).

[37] 2. Computational savings of more than 50% are obtainable through MPR with a minimal loss of model performance. However, computational savings are not directly related to the ratio of model spatial resolutions because MPR references and upscales parameters from a much finer data field (level-0), which requires considerable processing time.

[38] 3. Transfer of global MPR parameters across climatic and land-cover gradients are less quasi-scale independent than for spatial upscaling or downscaling. This is attributable to (a) uncalibrated basin features, such as forest coverage, which differ greatly from those used in establishing functional relationships between model parameters and basin physical characteristics, (b) the lack of sophisticated model parameterizations to related to localized processes such as snow, and (c) potential errors in the forcing data such as potential evapotranspiration.

[39] 4. Global parameters from MPR are quite stable and do not appear biased relative to their calibration location. Reasonably, high model fidelity was obtained when applying global parameters to domains (or basins) other than those used during calibration.

[40] The analysis conducted in this study serves as a proof-of-concept for establishing the MPR regionalization technique over new spatial domains. Although the preliminary results obtained in US river basins were satisfactory, further improvements in model parameterization (e.g., to account for more detailed snow processes) and regionalization functions (to constrain the global parameters of MPR), are warranted to enhance parameter transferability over ungauged basins. In general, we observe a deterioration in model performance when moving away from the calibration location, and therefore caution should be exercised when applying global parameters to a new domain, regardless of size, climate, terrain, and land-cover conditions. Better model performance over new domains should be expected when applying a set of global parameters estimated in near similar conditions of basin physical and climatological characteristics. In this study, we present a preliminary investigation into the performance of mHM and MPR for streamflow simulations. However, further study is needed to explore the capability of the distributed mHM model for simulating other water fluxes and state variables such as soil moisture, snowpack, and evapotranspiration estimates. More research is also required to assess the potential of the MPR technique over different climates, land-cover conditions, as well as, to different land surface models. Currently, work is underway to extend MPR to additional study domains and to quantify the relative impact of using different forcing products from the variety of available input data sets such as those provided by Maurer et al. [2002] and Livneh et al. [2013].


[41] We would like to thank people from various organizations and projects for kindly providing us the data which were used in this study, which includes the DWD, LUBW, BGR, BGK, Germany, and the NASA, USDA, USGS, NRCS, NLDAS, CIGAS-CSI, MRLC, US Army Corps of Engineers, Tulsa OK office, USA. We appreciate the helpful comments from the Editor Hoshin Gupta, Martyn Clark, and three anonymous reviewers for their valuable suggestions and critiques, which helped us to improve this manuscript.