Reliable representations of spatial distribution of seasonal snow and subsequent snowmelt are critical challenges for hydrological estimations, given their crucial relevance in mountainous regimes, especially because of the high sensitivity to climate change. Considering the snow effect on land and atmospheric processes, accurate representation of seasonal snow evolution is thus highly imperative to strengthen water resources development trajectories in these regions . Various modeling and measurement techniques are currently in practice which attempt to estimate the distribution of snow, but these methods have their own limitations. Prior studies on the comparison of snow models (; ) have highlighted the higher reliability of physically based approaches such as the energy balance approach in simulating the snow conditions. These complex models, although they offer a more realistic physical detail of the sub-processes , are often associated with intensive data requirement, which is generally a big limitation in mountainous catchments around the world . Likewise, in situ measurements of snow depth providing accurate measures, seldom cover a wider spatial extent and are prone to be non-representative due to local influences. Lack of snow-depth information and, to some extent, persistent cloud cover in the mountains limit the standalone usage of remote sensing images in snow estimation . However, these images can provide a plausible alternative to ground-based data, especially in data-scarce mountainous regions, since their resolution and availability do not depend on the terrain . The Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Terra and Aqua satellites provides one of the most extensively used snow-cover products worldwide, owing to its daily temporal resolution and a high spatial resolution of 500 m at the Equator. The MODIS snow-cover data performance, though seasonally and region dependent, has been found to be accurate enough for hydrological contexts . The cloud obstruction in MODIS, though significant, can be reduced by combining the Aqua and Terra MODIS images and other spatiotemporal filtering techniques .

Remote sensing integration in hydrological modeling has made important strides in recent years . More so, several studies have been carried out by coupling satellite-based snow-cover information with hydrological models such as the ASCAT soil water index; MODIS snow-cover- and discharge-based calibration of a hydrological model ; MODIS snow-cover-constrained multi-variable discharge calibration for hydrological models ; MODIS snow-covered-area-based calibration of a distributed hydrological model ; and model initialization . These studies highlight the value of MODIS snow-cover information in multi-variable calibration in addition to discharge, leading to a better representation of the hydrological processes, reduced uncertainty, and to some extent improved hydrological predictions. Apart from the multi-calibration approaches, implemented a step-based calibration technique to calibrate the individual modules of a hydrological model including snow, soil moisture, and runoff generation processes, which was concluded to be a well-informed runoff simulation. They used MODIS snow-cover data as a gap-filling information for the missing observed time-lapse photos of snow cover. used MODIS products in identifying the snow duration curve to be used in a snowmelt model and concluded that the coupling provides crucial information on snowmelt timing and magnitude. Likewise, there have been several studies to compare and improve the snow routine in various hydrological models in recent years. evaluated various formulations of the temperature index approach to analyze their response via the Hydrologiska Byråns Vattenbalansavdelning (HBV) model in 54 mountainous European catchments. also identified the best-performing variants of degree-day calculations for different regions in Colombia. They concluded that these specific targeted alterations improve the performance in terms of snow processes.

This paper draws its motivation from these studies to improve the simulation of snow accumulation and melt processes in data-scarce mountainous regions, using freely available data like MODIS snow-cover products. The widely used point-based snow depth and snow water equivalent measurements are often not representative due to the high variability of snow accumulation rendering calibration of snowmelt models based on point measurements highly uncertain. A standalone calibration of snowmelt modules based solely on pixel-wise MODIS snow-cover information was not found to be widely implemented. tested a MODIS fractional snow-cover area (SCA)-based calibration of a distributed hydrological model, SNOW17, with an areal snow depletion concept in which they concluded that calibrating only on MODIS SCA did not bring any improvement in the hydrological predictions. However, we identified the need to further explore the gap in exploiting the spatial distribution information of snow, which MODIS snow-cover data can provide on a daily basis and with a reasonable spatial detail. The purpose of this paper is, thus, to present a simple calibration method for snow accumulation and melt based on the satellite-based spatial binary (“snow”, “no-snow”) snow-cover information. This offers a wide range of applicability, allows for immediate verification with point measurements, and holds a high relevance in data-scarce regions, particularly in identifying time-continuous snow extents (with depth information) free from highly localized influences. The novelty of this study is to propose a standalone approach using MODIS snow-cover images for calibration of independent conceptual snowmelt models, thereby estimating model parameters from individual or sets of MODIS images. The data and the methodological approach can calibrate relatively complex snowmelt modules with reasonably accurate precipitation and temperature data without over-calibration, mainly owing to the robust binary data selected for calibration and the spatial extent of the satellite images. This also allows for the formulation of a flexible snowmelt module useful for distributed hydrologic modeling.

With the degree-day approach as a basis, we implemented different modifications to the snowmelt models incorporating different aspects governing snow hydrology such as precipitation-induced melt, radiation, and topography. For a better representation of the model performances, we evaluated the models in different layers of added detail. Sensitivity analyses for different thresholds that demarcate snow and no-snow pixels for both observed and simulated snow-cover in the study domain were carried out to evaluate these thresholds' influence on the model performances. To better understand and to validate the efficacy of the approach in terms of discharge, the calibrated melt outputs from the snowmelt model were also evaluated in a discharge-calibrated hydrological model. This allowed for the identification of more robust parameter sets, as the model uncertainty related to snow processes is significantly reduced. A simpler calibration of the hydrological models was achieved, as there were less parameters to be estimated. This approach also tends to reduce the hydrological model uncertainty as the set of equifinal parameters becomes smaller, which is a known challenge in hydrological modeling .

To develop and test simple snow models in mountainous or snow-dominated regions, the study area was selected as two distinct snow regimes: (a) characterized by intermittent snow and (b) characterized by partly longer-duration snow. For the former, Baden-Württemberg (BW) region in Germany was selected. Whole of Switzerland was considered to represent the longer-duration snow for the study. Figure  shows the study domain.

The BW region includes the Swabian Alps with an elevation rising to 1465 m a.s.l. from the lowest of 88 m a.s.l. Likewise, Switzerland includes the Swiss Alps region which covers the perennial snow/glacier area. The elevation ranges from below 200 to 4634 m a.s.l. The study areas exhibit an average snow season from October to April in Germany and September to June in Switzerland. For hydrological modeling, five catchments were selected (viz., Neckar catchments at Rottweil and Horb in BW and Reuss catchment at Seedorf, Aare catchment at Brienzwiler, and Thur catchment at Andelfingen in Switzerland). The Reuss and Aare catchments have a longer snow cover around the year and include glaciated areas. The properties of the catchments are shown in Table .

The data used for the study are the following:

Hydro-meteorology. Daily station meteorological data (viz. precipitation and minimum, maximum, and mean temperatures) from 2010–2018 were acquired for the study. For Germany, these variables were obtained from the Deutsche Wetterdienst (DWD), and for Switzerland they were obtained from the Federal Office of Meteorology and Climatology (MeteoSwiss). Likewise, daily discharge time series for selected catchments were acquired from the Bundesanstalt für Gewässerkunde (BFG) for Germany and the Federal Office for the Environment (FOEN) for Switzerland.

This study presents a distributed modeling approach with model computations done at pixel level of a gridded domain of 464 m × 464 m grids. For this, the input data were preprocessed and interpolated onto the aforementioned grid cells. A gridded schema was extracted for both regions using the MODIS snow-cover data as a reference. This schema was considered the reference gridded domain for the data interpolation and model run.

The methodological framework applied for the study is shown in Fig.  and is further discussed in subsequent sections.

It is a big challenge and a highly imperative one to improve the snowmelt routines in widely and successfully tested rainfall–runoff models like HBV . In this milieu, to evaluate the snow processes based on spatial distribution of snow, we implemented an image-based pattern calibration approach using MODIS-inferred snow-cover distribution for a single day or a duration of snow season of a given year. The calibration was done based on pixel-based binary information (“1”:“snow”, “0”:'`no snow”) from the MODIS images in Switzerland and Baden-Württemberg. The MODIS data, available freely across the world and at a daily resolution, provide a plausible alternative to ground-based data for immediate verification of snowmelt models. Widely used and computationally simplistic temperature index models with low data requirements were considered in the study and were modified wherever possible to gain enhanced model performance.

We found that all the model variants calibrated on a set of individual snow-cover images for the whole season were able to track the MODIS snow distribution with very good accuracy. These models were evaluated based on a Brier score which represents the total false recognition of snow and no-snow pixels. Results from all the models are comparable and very close in simulating the snow-cover distribution. The models' performance in terms of overestimation, underestimation, and total estimation errors were further scrutinized in different elevation zones. We observed that for Switzerland, characterized by the longer-duration snow, all the models were found to show decreasing overestimation error with increasing elevation, except Model 6 where the model error slightly increases in the mid-elevation zones. However, the model performances in terms of underestimation errors tend to increase with higher elevations. We found that the mean overall error remained the lowest for Model 6 with the radiation component for Switzerland. In Baden-Württemberg, the overall error is the lowest for all elevation zones with the radiation-based model. While some of the model variants were able to track the snow-cover distribution with better accuracy, we did not find a model-specific clear trend of prediction errors in different elevation zones. Based on the mean performance, Model 6 was deemed accurate enough to simulate the snow-cover distribution with a higher accuracy in identifying snow and no-snow pixels, reflected on the low Brier score values. As a reference model for further analysis, we selected this relatively complex variant with daily potential clear-sky radiation for both regions. The inclusion of radiation-induced melt has been found to provide a more realistic spatial distribution of melt rates . However, it is to be noted that since this approach is flexible enough to work with different snowmelt modules which can simulate the snow-cover distribution, we selected the relatively complex radiation-based model to assess the added value of the robust binary data selected for calibration purpose.

We also carried out a sensitivity analysis on the different thresholds used in the study to differentiate between the snow and no-snow pixels. We found out that a NDSI threshold of 30, a cloud percentage threshold of 10 %, and a SWE threshold of above 2.0  mm perform with very good accuracy for a seasonal calibration where all MODIS images fitting the cloud threshold criteria are used to calibrate the models in both regions. A closer look into the analysis suggests that, for Baden-Württemberg, NDSI thresholds of 30 and 40 give similar results when the SWE threshold of higher than 2.0 mm is used with 10 % cloud thresholds. In Switzerland, NDSI threshold of 30 showed the best performance with SWE thresholds higher than 0.5 mm. However, it is to be mentioned that this analysis was done assuming MODIS as the observed snow-cover distribution. Earlier studies on the NDSI thresholds have suggested that a threshold of 40 can be used for robust estimates of snow cover from MODIS. However, in reality, the spatial detail of MODIS and the associated uncertainty make it harder to know where the snow actually is. Coupled with this is the uncertainty associated with the precipitation data. These added uncertainties make it harder to recommend a definite threshold for future applications. The adopted calibration technique was found to be more sensitive towards the NDSI threshold, particularly in Switzerland, as can be observed from Appendix Fig. . In contrast, Appendix Fig.  shows that the sensitivity to NDSI is not that significant in Baden-Württemberg. It is thus our observation that a NDSI threshold of 20–50 can be considered to demarcate the snow/no-snow information for MODIS-based snowmelt simulations, along with a SWE threshold of 0.5–5 mm for longer-duration snow conditions and 2–5 mm for relatively shorter-duration snow conditions, without much loss in model performance. have also identified a SWE thresholds of 2.5 mm as optimum for error analysis with MODIS SCA. A cloud detection threshold of 10 % was found to be the ideal threshold for the selection of MODIS images for calibration, although our methodology is not that sensitive in terms of cloud coverage as can be seen in the appendix figures. This highlights the fact that this calibration on binary pixel information can also be done on patches of snow-covered pixels free from clouds, which makes this approach very flexible. However, different studies have found cloud threshold to be a critical factor during the evaluation of model errors. adopted a cloud threshold of 20 % for a multi-variable hydrological model calibration. suggested a cloud threshold of 80 % as there were no significant differences in model errors for < 50 % and 50 %–80 % cloud cover in their study.

The sensitivity analysis on the selection of dates of the MODIS images for calibration showed that the selection of the dates has a very strong impact on the model performance and in turn on transferability of parameters. The melt season calibration in Switzerland and the onset season calibration in Baden-Württemberg were found to have the best validation in other seasons and periods. With a more clearly defined melt season in Switzerland, we found out that the images towards the end of the snow season were adequate enough to simulate the snow processes within the snow season with good accuracy, and these calibrated parameters were found to be robust as shown by the spread of Brier scores in the validation periods (refer Fig. ). However, in Baden-Württemberg, which is characterized by a distinct onset but a more uncertain melt season (lesser snow availability), the onset season calibration was observed to be more robust and transferable to other validation periods. On a catchment level, three catchments in Switzerland and two in Baden-Württemberg were selected. The snowmelt model was calibrated using multiple images for winter seasons throughout the time period to obtain a set of 1000 robust parameter vectors. The temperatures demarcating snow and melt onset and the radiation melt factor were deemed sensitive to the overall Brier scores. The Brier scores from these 1000 simulations were compared with the ones estimated with parameters in the HBV's snow routine. The calibrated snow model significantly outperforms the HBV's snow model calibrated on discharge in all of the catchments. This has also been discussed by and in their respective studies showing that calibration on SCA in addition to runoffs improved the snow model efficiency. Furthermore, our results clearly show that the uncertainty in simulation of the snow-cover distribution is significantly reduced when using a dedicated snowmelt model, as the snow parameters in the HBV calibrated on discharge are compensated with other non-snow parameters. This compensation leads to a more uncertain representation of the snow accumulation and melt dynamics. This decrease in uncertainty with a simplified calibration approach using freely available data is noteworthy as the calibrated parameter vectors are more robust as compared to the ones calibrated on discharge. Similar findings have been pointed out by , where they discussed the increased robustness of the snow model parameters when SCA was added to the calibration. Since this methodology implements the calibration at pixel level on binary (“snow”, “no-snow”) information instead of depths, relatively complex snowmelt models are also calibrated with more robustness and without over-calibration of the models. This can be attributed to the robust data selected for calibration and the spatial extent of the satellite images used for simulation. It is to be noted that this study does not intend to assess the performance of any specific hydrological model predictions; however, it does aim to assess the performance of the melt outputs of snowmelt models calibrated on snow-cover distribution in a basic hydrological model. We deem it important to point out that though two of the Swiss catchments, Aare and Reuss, are glaciated, the glacial melt was not taken into account. This was mainly because of the MODIS limitation to identify the glaciers and to avoid further parameterization of the hydrological model to include a glacier component. Since our aim is to evaluate the snowmelt model calibration, both hydrological models were calibrated on equal terms with a similar approach with results comparable to each other. We found good improvement in the NSE performance in all the catchments while using the modified HBV. also concluded that the median runoff model efficiency increased when MODIS data were used for the calibration in comparison to a traditional discharge calibration. concluded in a similar tune with their results showing MODIS fractional snow-covered area (fSCA) improving the internal snow timings as well as the hydrological simulations. Our results further show that the NSE dispersion is also reduced with the modified HBV simulations, indicating a reduction in model uncertainty as both sets of parameters required for calibration as well as the set of equifinal parameters become smaller. This gain in performance comes with better computational efficiency, as the modified HBV calibration converges faster. This allows for incorporation of additional parameters in the independent snowmelt models to better represent the snow dynamics, as opposed to the fact that additional parameters in hydrological models impose further complexity during calibration. With a dedicated snowmelt model, this can be achieved as it is relatively quicker to calibrate on the images, and the resulting melt can be used in the hydrological models for efficient calibration. also concluded that a combination of MODIS fractional snow-cover area and streamflow data led to a reduction of predictive uncertainty of a hydrological model, thereby leading to sharper and reliable flow simulations. Furthermore, the strength of this approach lies in the simplicity, spatial flexibility, and global availability of the model input data, which can be very useful for snowmelt and hydrological predictions in data-scarce regions.

The study presented a methodology to evaluate a daily MODIS snow-cover-based calibration in identifying distribution patterns of snow in snow-dominated regimes in Switzerland and Baden-Württemberg (Germany). Specifically, different model modifications were employed to assess the improvement in the simulation of snow distribution with lesser input requirements. By calibrating at pixel level on binary information, relatively complex snowmelt modules can be calibrated with more robustness, as the uncertainty associated with calibration data is reduced, as is often the case with calibrations based on snow depth or snow water equivalent. From our results, we can conclude the following:

a.

It was observed that the methodology does well in mimicking the snow-cover distribution in regions with relatively higher accuracy with all the models.

The reduction in model uncertainties, primarily with the snow-distribution estimation and with the discharge simulation, adds value to provide improved conceptualization of the temperature-index model routines and further potential model updating in future work. Furthermore, this approach is not dependent on the choice of hydrological model, as it can be extended to any hydrological model that can identify the snow-cover distribution.