Our study area is the East–Taylor subbasin (hydrologic unit code 14020001; Fig. 1), which is a mountainous watershed in Colorado, western United States. East–Taylor subbasin encompasses several watersheds including East River, Taylor River, and Coal Creek. These watersheds have been subjected to intensive research activity, some of which contain highly instrumented test beds developed for understanding the impact of watershed changes on water availability and quality (Hubbard et al., 2018). East–Taylor subbasin is also part of the Upper Colorado River basin (UCRB; hydrologic unit code 14), which is a site of the United States Geological Survey (USGS) Next Generation Water Observation System (NGWOS; Gallaudet and Petty, 2018). In general, UCRB is an important study area as it drains into the Colorado River which is the principal source of water and jobs for 40 million people in the southwestern United States and Mexico (James et al., 2014). The Colorado River is under increasing stress due to drought and changing seasonality of snowmelt (Milly and Dunne, 2020), which can significantly impact the regional economies. Generating hyper-resolution datasets of gridded meteorological forcing in UCRB can help with quantitative modeling efforts geared towards water security for the region.

We start with a relatively small study area within UCRB to make it easier to visualize and critically evaluate the datasets. The novelty of the downscaling methodology further motivates us to start with a smaller study area (i.e., East–Taylor subbasin) before expending resources to generate datasets that cover a larger area (i.e., UCRB and beyond). Since the East–Taylor subbasin is an area of intensive research activity, the generated datasets can be rapidly incorporated into land-surface and ecohydrological modeling. This will also help us to identify any missing features in the datasets which may drive further refinement of the underlying downscaling methodology (Sect. 3).

The above data streams (Sect. 2.2) were subjected to various preprocessing steps as described below.

We employ random forests (RFs) to implement our spatial downscaling methodology. RFs are a non-parametric machine learning method based on an ensemble of decision trees (Breiman, 2001). Decision trees seek to minimize the error in modeling the target variable by recursively partitioning the input feature (or predictor) space into smaller subspaces. For regression models, a typical error criterion is the mean-squared error. The RF model employs bootstrapping to generate a different set of data points for each decision tree. The final model output is obtained by mean aggregation of the output of all decision trees in the ensemble. RF models also provide measures of the relative “feature importance” of each predictor variable. We implemented RFs using Python's scikit-learn module (Pedregosa et al., 2011). The hyperparameter values employed in our RF models are specified in Appendix B.

Our data-driven downscaling methodology consists of two steps: (i) learn the mapping between topographic features and the daily climate variable (at the native resolution of 800 m), and (ii) apply the learned mapping to model the downscaled climate variable using topographic features (at a resolution of 400 m). Figure 3 shows the schematic of the methodology. The gridded climate variable V can be expressed as the following function f: 1V=f(x,y,z,w1–10), where x, y, and z correspond to longitude, latitude, and elevation, respectively. These three spatial coordinates quantify the three-dimensional topography and enable the data-driven model to learn local relationships between V and physiography – relationships that correspond to expert knowledge embedded in the PRISM dataset. Finally, w1–10 corresponds to the 10 most correlated weather stations for each grid point. We use w1–10 as a shorthand notation for w1, w2, …, w10, where wi corresponds to the ith most correlated weather station for a grid point. w1–10 can be thought of as 10 nearest neighbors for each grid point. The PRISM dataset is developed using a weighted linear regression of weather station data. By using w1–10, we strive to give our machine learning model the same raw data that are used by the PRISM methodology. We picked 10 stations since it seems to correspond to the upper limit of the minimum number of stations that PRISM uses to develop a climate–elevation regression for a grid point (Daly et al., 1994). The use of w1–10 helps to constrain or regularize the relationship learned between the climate variable and topography, since it more explicitly forces the machine learning model to consider point measurement data. We determined w1–10 using the entire 12-year time series of the climate variable and weather stations. Figure 4 shows a map of w1. Note that since we are doing spatial downscaling, we learn the function f separately for each day. This also enabled us to get estimates of relative feature importance of each predictor variable, which are presented in Appendix C.

Finally, we subjected the downscaled precipitation grids to a variable filter as described by Daly et al. (2008). The filter performs a distance-weighted average of all surrounding grid cells and ensures a smooth precipitation field in low-gradient areas, without affecting the high-gradient areas.

Gridded estimates of precipitation and temperature should exhibit a spatial variation that is consistent with the resolution of the grid. Projecting coarse-resolution meteorological variables on a fine-resolution grid results in discontinuous spatial gradients which can impact the modeling of land-surface processes (Maina et al., 2020). This implies that spatial gradients of the downscaled climate variables should exhibit a more gradual (or smoother) variation, when compared to their coarse-resolution counterparts. We explore the relative smoothness of the downscaled and original datasets by quantifying their roughness.

To quantify the roughness of a gridded climate variable, we start by computing its Laplacian. The Laplacian L of a gridded variable is estimated by convolving the gridded variable with the following 3×3 filter: 0101-41010. The Laplacian can be used to visualize changes in gradients (or roughness) of the gridded variables. Its ability to capture the roughness of an image has long been utilized in computer vision for edge detection (Torre and Poggio, 1986). We estimate the roughness J of a gridded variable by summing the element-wise squares of its Laplacian: J=∑i,jLi,j2, where Li,j corresponds to the i,jth element of L. This approach to estimate roughness is motivated by the definition of roughness penalty used for fitting smooth splines to data (Gu, 2002). We expect the gridded variable at the downscaled resolution to have a lower roughness when compared to the original resolution. To compare the roughness at the two resolutions, we define a quantity called the roughness ratio (RR) as follows: 2RR=J400/J800, where the subscript corresponds to the spatial resolution of the gridded variable. RR <1 implies that J400<J800, which means that the datasets are smoother at the downscaled resolution.

In addition to exhibiting smooth spatial gradients, it is also important to check that the downscaled datasets preserve the spatial variability prevalent in the original datasets. We quantify the spatial variability of the climate variables by computing empirical semi-variograms using a discrete form of Matheron's estimator (Matheron, 1963): 3γh=12Nh×∑i=1NhZxi-Zxi+h2, where γ(h) refers to the semi-variogram, which is a function of distance or lag h, N(h) is the number of pairwise points for a given value of h, and Z(xi) is the value of a given field Z (here, precipitation or temperature) at location xi. If γ increases with h, it implies that the observed field Z is more dissimilar (or uncorrelated) at larger distances. We compute and compare the semi-variograms at both the downscaled and the original resolutions.

The process of downscaling should not introduce any bias in the hyper-resolution datasets. We can verify this by upscaling the downscaled datasets back to the original resolution (i.e., 800 m) and quantifying the mean residual error with respect to the original datasets (also at 800 m resolution). For a given time point, we quantify the mean residual error R over the entire study area as follows: 4R=1n∑jVj‾-Vj, where V refers to the value of the climate variable in the original dataset, V‾ refers to the upscaled value of the climate variable obtained from the downscaled dataset, the subscript j is the index of the grid point at the original resolution, and n is the total number of grid points in the dataset at the original resolution. The upscaling was done via bilinear interpolation. Ideally, the mean residual error should be close to zero, which implies that the downscaled datasets do not exhibit any bias when compared to the datasets at the original resolution.

PRISM assumes that for a localized region, elevation is the most important factor in the distribution of temperature and precipitation (Daly et al., 2008). Therefore, it is of interest to investigate how elevation influences the downscaled datasets. We do this using partial dependence plots (PDPs; Friedman, 2001), which show the marginal effect that a feature (here, elevation z) has on the outcome of a model. For regression, the partial dependence function is defined as (Molnar, 2019) 5f‾z=EXCf‾z,XC, where z is the feature for which we obtain a PDP, and XC denotes the other features used in the machine learning model f‾. Here, f‾ approximates the model f, as defined in Eq. (1), which is used to generate the downscaled datasets. The partial dependence function can be approximated using a Monte Carlo simulation whereby we consider all the instances of our data (which are used to learn f‾) and replace the true value of z with a realization of z instead. We can then obtain the average model prediction for each realization of z. We estimated the partial dependence functions for models used to generate downscale estimates of both precipitation and mean temperature.

Figures 5 and 6 show examples of downscaled precipitation and mean temperature fields, along with their original counterparts. To visualize the differences, we have zoomed into the northwest extent of the basin as indicated in subfigures (b). The northwest extent of the basin encompasses the East River watershed, which is an area of sustained research activity (Hubbard et al., 2018). We note the prevalence of smoother spatial gradients at the downscaled resolution (400 m) when compared with the original resolution (800 m).

We now quantify the smoothness (or roughness) of precipitation and temperature fields (as described in Sect. 4.1). Figure 7 shows an example of the Laplacian of precipitation at both the downscaled and original resolution, corresponding to the date shown in Fig. 5. For consistency, the precipitation at the original resolution has been projected to the downscaled grid. We note that the Laplacian for the downscaled precipitation varies smoothly. The Laplacian for precipitation at the original resolution is characterized by a checker-board pattern, which visualizes the need for generating hyper-resolution datasets while implementing hydrological models at hyper-resolutions.

Figure 8 shows the distributions of RRs for both precipitation and mean temperature. In both cases, the values of RR are well below 1, signifying that the spatial gradients of datasets are smoother at the downscaled resolution.

Figure 9 shows examples of semi-variograms of precipitation and temperature fields. These examples correspond to the date in Figs. 5 and 6 (i.e., 5 December 2019). The variability at the downscaled resolution is similar to that at the original resolution. This shows that the downscaled datasets preserve the spatial structure of the climate field present in the original datasets.

Figure 10 shows the distributions of mean residue (Sect. 4.3), where each instance corresponds to the mean residual error for a randomly selected time point. We clarify that “mean” in this context refers to the spatial mean over the entire study area. We observe that the estimated values of mean residue (as indicated by the peak value of the histogram) for both precipitation and mean temperature are close to zero. The small amount of residual error can be attributed to the fact that the downscaled dataset is generated using a machine learning model f‾, which is an approximation of the true function f. Mean residual values of zero imply that the downscaled estimates do not exhibit any bias when compared with the dataset at the original resolution.

Figure 11 shows PDPs that marginalize the effect of elevation on each climate variable. For both climate variables, we show PDPs for 10 randomly selected days. Although PDPs were obtained for 100 d (as documented in the beginning of Sect. 5), we show results only for 10 d to prevent overcrowding of the plots. Furthermore, to enable visualization of multiple partial dependence functions on the same plot, we shifted each function by its mean value. The machine learning model used to generate downscaled datasets captures an increase (decrease) in precipitation (mean temperature) with increase in elevation, which is consistent with the local climatology and the PRISM datasets (Daly et al., 2008).

We developed a novel data-driven approach that models high-resolution SWE data obtained via lidar (as described in Sect. 2.2.4). Our feature space comprised several meteorological variables at downscaled (∼400 m) and original (∼800 m) resolutions. As part of the use case, we also evaluated if using downscaled meteorological variables can improve the modeling of SWE, when compared to using meteorological variables at original resolutions. Any improvement in snowpack (SWE) modeling can be considered a validation of the spatial patterns represented by the downscaled datasets. We provide a brief description of the four meteorological variables derived for this purpose, following Mital et al. (2022): i.

Accumulated snowfall. Snowfall is the primary mechanism behind snow accumulation. As snow accumulation takes place over the entire snow season, we consider accumulated snowfall from the start of the snow season (defined as 1 October) till the date of observation of the snowpack. Precipitation on a given day is considered to be snow if the mean air temperature is less than or equal to 0 ∘C.

Figure 12 shows the schematic of the modeling approach, adapted from our previous work (Mital et al., 2022). We developed two RF models. RF model 1 used meteorological variables (i–iv) at the original (∼800 m) resolution, while RF model 2 used meteorological variables at the downscaled (∼400 m) resolution. Both models use topographic variables (v–ix) at the downscaled resolution. The target variable in both cases was SWE, also at the downscaled resolution. This enabled us to isolate the effect of using downscaled estimates of meteorological variables. The hyperparameter values for the RF models are specified in Appendix B.

The RF models of spatially distributed SWE were evaluated using a leave-one-out approach. As described in Sect. 2.2.4, there are a total of eight distinct maps available within the study area. We trained each RF model using seven maps and evaluated their respective abilities to model the held-out map. This exercise was conducted eight times, where each time a different map was considered as a held-out map. We evaluated the model performance by computing the Nash–Sutcliffe efficiency (NSE; Nash and Sutcliffe, 1970) on the held-out map. NSE is defined as 6NSE=1-MSEσo2, where MSE is the mean-squared error of the model, and σo is the standard deviation of the observations in the held-out map. NSE is dimensionless, ranging from -∞ to 1. Higher values are desirable and are consistent with lower values of MSE.

Table 1 shows the results of the modeling exercise, wherein we modeled SWE at 400 m resolution using both the original (RF model 1) and downscaled (RF model 2) meteorological variables. We observed that downscaled variables yield improvements (as indicated by higher NSE values) in six out of eight instances. The negative NSE values for GE: 24 May 2018 are due to that particular snapshot having the lowest fractional snow cover area compared to other snapshots (Fig. 2). This implies that the relationships between the predictors and SWE are different when compared to other snapshots (Mital et al., 2022). Overall, the results in Table 1 suggest that even if the downscaled dataset may not capture all the spatial variability at hyper-resolutions, it still constitutes a superior product compared to the original dataset especially when it comes to modeling hydrological variables at hyper-resolutions. Figure 13 shows scatter plots between the observed and predicted (modeled) SWE using RF model 2.

Additional use cases of downscaled datasets involve studies that investigate the impact of spatial and temporal resolution of gridded meteorological forcing on watershed hydrological responses (Shuai et al., 2022; Maina et al., 2020). For instance, Shuai et al. (2022) explored the effects of spatial and temporal resolution of gridded meteorological forcing on watershed hydrological responses. The study used integrated hydrological modeling and was conducted in the Coal Creek watershed, which is a mountainous sub-watershed located at the western edge of the East–Taylor subbasin. The downscaled daily datasets were used as high-resolution forcing variables, and the simulated streamflow was found to be consistent when compared with the results of coarser-resolution forcings. The study also considered a number of additional hydrological variables (i.e., SWE, snowmelt, ponded depth, groundwater level, soil moisture, and evapotranspiration). For more details, we refer the reader to Shuai et al. (2022).