A quantitative method to decompose SWE differences between regional climate models and reanalysis datasets

The simulation of snow water equivalent (SWE) remains difficult for regional climate models. Accurate SWE simulation depends on complex interacting climate processes such as the intensity and distribution of precipitation, rain-snow partitioning, and radiative fluxes. To identify the driving forces behind SWE difference between model and reanalysis datasets, and guide model improvement, we design a framework to quantitatively decompose the SWE difference contributed from precipitation distribution and magnitude, ablation, temperature and topography biases in regional climate models. We apply this framework within the California Sierra Nevada to four regional climate models from the North American Coordinated Regional Downscaling Experiment (NA-CORDEX) run at three spatial resolutions. Models generally predict less SWE compared to Landsat-Era Sierra Nevada Snow Reanalysis (SNSR) dataset. Unresolved topography associated with model resolution contribute to dry and warm biases in models. Refining resolution from 0.44° to 0.11° improves SWE simulation by 35%. To varying degrees across models, additional difference arises from spatial and elevational distribution of precipitation, cold biases revealed by topographic correction, uncertainties in the rain-snow partitioning threshold, and high ablation biases. This work reveals both positive and negative contributions to snow bias in climate models and provides guidance for future model development to enhance SWE simulation.


a. Uncertainties in SNSR SWE
The SNSR derived SWE was compared with 108 snow pillow and 202 snow course in-situ measurement sites throughout the Sierra Nevada (Margulis et al., 2016). For the 202 snow course sites, the mean error in SNSR was found to be less than 3 cm and the root-mean-square error was 13. In the 108 snow pillow measurement sites, the mean error in SNSR was 1 cm and the root-mean-square error was 11 cm. Averaged over all 310 measurements, the mean error is 2.3 cm, indicating the systematic error of SNSR is 2.3 cm; root-mean-square error is averaged 12.3 cm indicating a random error of 12.3 cm at each site. The random error at each site results in the standard error of the mean by 12.3/√(310) = 0.7 cm, or 1.4 cm with a 95% confidence interval. Therefore, the total uncertainty is √(2.3 2 + 1.4 2 ) @ 3 cm over the survey time and area when and where the mean SWE is 1.05 m, indicating a 3% uncertainty. This uncertainty affects the decomposition of model-reference difference of SWE where SNSR SWE is used in the calculation, i.e., row and in Fig. 3. In Table S1, we list each of the datasets used in Fig. 3 and include the true magnitudes of each variable along with their uncertainties. For example, reference SWE is 190 mm with 3% uncertainty, i.e., 190 (±6) mm.

b. Uncertainties in PRISM daily temperature and precipitation
The PRISM derived T were compared with in-situ measurements in the leeward side of the Sierra Nevada (Strachan and Daly, 2017). A random error with standard deviation of 1.67 °C was found. Our surveyed spatial-temporal extent covers about 3000 PRISM grids point over 3000 days. Therefore the random error only contributes to negligible error of the mean, which is 1.67/√(3000 x 3000) < 0.001 °C. However, a cold bias associated with topography was reported in PRISM daily T, with -0.75 °C bias in daily minimum T (Tmin) and -1.95 °C bias in daily maximum T (Tmax), or -1.35 °C in mean T. Further, we compared the PRISM and Livneh 2015 (L15) reanalysis dataset and found PRISM to be warmer than L15 by 1.1 °C in the windward side of Sierra Nevada. It is reasonable to believe the 95% confidence interval is below the upper limit of the systematic error (1.35 °C), which would result in a ± 69 mm uncertainty in snowfall. This uncertainty should be considered when comparing snowfall calculated from reference T and from modeled T. In Table S1, this is included in row REF in column $ , $ , $ " . PRISM derived P was shown to have an estimated seasonal bias of 0-3% in North Carolina (Daly et al., 2017). In the Sierra Nevada, a -1% and -4% seasonal P bias was found for two reanalysis datasets that rescaled their estimates to the PRISM climatology (Lundquist et al., 2015). Given these two in-situ validation attempts of PRISM derived P, we assume a ±3% uncertainty due to systematic error in our surveyed area, which would lead to ±3% (± 10 mm) uncertainty in snowfall. This uncertainty should be considered when comparing snowfall calculated from reference P and from modeled P. Similar to PRISM daily T, the random error of PRISM daily P make negligible contribution to the standard error of the mean due to the large sample size. In Table S1, uncertainties in PRISM daily P is included in row REF in c. Uncertainties about when precipitation occurs We use daily total P and daily mean T to calculate the daily total snowfall in both reference and model datasets. The underlying assumption is that all precipitation occurs at daily mean T. However, precipitation could occur at any time of the day, and we do not know the exact distribution of P with T from our datasets. Therefore, we use a Monte Carlo method to estimate the associated uncertainty in snowfall, by assuming P occurs at a random T between Tmax and Tmin. The random T follows uniform distribution between Tmax and Tmin. It should be noted that the time of day when P occurs is not completely independent between grid cells, which means a reduced degree of freedom in random samples. To reduce the degree of freedom accordingly, we assume the random T has the same relative distance between Tmin and Tmax on the same day at all grid points. Therefore, snowfall estimates are calculated using daily total P and the generated random T. We repeat the generation of random T and calculation of snowfall until the mean snowfall converges. The associated uncertainties in snowfall equals twice the standard deviation and represents a 95% confidence interval. This results in an 8 mm uncertainty in reference snowfall, and a 4-9 mm uncertainty (dependent on the amount of P and diurnal variability of T) in NA-CORDEX snowfall in column $ , $ , $ ) , $ * , $ , $ + , $ " and $ in Table S1.
d. Uncertainties about rain-snow partitioning Snowfall in the Sierra Nevada has been shown to occur between 0 -3 °C, with 90% precipitation falling as snow at 0 °C, and 10% at 3 °C (Lundquist et al., 2008;US Army Crops of Engineers, 1956). To assess the associated uncertainty with this observed estimate of rain-snow partitioning, we assume a random rain-to-snow percentage following uniform distribution between 0 and 1 at each grid cell and each day. We then apply a Monte Carlo method and found that the resultant uncertainty in the total snowfall is below 1 mm. This is assumed to be negligible.

e. Uncertainties in lapse rate
Lapse rates on the windward side of Sierra Nevada were found to range between 3.5 and 5.0 °C/km (Wolfe, 1992). Assuming the lapse rate is uniformly distributed between 3.5 and 5.0 °C/km, then 95% confidence interval for lapse rate is also between 3.5 to 5.0 °C/km. If we modify the lapse rate to 3.5 or to 5.0 °C /km, this changes $ " and $ + by 1 to 11 mm in addition to the uncertainties caused by other factors. The total uncertainties are shown in Table S1.

f. Propagation of uncertainties
For variables influenced by more than one uncertainty, total uncertainty is the root sum square of each uncertainty. Therefore, the total uncertainty is a combined estimate of systematic errors and random errors with a 95% confidence interval.
We calculate the uncertainties in ablation (Table S1, column M) and in decomposed model-reference difference using the upper/lower bound in the 95% confidence interval of upstream features, so the uncertainties propagate to determine the uncertainty in the decomposition presented in Fig. 3.