The Use of Similarity Concepts to Represent Subgrid Variability in Land Surface Models: Case Study in a Snowmelt-Dominated Watershed

Andrew J. Newman National Center for Atmospheric Research,* Boulder, Colorado

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Martyn P. Clark National Center for Atmospheric Research,* Boulder, Colorado

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Adam Winstral Northwest Watershed Research Center, Agricultural Research Service, U.S. Department of Agriculture, Boise, Idaho

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Danny Marks Northwest Watershed Research Center, Agricultural Research Service, U.S. Department of Agriculture, Boise, Idaho

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Mark Seyfried Northwest Watershed Research Center, Agricultural Research Service, U.S. Department of Agriculture, Boise, Idaho

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Abstract

This paper develops a multivariate mosaic subgrid approach to represent subgrid variability in land surface models (LSMs). The k-means clustering is used to take an arbitrary number of input descriptors and objectively determine areas of similarity within a catchment or mesoscale model grid box. Two different classifications of hydrologic similarity are compared: an a priori classification, where clusters are based solely on known physiographic information, and an a posteriori classification, where clusters are defined based on high-resolution LSM simulations. Simulations from these clustering approaches are compared to high-resolution gridded simulations, as well as to three common mosaic approaches used in LSMs: the “lumped” approach (no subgrid variability), disaggregation by elevation bands, and disaggregation by vegetation types in two subcatchments. All watershed disaggregation methods are incorporated in the Noah Multi-Physics (Noah-MP) LSM and applied to snowmelt-dominated subcatchments within the Reynolds Creek watershed in Idaho. Results demonstrate that the a priori clustering method is able to capture the aggregate impact of finescale spatial variability with O(10) simulation points, which is practical for implementation into an LSM scheme for coupled predictions on continental–global scales. The multivariate a priori approach better represents snow cover and depth variability than the univariate mosaic approaches, critical in snowmelt-dominated areas. Catchment-averaged energy fluxes are generally within 10%–15% for the high-resolution and a priori simulations, while displaying more subgrid variability than the univariate mosaic methods. Examination of observed and simulated streamflow time series shows that the a priori method generally reproduces hydrograph characteristics better than the simple disaggregation approaches.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Andrew Newman, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. E-mail: anewman@ucar.edu

Abstract

This paper develops a multivariate mosaic subgrid approach to represent subgrid variability in land surface models (LSMs). The k-means clustering is used to take an arbitrary number of input descriptors and objectively determine areas of similarity within a catchment or mesoscale model grid box. Two different classifications of hydrologic similarity are compared: an a priori classification, where clusters are based solely on known physiographic information, and an a posteriori classification, where clusters are defined based on high-resolution LSM simulations. Simulations from these clustering approaches are compared to high-resolution gridded simulations, as well as to three common mosaic approaches used in LSMs: the “lumped” approach (no subgrid variability), disaggregation by elevation bands, and disaggregation by vegetation types in two subcatchments. All watershed disaggregation methods are incorporated in the Noah Multi-Physics (Noah-MP) LSM and applied to snowmelt-dominated subcatchments within the Reynolds Creek watershed in Idaho. Results demonstrate that the a priori clustering method is able to capture the aggregate impact of finescale spatial variability with O(10) simulation points, which is practical for implementation into an LSM scheme for coupled predictions on continental–global scales. The multivariate a priori approach better represents snow cover and depth variability than the univariate mosaic approaches, critical in snowmelt-dominated areas. Catchment-averaged energy fluxes are generally within 10%–15% for the high-resolution and a priori simulations, while displaying more subgrid variability than the univariate mosaic methods. Examination of observed and simulated streamflow time series shows that the a priori method generally reproduces hydrograph characteristics better than the simple disaggregation approaches.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Andrew Newman, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. E-mail: anewman@ucar.edu

1. Introduction

Spatial variability in land surface and hydrologic processes is driven by a myriad of factors and has both stochastic (random) and deterministic (nonrandom) components (Seyfried and Wilcox 1995). For example, in the Reynolds Creek catchment (Idaho, United States), variability in groundwater recharge and snow accumulation and melt are driven by vegetation, soil characteristics, and topography. Runoff and groundwater recharge are impacted by small-scale topographic differences while dominant patterns in snow are impacted by larger-scale topographic features (Seyfried and Wilcox 1995). For catchments in Australia, spatial variability in soil moisture depends on the moisture state of the catchment; in wet conditions topographic controls explain a majority of the variance, while in dry conditions the variance appears random in nature (Grayson et al. 1997; Western et al. 1999).

Spatial complexity is commonly represented in hydrologic models [and some land surface models (LSMs)] by using hydrologic similarity concepts to aggregate high-resolution information into similar areas (Beven and Kirkby 1979; Beven 1986; Sivapalan et al. 1987; Wood et al. 1988, 1990; Koster and Suarez 1992; Blöschl 2001). Many of these methods are univariate in nature; they use one spatially varying parameter to aggregate a catchment into a relatively few number of classes. For example, disaggregation into classes can be based on vegetation type (e.g., Avissar and Pielke 1989; Koster and Suarez 1992; Liang et al. 1994), elevation (e.g., Nijssen et al. 1997), or use of topographic indices such as the topographic wetness index (Beven and Kirkby 1979) or topographic soil index (TSI; Beven 1986; Sivapalan et al. 1987). As an illustration of the effectiveness of these approaches, Famiglietti and Wood (1994a,b) aggregated a catchment using TSI, applied a macroscale model, and showed good results compared to a spatially distributed model. These approaches are more generally termed mosaic schemes (e.g., Avissar and Pielke 1989; Koster and Suarez 1992) in the context of atmospheric mesoscale model land surface schemes, which treats a catchment as being composed of various subgrid tiles that each have distinct differences in their land surface or hydrologic attributes. In LSMs, it is common to assume that the subgrid tiles have negligible interaction (e.g., no lateral flow of water among subgrid tiles), and the gridcell-mean conditions are simply a fractional sum of all the subgrid tiles (Avissar and Pielke 1989; Koster and Suarez 1992).

While the mosaic approach is an improvement over homogeneous (lumped) assumptions (Pielke and Mahrer 1975; Deardorff 1978; McCumber and Pielke 1981), disaggregation focused on one or two topographic-based characteristics may neglect a large percentage of spatial variability for any given variable (e.g., soil moisture; Western et al. 1999). Also, spatial patterns may repeat or be time independent for ecologically or hydrologically influential variables like soil moisture, snow depth, and snow duration (Western et al. 2001; Deems et al. 2008; Ivanov et al. 2008; Sturm and Wagner 2010; Schirmer et al. 2011; Schirmer and Lehning 2011). However, even these repeatable patterns are likely not completely described by one or two physiographically derived parameters (Western et al. 1999; Winstral et al. 2002; Sturm and Wagner 2010; Schirmer et al. 2011). For example, spatial patterns in snow water equivalent (SWE) are shaped by many processes operating over a hierarchy of spatial scales (M. P. Clark et al. 2011). Therefore, multivariate mosaic approaches may be better suited to represent subgrid spatial complexity.

The purpose of this paper is to use the well-known concepts of hydrologic similarity and representative elementary areas or hydrologic response units (HRUs; Beven and Kirkby 1979; Leavesley et al. 1983; Sivapalan et al. 1987; Wood et al. 1988, 1990; Kouwen et al. 1993; Flügel 1995; Famiglietti and Wood 1995; Pomeroy et al. 2007; Das et al. 2008; Viviroli et al. 2009; Fiddes and Gruber 2012; Fang et al. 2013) and apply them to surface physiographic parameters to improve representation of subgrid variability in LSMs in atmospheric mesoscale models. Improved representation of subgrid variability may improve fully coupled atmospheric–LSM simulations (Li et al. 2013). Also, extending the definition of representative elementary areas or HRUs to be noncontiguous and to use an objective and unsupervised method will improve the generalization of the HRU concept (i.e., Pomeroy et al. 2007; Fiddes and Gruber 2012).

Finally, we want to begin to move the LSM community to include more physically based representations of horizontal complexity. Figure 1 presents (summarized in Table 1) many current models used to model the myriad surface and subsurface processes in the hydrosphere via their vertical and horizontal complexity. In this case, vertical complexity refers to processes that are treated in a vertical column where the column is either the entire grid cell or the mosaic tiles. Models including processes like plant dynamics (growth, carbon uptake, interception, evapotranspiration, etc.), precipitation, radiation, and vertical infiltration have higher vertical complexity. Horizontal complexity refers to representation of the grid cell and processes between vertical columns. Models including HRUs or gridded, distributed models, which include processes like snow redistribution, overland flow, subsurface lateral flow, aquifer–river interaction, and channel routing, have higher horizontal complexity. LSMs tightly coupled to atmospheric models are typically vertically complex, but lack horizontal complexity (i.e., Noah-MP, JULES, and CLM; see Table 1 for full model names).

Fig. 1.
Fig. 1.

Subjective classification of existing hydrologic and land surface models in terms of their horizontal and vertical complexity. This classification is not meant to be exhaustive in its inclusion of models, nor is it meant to be definitive in “ranking” the complexity of the models. It is for illustrative purposes to show differences in model structure and process complexity.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

Table 1.

Summary of models included in Fig. 1 with reference to select model development paper(s).

Table 1.

The next section describes the catchments and LSM used, which is then followed by discussion of the high-resolution forcing datasets and simulation results. Next, the multivariate clustering technique is developed and several common catchment implementations are discussed. An intercomparison of the various methods for catchment-averaged variables and performance metrics for catchment streamflow are then presented. Finally, concluding remarks and future directions are given.

2. Data description

a. Reynolds Creek Experimental Watershed

The Reynolds Creek Experimental Watershed (RCEW) was chosen as the test basin for this proof of concept work because of the availability of long-term observations and high-resolution physiographic information. Two catchments within the RCEW are examined in this paper, the Reynolds Mountain East (RME) and Tollgate catchments. The RME catchment is a small snowmelt-dominated headwater catchment with an area of 0.38 km2, while the Tollgate catchment is a larger snowmelt-dominated catchment (54 km2). The RCEW with the Tollgate and RME catchments noted is shown in Fig. 2. Continuous forcing data are available from the start of water year (WY) 1984 through the end of WY 2008 at two instrumented meteorological sites within RME (Reba et al. 2011) and 16–20 sites for the same time period within the Tollgate catchment. For RME, a high-resolution, 10-m digital elevation map (DEM) with corresponding 10-m soil and vegetation data (Seyfried et al. 2009), outlet streamflow, and SWE surveys (Winstral and Marks 2014) are available. The RME and higher elevations of Tollgate reach their peak SWE around 15 February (Winstral and Marks 2014). The lower portions of Tollgate maintain an ephemeral snowpack that is generally snow-free at the time of peak SWE in the higher elevations (A. Winstral 2013, personal communication). For Tollgate, 30-m DEM, soil, and vegetation data are available. Precipitation data across RME and Tollgate are corrected using the dual-gauge approach (Hanson 1989; Hanson et al. 2004).

Fig. 2.
Fig. 2.

(a) RCEW with the RME and Tollgate catchments contoured in red and black, respectively. (b) Tollgate catchment with RME contoured in red. Black and blue plus signs in (b) indicate observations used in Tollgate forcing data generation; blue plus signs indicate observations used for RME only. The RCEW is located in southwestern Idaho.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

Vegetation, soils, and snow distributions exhibit considerable variability in the RME and Tollgate catchments. Six main vegetation types are present, ranging from grass to mountain sagebrush through riparian, aspen, and conifer stands. Six corresponding soil types are also defined with differences in soil depth, number of layers, and parameter values (e.g., saturated soil water content; Seyfried et al. 2009). SWE variability much larger than a factor of 2 has been documented in the RME catchment in previous studies with several known snowdrift and snow scour areas (Winstral and Marks 2002; Liston and Elder 2006a; Winstral et al. 2013). The soil, vegetation, and SWE differences combine to produce large variability in runoff generation across the RME (Seyfried et al. 2009) and Tollgate catchments.

b. Land surface model

A state of the art LSM, the Noah-MP (Niu et al. 2011) was chosen for this study. Noah-MP is a complex, physically based model that is a freely available community-developed LSM and includes multiple physics options for various processes (i.e., runoff, snow albedo, and stomatal resistance; Niu et al. 2011). Relevant to this study, the vegetation canopy is represented explicitly, and a “semi-tile” approach is used to represent differences in energy fluxes over vegetation and bare ground (Niu et al. 2011). Snow cover is treated via a multilayer approach with up to three layers possible, dependent on snow depth. Surface temperatures are solved via energy balance equations and the temperature profile throughout snow and soil is also predicted (Niu et al. 2011). These changes to representation of vegetation, snow physics, surface energy balance, and other areas in Noah-MP result in improved SWE, runoff, and flux estimates over the older Noah version 3 LSM (Niu et al. 2011).

While Noah-MP is vertically complex, its horizontal complexity is relatively simple when compared to a hydrologic model (Fig. 1). Noah-MP only considers a 1D column of soil and does not include surface or subsurface routing. Surface and subsurface runoff are included via one of four options: two TOPMODEL-based (Beven and Kirkby 1979; Sivapalan et al. 1987) approaches, one with a simple groundwater model (Niu et al. 2007) and one with an equilibrium water table (Niu et al. 2005); a Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1981; Dickinson 1984; Dickinson et al. 1986, 1993; Yang and Dickinson 1996) surface runoff formulation with free drainage; and a water balance model based on Schaake et al. (1996). In this work, the second TOPMODEL option is used. Examination of increasing the horizontal complexity of LSMs via vertical column interactions is the subject of ongoing research.

3. High-resolution simulations

With the availability of 10-m topography, vegetation, and soil data, very high–resolution simulations of the RME catchment are possible. Simulations on this grid represent the intrinsic variability in the RME catchment, understanding, of course, that some model parameterizations (e.g., fractional subgrid snow cover) are less applicable at this scale. Necessary forcing data are generated by distributing hourly data from the two long-term meteorological sites in the RME catchment across the 10-m DEM using the high-resolution meteorological forcing distribution system (MicroMet) module of SnowModel (Liston and Elder 2006a,b). SnowModel is a complete snow modeling system that models snow transport and snowpack evolution over various terrain and vegetation types (Liston and Elder 2006a). Within SnowModel, the MicroMet module uses quasi-physically based relationships to distribute temperature, relative humidity, wind speed and direction, short- (SW) and longwave radiation, pressure, and liquid equivalent precipitation across an arbitrary DEM (Liston and Elder 2006b).

a. Precipitation forcing data

While MicroMet distributes liquid equivalent precipitation across the catchment, the total water input to the land surface is actually the summation of liquid precipitation plus the net frozen precipitation, which is total frozen precipitation plus net snow transport. To arrive at the total water input used to drive Noah-MP, two different approaches are explored. For the first case, a long-term SnowModel simulation is performed on a 10-m grid spacing domain slightly larger than the RME catchment. The net transport is calculated at each RME grid cell for each WY simulated to determine a winter-average precipitation enhancement factor (PEF):
e1
where P is the total liquid equivalent precipitation for snowfall events [where partitioning between rain and snow uses the approach in the Snow Thermal Model (SNTHERM; Jordan 1991), as described by Jin et al. (1999)] and QT is the net snow transport for a 10-m grid cell. The SnowModel-derived PEF is then generated for each WY.
In the second case, the WYs 1990–2000 SnowModel output was used to give an average estimate of the RME catchment total water input. The estimated catchment net total water input from SnowModel is ~70% of the corrected sheltered gauge precipitation, meaning ~30% of the winter precipitation falling is transported out of the catchment or sublimated in situ via blowing snow sublimation. Then a linear regression model similar to that of Winstral et al. (2002), using only terrain-based parameters, was used to estimate the PEF across the 10-m domain:
e2
where β0, β1, and β2 are constants; Sx100 is a measure of sheltering index from Winstral et al. (2002); and D0 is a drift zone enhancement binary value (one in drifts, zero elsewhere) computed using the same metrics as Winstral et al. (2002) with slightly different thresholds. Essentially, Sx100 is a measure of how the upwind topography varies; it is positive when there is higher topography upwind of the point of interest and negative when there is only lower topography. Drift zones are sheltered areas downwind of topographic slope breaks that likely contain areas of deep snow drifts. While this definition of PEF requires the use of SnowModel, it provides a first attempt at determining an a priori PEF using field data or available estimates of snow accumulation in a catchment (see section 6 for further discussion). The resulting PEF function for areas with and without drifting versus Sx100 is shown in Fig. 3a, while Fig. 3b displays the PEF over the RME catchment. Drift and scour zones are also evident in Fig. 3b via enhanced or diminished PEF values. Both PEF functions are applied only for precipitation falling as snow as determined by using air temperature. When the air temperature is less than 0.5°C, precipitation is considered all snow, when it is greater than 2.5°C it is considered all rain. In between 0.5° and 2.0°C, there is a linear increase in the fraction of rain from 0 to 0.4. Between 2.0° and 2.5°C the fraction of rain is set at 0.4 [following SNTHERM (Jordan 1991), as described by Jin et al. (1999)].
Fig. 3.
Fig. 3.

(a) Frozen PEF for drift and no drift zones with (b) the spatial distribution of the frozen PEF in the RME catchment.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

b. Distributed results

Figure 4 illustrates spatial simulations on the 10-m grid from Noah-MP driven by WYs 2001–08 forcing data. The SnowModel-based PEF simulation uses the SnowModel WYs 2001–08 PEF values [Eq. (1)], while the terrain-based PEF simulation uses Eq. (2) constrained by the 1990–2000 bulk transport estimates. Total water input (TWI), maximum SWE, mean soil moisture for March–July, and total runoff (base flow plus surface runoff) for the two simulations highlight the intracatchment variability. Figure 4 (left) displays the distributed simulation using the terrain-based PEF [Eq. (2); the a priori PEF technique is denoted 10-apriori in the text], while Fig. 4 (right) displays the SnowModel-derived dynamic (changing in time) PEF [Eq. (1)] simulation, which is denoted 10-aposteriori. Several drift and scour zones are evident in both simulations (Figs. 4a–d), with the 10-apriori (10-aposteriori) simulation having a maximum TWI and maximum SWE of 1196 (1755) and 765 (1299) mm, while the mean 2001–08 catchment TWI (SWE) is 606 (343) and 677 (390) mm for the 10-apriori and 10-aposteriori simulations, respectively. The treatment of vegetation in 10-aposteriori is very apparent as well (Fig. 5a) with large areas of nearly constant TWI and maximum SWE corresponding to areas of forest that have large snow-holding depths, allowing for accumulation but little to no transport. In the 10-apriori simulation, only topographic considerations are made, which highlights topographically driven drift zones but may underestimate snowfall in forested regions due to the lack of snow-holding capacity impacts from vegetation.

Fig. 4.
Fig. 4.

High-resolution results using the (left) terrain- and (right) SnowModel-based precipitation multipliers. (a),(b) TWI (mm yr−1); (c),(d) max SWE (mm); (e),(f) March–July (MAMJJ)-average saturation soil moisture (%); and (g),(h) WY total runoff (mm yr−1). Values are the 2001–08 mean.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

Fig. 5.
Fig. 5.

(a) Vegetation class, (b) estimate of mean yearly surface incident SW down (W m−2) including terrain slope and aspect, (c) sheltering index, and (d) drift zones for the RME catchment.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

The mean percentage of saturation soil moisture distribution highlights the areas of different soil and vegetation types in both simulations (Figs. 4e,f). Drift zones (areas of high TWI or SWE) are apparent as well. Total runoff variations show influences of the previous three parameters (Figs. 4g,h). Areas of more runoff within the same soil type correspond to areas of higher TWI and soil moisture, while soils with more holding capacity have less runoff for a given TWI or SWE. Forested areas in the 10-aposteriori simulation have more total runoff than the 10-apriori simulation because of higher TWI. The 10-aposteriori simulation has larger maximum and mean runoff than the 10-apriori because of larger maximum and mean TWI. The distribution of runoff (and TWI and SWE) is more concentrated in the 10-aposteriori simulation, with the top 5% of runoff generating grid cells producing 11% more runoff in the 10-aposteriori simulation. Finally, both simulations agree with Seyfried et al. (2009) in that small areas of the grid can be considered runoff hotspots that generate a disproportionate amount of the catchment runoff.

c. Processes driving variability

Many processes drive the subcatchment variability seen in the high-resolution simulations. Most critically is snow redistribution, which produces the drift and scour zones seen in Figs. 4a and 4b, which impact the TWI variability in the catchment. Snow redistribution is controlled primarily by topographic and vegetative variations across the catchment (Winstral and Marks 2002; Liston and Elder 2006a) in conjunction with consistent synoptic storm patterns. Table 2 gives the snow-holding depth used for the SnowModel simulation for each vegetation class. Additionally, topographic and vegetative shading impacts melt rates across this catchment, many times with a negative correlation to snow depth (e.g., areas of deep snowmelt slowest; Marks et al. 2002).

Table 2.

Summary of the six vegetation types and some basic characteristics: leaf area index (LAI), stem area index (SAI), and vegetation snow depth–holding capacity in Noah-MP or SnowModel.

Table 2.

In regards to soil moisture and runoff generation, vegetative, soil, and snow redistribution processes act in concert to generate the observed and modeled variability. Accounting for the distribution in soil column depths, hydraulic conductivity, vegetation type, etc. gives rise to variable soil moisture patterns, runoff generation (Figs. 4e–h), and spring/summer sensible and latent heat flux variations (not shown). Zones of low soil water–holding capacity and less vegetative evapotranspiration demand generate more runoff and lower spring/summer-mean soil moisture for a similar TWI (Fig. 4). These runoff hotspots generate a disproportionate amount of runoff from this catchment and their representation is critical to properly simulate runoff (Seyfried et al. 2009).

d. Summary

High-resolution simulations of the RME catchment with Noah-MP contain much subgrid variability that is driven by many processes. Vegetation and soil variability combine with, for example, snow redistribution, vegetative evapotranspiration (ET) demand, and infiltration and percolation to produce complex patterns of total water input to the soil zone, soil moisture, runoff, and land–atmosphere energy fluxes that are important to represent in LSMs used in studies like Rasmussen et al. (2011). This complex variability contained in the high-resolution simulations is not easily accounted for by traditional univariate mosaic approaches used in current LSMs. The next sections discuss the uni- and multivariate mosaic approaches over RME and then scale the subgrid approaches up to a larger catchment, the Tollgate catchment, which contains several typical 3-km grid spacing (9 km2) mesoscale model grid cells.

4. Catchment disaggregation

a. Multivariate disaggregation

Most past and current mosaic disaggregation approaches are univariate; they use one land characteristic, commonly vegetation type or elevation, across all grid cells or watersheds. To incorporate a variable number of land parameters into a generalized and optimized watershed disaggregation framework, we make use of the k-means cluster analysis method as implemented in MATLAB following Seber (1984) and Späth (1985). The k-means cluster analysis method is a nonhierarchical clustering algorithm that minimizes the sum of data points to cluster centroid distances, summed over all clusters. This results in data clustering where the intracluster variability will be minimized and the intercluster variability will be maximized. The k-means method can have an arbitrary number of input vectors of arbitrary length and aggregate the input data into an arbitrary number of user-specified clusters. Processing of the input vectors is required to ensure each input vector gets the proper weighting. In this case, all input vectors are normalized by their maximum value, similar to Harrington et al. (1995), except for vegetation, which is left unnormalized and thus is the leading driver of cluster separation. Variable land characteristics (in number and parameter) may be used for each grid cell across the entire model domain, creating a generalized routine that provides optimized grid cell or watershed disaggregation via the k-means clustering method.

The 10-aposteriori simulation output for WYs 1990–2000 is used to determine an a posteriori disaggregation using land characteristics, forcing data fields and output from Noah-MP. Input fields for the k-means clustering were chosen via trial and error until a minimal number of inputs disaggregated the watershed in a manner that generated distinct cluster separation and gave a physically consistent catchment mosaic. The 10-aposteriori simulation of TWI (Fig. 4b) and total runoff (Fig. 4h) in combination with vegetation type (Fig. 5a) and surface incident–mean clear sky, shortwave down radiation loading (Fig. 5b) produced a subjectively optimal catchment disaggregation, in close agreement with the snow depth spatial variability clustering results of McCreight (2010). Disaggregation in the a posteriori case is allowed to vary for each WY (see Table 3) to account for the changes in total water and runoff distributions across the watershed between WYs. This is distinct from the other disaggregation types, all of which have static disaggregation maps and allow for an estimate of interannual variability of the subcatchment tiling. An example disaggregation map (WY 2000) for the a posteriori case is given in Fig. 6a. Note that the HRUs are not required to be contiguous in this case, similar to Pomeroy et al. (2007) and Fiddes and Gruber (2012).

Table 3.

General description of disaggregation type, forcing data, precipitation, and subcatchment tiles.

Table 3.
Fig. 6.
Fig. 6.

The k-means cluster membership with dominant vegetation type for the (a) a posteriori and (b) a priori disaggregations. Black contours denote drift zones from Fig. 5d.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

The second k-means clustering method was developed to mimic the mean a posteriori clusters using only a priori land characteristics (Fig. 6b) and to thus be applied in an objective and unsupervised manner with minimal preprocessing requirements (e.g., no requirement to first run a high-resolution model, as in the a posteriori approach). Land characteristics included in the a priori clustering are shown in Fig. 5 and can be determined prior to any integration of Noah-MP or models required to estimate snow transport and PEF (SnowModel in this case). The parameters for the a priori clustering are vegetation type (Fig. 5a), mean shortwave down (Fig. 5b), sheltering index (i.e., Sx100; Fig. 5c), and drift zones (i.e., D0; Fig. 5d; Winstral et al. 2002). These parameters were chosen because they capture a majority of the subcatchment variability in RME discussed in section 3 and previous work (Harrington et al. 1995; Winstral and Marks 2002; Seyfried et al. 2009). Each vegetation class has a unique soil type following Seyfried et al. (2009); sheltering index and drift zones have been shown to describe snowpack variability in the region (Winstral and Marks 2002; Winstral et al. 2002). Finally, mean shortwave down provides an index of topographic shading and available energy at each grid cell. The a priori mosaic approach is developed with the goal of inclusion into Noah-MP or any LSM supporting a mosaic subgrid scheme.

The a priori clustering based on physiographic information is (by definition) time invariant, which assumes that spatial patterns in hydrologic processes repeat from year to year (see, e.g., Western et al. 2001; Deems et al. 2008; Ivanov et al. 2008; Sturm and Wagner 2010; Schirmer et al. 2011; Schirmer and Lehning 2011). To evaluate the validity of this assumption, Fig. 7 illustrates the variability of the WYs 1990–2000 a posteriori cluster fractional catchment area for each water year, along with the static a priori cluster areas remapped to match the classifications of the a posteriori disaggregation. Note that the interannual variability in the a posteriori disaggregation is determined by the high-resolution 10-aposteriori simulation. Interannual variability among the drift classes [classified as drift sage (DS) and deep drift sage (DDS) in the a posteriori cluster map in Fig. 7] is substantial, almost a factor of 10 for the DDS area. The a priori disaggregation approach is within the envelope of the estimated interannual drift zone variability, suggesting it represents the mean effects of snow depth variability in the RME catchment.

Fig. 7.
Fig. 7.

Variation of fractional cluster area for the a posteriori method (various open and colored symbols) for the testing period (1990–2000) along with the static a priori area (filled black squares).

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

b. Common mosaic implementations

Three types of commonly used LSM subgrid disaggregation approaches were performed on the RME catchment, including 1) no disaggregation, 2) elevation bands, and 3) vegetation type disaggregation. Comparisons of the clustering methods to these disaggregation techniques illustrate how the multivariate mosaic approach compares to current approaches. Table 3 summarizes the important aspects of the common implementations, multivariate disaggregations, and the high-resolution simulations. The most basic disaggregation is a lump simulation (Lu), that is, no disaggregation, which treats the entire catchment or grid box as one point with big sage everywhere. Disaggregation using elevation bands (elevation in text) using three equally spaced (in elevation) bands (sage is the dominant vegetation in each elevation band) and vegetation type (vegetation in text) are the next levels of complexity. Elevation disaggregation for this catchment is likely not necessary (given the small elevation range), but it is a common disaggregation method and included for completeness. Figure 8 displays the elevation and vegetation disaggregation maps with the drift index overlaid. Comparing to Fig. 6, one can see that potential drift and shaded zones (from Figs. 5c,d) are combined within larger subgrid tiles in the elevation and vegetation approaches, which results in a loss of information. The a posteriori and a priori multivariate disaggregations capture the RME catchment variability better (Fig. 6) without significantly increasing the number of subcatchment tiles (8 and 11 simulation points compared to 3 and 6 for elevation bands and vegetation mosaic, respectively; see the drift clusters in both multivariate disaggregations).

Fig. 8.
Fig. 8.

RME disaggregation using (a) three equally spaced (in elevation) elevation bands and (b) vegetation type. Black contours denote drift zones as specified in Fig. 5d.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

Figure 9 displays box-and-whisker plots for SW down (Fig. 5b) and Sx100 (Fig. 5c) for the vegetation and a priori disaggregation approaches. The differences in sheltering are more defined in the a priori tiles (Figs. 9b,d), with a larger range of values between tile means and smaller interquartile ranges for each tile. In regards to SW down, there is again more spread among tile-mean values. In particular, the large variability in sage class is captured more completely in the a priori disaggregation for both SW down and sheltering index. Physically, the division of sage via sheltering index (ignoring drift sage) and SW down is important because of the fact that sage spans a large range of sheltering in RME. This results in a large range of TWI (Figs. 4a,b) across the sage in the catchment, which would not be captured treating it as one tile. Capturing the covariability of sheltering and energy input should help improve SWE, soil moisture, streamflow, etc. simulations, as will be shown below.

Fig. 9.
Fig. 9.

Box-and-whisker plots for estimated mean SW down (W m−2) and sheltering index for the (a),(b) vegetation and (c),(d) a priori disaggregations. Blue boxes denote the interquartile range, red line denotes the median value, notches in interquartile range around median denote 95% confidence interval of the median, whiskers denote the 10th–90th percentiles, and red plus signs denote outliers.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

c. Forcing data

To be consistent across disaggregation types, the MicroMet-derived distributed forcing data were used to derive the mosaic forcing data for each simulation regardless of disaggregation case. In other words, the mean of the distributed forcing data was used for the lump case and for each tile in the vegetation case, which is typical in the standard mosaic approach. For the elevation bands, a posteriori and a priori cases, the mean of the distributed forcing data for a given subcatchment tile or cluster was used. This can be considered an increase in the complexity and realism of the disaggregation approach.

5. Intercomparison of subgrid methods

Simulations over WYs 2001–08 are used for the intercomparison of the various subgrid methods (Table 3).

a. Monthly averages

Monthly-average sensible and latent heat fluxes clearly show the seasonal cycle with negative sensible and near-zero latent heat flux in the winter months, with a maximum in sensible and latent heat fluxes in spring/summer (Figs. 10a,b). Intermethod differences are most pronounced during the spring and summer period. There is a range of ~10 W m−2 in April and 15 W m−2 in June and July for sensible heat flux between the various methods. The lump simulation has the least negative sensible heat flux in March and April while the vegetation simulation has the smallest sensible heat flux during summer. The 10-aposteriori, 10-apriori, a posteriori, and a priori simulations are within 7 W m−2 for every month except April and May, when the 10-apriori and a priori simulations have less snow cover than the 10-aposteriori and a posteriori simulations. Differences in summer latent heat arise as various simulations dry out at faster or slower rates from May to August. The lump and 10-apriori simulations are the most water limited, with the elevation and vegetation simulations generally having the largest latent heat fluxes through the summer. Latent heat flux variations can reach up to 18 W m−2, but variations of ~10 W m−2 (roughly 25%–30%) are consistently present from May to August.

Fig. 10.
Fig. 10.

Monthly-mean values of (a) sensible heat flux (W m−2), (b) latent heat flux (W m−2), (c) net radiation (W m−2), and (d) catchment total runoff (mm month−1) for the 2001–08 period for the various disaggregation and high-resolution simulations: lump (Lu), elevation (El), vegetation (Veg-U), a priori (Ap), a posteriori (Dy), 10 a priori (10-Ap), and 10 a posteriori (10-Dy).

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

The net radiation budget (Fig. 10c) has two notable differences between the simulations. In March and April, the a priori and 10-apriori simulations have slightly more net incoming radiation. During the summer, the lump and elevation simulations have less net radiation input to the surface because of the vegetation types in the lump and elevation simulations having only one and two types, respectively, resulting in different catchment-averaged fractional vegetation and leaf area index values. Monthly-average streamflow sharply increases in May, corresponding to snowmelt with a consequent sharp decrease after, while low flow comes in late winter before melt begins (Fig. 10d). Differences in the simulations become apparent in March with the 10-aposteriori, 10-apriori, a posteriori, and a priori cases having earlier onset of melt. This corresponds to the inclusion of slope and aspect radiation differences resulting in larger net radiation in these simulations (Figs. 5b, 10c). Mean peak discharge in May ranges between 186 (10-apriori) and 269 (a posteriori) mm month−1 with the a posteriori and 10-aposteriori simulations having the most runoff (Fig. 10d) due to more SWE (not shown).

b. Seasonal diurnal averages

Diurnal averages for winter (October–March) and summer (April–September) latent and sensible heat flux highlight the vegetation differences (Fig. 11). The lump simulation has only sage specified for the entire catchment, and this results in large differences from the other common (elevation, vegetation) disaggregation simulations for sensible (latent) heat fluxes for the winter and summer seasons, up to 25% (27%) in winter and 11% (20%) in summer. The elevation simulation is also primarily sage and is very similar to the lump run for winter and summer sensible heat. They (lump and elevation) diverge for latent heat flux estimates due to the elevation simulation having a portion of the catchment containing the riparian vegetation and soil type. Diurnal net radiation for the three common LSM (lump, elevation, and vegetation) implementations is very similar, with the vegetation simulation having slightly more peak net radiation due to a lower mean catchment albedo (inclusion of lower albedo forest regions). Diurnal runoff variations in the common implementations are a product of SWE and soil differences, the lump simulation having the most SWE and smallest soil-holding capacity resulting in larger spring/summer runoff.

Fig. 11.
Fig. 11.

(left) Winter (October–March; ONDJFM) and (right) summer (April–September; AMJJAS) diurnal-average (a),(b) sensible heat flux (W m−2); (c),(d) latent heat flux (W m−2); (e),(f) net radiation (W m−2); and (g),(h) catchment total runoff (mm h−1) for the 2001–08 period.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

The a priori, a posteriori, and both 10-m-resolution simulations have similar sensible and latent heat fluxes. This again relates to slightly different vegetation and soil specifications between the a priori and a posteriori simulations along with minor changes in available near-surface soil moisture due to SWE differences between them. Net radiation is larger in the 10-aposteriori, 10-apriori, a posteriori, and a priori simulations than lump, elevation, and vegetation because of the inclusion of slope and aspect impacts, which are greater at small solar elevation angles (winter). Total runoff differences between 10-aposteriori, 10-apriori, a posteriori, and a priori are primarily confined to the 10-apriori run (Figs. 11g,h) as in the monthly means (Fig. 10d); differences between the 10-apriori, 10-aposteriori, and a priori simulations are less than 10%. The 10-apriori simulation has the lowest mean TWI over the course of WYs 2001–08, resulting in less available water for runoff.

c. Snow water equivalent intercomparisons

Representation of subcatchment SWE variability is an important variable for water cycle or climate change impact studies in snowmelt-dominated regions. SWE variability impacts soil moisture, runoff, and fluxes from the land surface (Fig. 4 and section 6). Inherently, the lump simulation has no SWE variability across the catchment; a mean value is modeled everywhere (Fig. 12a) while the other catchment disaggregations will have different degrees of subcatchment SWE variability. As was shown in Fig. 8, the elevation and vegetation mosaics do not capture subcatchment drift zones, which is also evident in Figs. 12b and 12c as compared to Fig. 12f.

Fig. 12.
Fig. 12.

The 2002–08 mean near-peak SWE for the (a) lump, (b) elevation, (c) vegetation, (d) a priori Noah-MP simulation, (e) a posteriori Noah-MP simulation, and (f) observations.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

The a priori and a posteriori simulations best capture the SWE variability across the RME, albeit with a substantial underestimate of SWE in the deeper drifts. The elevation simulation does not capture any distinct drift or scour zones and has nearly uniform SWE across the three bands. This is due to the fact that each elevation band contains both drift and scour zones. The vegetation simulation does reproduce more of the observed SWE variations, mainly due to the relationship between vegetation types and SWE (or TWI), wherein forested areas are generally in or downstream of drift zones and low sage and grassy areas are generally in scour zones.

d. Hydrograph intercomparisons

Observed daily streamflow at the catchment outlet (Pierson et al. 2001; Reba et al. 2011) is used for hydrograph performance intercomparisons.

The daily streamflow time series data were also used for quantitative evaluation of the various methods via the Pearson correlation coefficient and the Nash–Sutcliffe (NS) coefficient (Nash and Sutcliffe 1970). As the complexity of the approach increases, the simulated streamflow better represents observations as noted in all three metrics (Fig. 13). The 10-apriori simulation performs the best for both metrics, but is only better at the 95% level than the a priori simulation for NS score, which leads to an important result: there is no statistically significant difference between the a priori, a posteriori, 10-apriori, and 10-aposteriori simulations for daily streamflow Pearson correlation and NS coefficient and only significant differences in the NS coefficient between the a priori and 10-apriori simulations for WYs 2001–08 (Fig. 13). The a priori disaggregation is statistically significantly better than the lump and elevation approaches for both metrics, while a priori is better than vegetation for NS coefficient (95% level).

Fig. 13.
Fig. 13.

(a) Pearson correlation coefficient and (b) NS coefficient for daily runoff over 2001–08. Red asterisks denote sample estimate, with the black bars denoting the 95% confidence interval generated via bootstrapping.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

It is interesting to note the degradation of the three performance metrics between the 10-apriori and 10-aposteriori simulations even though it is not statistically significant. As noted above, the 10-apriori simulation is forced with the static terrain-based PEF, while the 10-aposteriori is forced with the dynamic SnowModel-based PEF. From Winstral and Marks (2002) and Liston and Elder (2006a), three primary drift zones are present in the RME catchment, which is replicated very well by the static PEF (Fig. 3b). However, SnowModel sometimes simulates too little drift area (and possibly SWE) in the center and bottom right (Liston and Elder 2006a, their Fig. 10) drift zones (Fig. 4d). This results in less realistic precipitation forcing in the 10-aposteriori simulation and a possible slight degradation in streamflow performance metrics. It is noteworthy that the a priori sheltering indices and drift zone definitions in Winstral and Marks (2002) were developed in the RCEW, whereas SnowModel is a generalized model without catchment-specific parameters. An open question going forward will be to examine the performance of the Winstral and Marks (2002) parameters in other regions of complex terrain.

Although the gridded and multivariate HRU simulations more closely reproduce the observed hydrograph than the common mosaic approaches, there are shortcomings. In most years, the onset of melt is later in the model than observed (Fig. 14), while the recession of the spring melt is sometimes faster than observed (Fig. 14). These differences can be attributed to many different factors, associated with both uncertainty in the model forcing data (e.g., spatial representativeness of the stations used in the interpolation) and weaknesses in model structure (e.g., reliance on simple surface runoff and base flow parameterizations with no horizontal surface or subsurface connectivity). Increasing the horizontal complexity via HRUs in Noah-MP does improve the simulations as shown above, but there is still much progress to be made.

Fig. 14.
Fig. 14.

Time series of daily catchment total runoff (mm day−1) for the (left) high-resolution and k-means disaggregations and (right) common disaggregation approaches for (a),(b) 2001; (c),(d) 2002; (e),(f) 2007; and (g),(h) 2008.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

6. Extension to larger scales

a. Description

For the Tollgate watershed, an elevation detrended kriging (DK; Garen and Marks 2005) approach was used to distribute the point forcing data to the 30-m DEM. In this case, the catchment and station data spanned a large elevation range. Therefore, the DK algorithm can provide more accurate estimates of the elevation lapse rate for the various forcing fields (i.e., temperature and precipitation) than climatological estimates (Stahl et al. 2006), such as those in MicroMet. The 30-m gridded forcing data were used to produce Noah-MP forcing data for only the lump, elevation, vegetation, and a priori approaches for WY 2006.

Additional changes were made to the k-means algorithm and PEF function for this example in an effort for further automation and future implementation into an atmospheric model like the Weather Research and Forecasting (WRF) Model. Initially, an example 3-km grid was overlaid on Tollgate and the subgridcell mosaics were produced for each grid cell (or partial grid cell) within the catchment, in line with what a coupled simulation will produce. Also, the weights assigned to each k-means input vector are objectively set by dividing the normalized standard deviation for each input vector by the smallest normalized standard deviation. This results in an input vector where the least varying input has a weight of one and every other input has a weight greater than one. Finally, the mean PEF for the a priori simulation is now kept at one, which is a necessary condition for coupled simulations to conserve water mass.

b. Comparison of subgrid approaches

Time series of WY 2006 daily SWE show distinct differences across the larger Tollgate catchment (Fig. 15). During the accumulation phase, SWE increases most rapidly in the a priori simulation, followed by elevation, vegetation, and finally the lump simulation (Fig. 15). This is due to the inclusion of precipitation variations across the elevation bands and not across vegetation types. The lump simulation produces more winter melt across the catchment as compared to the other methods. The melt season is marked by rapid SWE loss in the lump simulation. The elevation and vegetation cases have SWE persisting further into the season, with the a priori simulation producing a pronounced extension to the snowmelt season (Fig. 15). This is due to the inclusion of snow redistribution, radiation loading, etc. in the a priori mosaic, as discussed previously.

Fig. 15.
Fig. 15.

Tollgate catchment-averaged WY 2006 SWE.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

These SWE variations, in addition to the variations in vegetation type and soil characteristics across the simulations, impact the radiation budget and the partitioning of latent and sensible heat fluxes (Fig. 16). Examination of the diurnal cycles of net radiation and latent and sensible heat fluxes (same as Fig. 11) highlight energy differences at the Tollgate catchment scale as well. The lump simulation has the most (least) sensible heat flux and net radiation in the winter (summer; Fig. 16). This is due to more snow-free area in winter, less available water in summer, and the lack of vegetation other than sage across the entire catchment in the lumped simulation. The a priori disaggregation has the least net radiation during winter and the most during summer (Figs. 16e,f). This is due to more snow-covered area in winter in addition to radiation loading impacts, which then supplies more net radiation during the summer season, even as compared to the vegetation simulation.

Fig. 16.
Fig. 16.

(left) Tollgate winter (ONDJFM)-and (right) summer (AMJJAS)-average diurnal cycle of (a),(b) latent heat flux; (c),(d) sensible heat flux; and (e),(f) net radiation for the Lu, El, Veg-U, and Ap simulations.

Citation: Journal of Hydrometeorology 15, 5; 10.1175/JHM-D-13-038.1

7. Conclusions and next steps

A multivariate approach to watershed disaggregation using k-means clustering is described and tested in uncoupled mode here. The approach can be generalized to any scale, takes advantage of hydrologically self-similar subsets of a basin or grid cell, and can accommodate a variety of input vectors (Kumar et al. 2013; McCreight 2010; Fiddes and Gruber 2012). Therefore, it can provide a more optimal way to capture the variability of a watershed without resorting to a fully distributed simulation (Harrington et al. 1995; Fiddes and Gruber 2012). To test the method, the RME and Tollgate catchments were selected as they provide well-documented and instrumented catchments with variability in vegetation, soil, and total water input (Figs. 4, 5). Two distributed high-resolution simulations on the 10-m-resolution RME grid with static and dynamic precipitation forcing (10-apriori and 10-aposteriori) were performed along with three common mosaic approaches: lump, elevation bands, and vegetation mosaic with uniform forcing. Finally, two multivariate clustering approaches using multiple land characteristics, SnowModel, and Noah-MP output in an a posteriori case and only a priori land characteristics in an a priori case were evaluated. Use of the a priori PEF function in the LSM allows for implicit inclusion of snow redistribution processes.

The multivariate clustering method is able to capture more of the subcatchment variability in the RME catchment (Figs. 5, 6, 8, 9). Monthly flux differences are generally less than 20%–30% for sensible heat flux, latent heat flux, and net radiation between all methods while peak runoff differences are up to 30%. The two high-resolution and two multivariate clustering simulations generally have very good agreement (<10%) for sensible heat flux and net radiation (Figs. 10, 11). Larger intermethod differences arise for summer latent heat fluxes and runoff, especially when comparing to the 10-apriori simulation, which is the most water limited. Diurnal variations of the various energy components and runoff show similar differences as the monthly means. The traditional mosaic approaches (lump, elevation, and vegetation) have less sensible heat flux and net radiation for both summer and winter while they bracket the four complex methods (the two high resolutions and k-means disaggregations) for summer latent heat flux. Examination of observed and simulated streamflow time series for WYs 2001–08 shows there is no statistically significant improvement over the lump, elevation, and vegetation simulations for Nash–Sutcliffe efficiency (Fig. 13), demonstrating some of the potential of improved disaggregation approaches in LSMs.

To evaluate the applicability of the method at larger spatial scales, four mosaic approaches (lump, elevation, vegetation, and a priori) were simulated for WY 2006 for the Tollgate catchment. A representative horizontal gridcell spacing (3 km) for an atmospheric mesoscale model was applied to the catchment, and then the mosaic approaches were undertaken on each grid cell, as would occur when running an LSM coupled to an atmospheric model. The a priori gridcell disaggregation method produces an extended melt season, which impacts the net incoming energy and its partitioning into sensible and latent heat fluxes (Figs. 14, 15).

There are several key points worth repeating. First, the multivariate subgrid mosaic approach captures more subgrid variability than univariate approaches. Second, the flexibility and objectivity of the k-means approach provides a framework to extend the mosaic definitions over large areas easily (Fiddes and Gruber 2012). Third, inclusion of variable forcing across the subgrid tiles improves representation of subgrid variability. More generally, this paper describes an important first step to including more horizontal complexity in LSMs, while improving offline simulations of SWE and streamflow and increasing subgrid variability present in the model. However, shortcomings in the SWE and streamflow simulations are still present. Future examination of coupled simulations within WRF will be undertaken to further assess the impacts of various mosaic approaches (e.g., Li et al. 2013). Finally, inclusion of horizontal connectivity between mosaic tiles and grid cells should address some of the shortcomings arising from unresolved hydrologic processes.

Acknowledgments

The authors thank Glen E. Liston for making the SnowModel code available. The authors would also like to thank three anonymous reviewers for improving this manuscript. This work was supported by a postdoctoral fellowship in the Advanced Study Program at the National Center for Atmospheric Research.

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