Elevation-dependent compensation effects in snowmelt in the Rhine River Basin upstream gauge Basel

In snow-dominated river basins, floods often occur during early summer, when snowmelt-induced runoff superimposes with rainfall-induced runoff. An earlier onset of seasonal snowmelt as a consequence of a warming climate is often expected to shift snowmelt contribution to river runoff and potential flooding to an earlier date. Against this background, we assess the impact of rising temperatures on seasonal snowpacks and quantify changes in timing, magnitude and elevation of snowmelt. We analyse in situ snow measurements, conduct snow simulations and examine changes in river runoff at key gauging stations. With regard to snowmelt, we detect a threefold effect of rising temperatures: snowmelt becomes weaker, occurs earlier and forms at higher elevations. Due to the wide range of elevations in the catchment, snowmelt does not occur simultaneously at all elevations. Results indicate that elevation bands melt together in blocks. We hypothesise that in a warmer world with similar sequences of weather conditions, snowmelt is moved upward to higher elevation. The movement upward the elevation range makes snowmelt in individual elevation bands occur earlier, although the timing of the snowmelt-induced runoff stays the same. Meltwater from higher elevations, at least partly, replaces meltwater from elevations below.


GRAPHICAL ABSTRACT INTRODUCTION
Alpine landscapes react particularly sensitively towards climatic changes. By the end of the century, glaciers in the European Alps most likely will be gone, and seasonal snowpacks downsized to a small fraction (Horton et  In this study, we analyse snow observations, conduct snow simulations and analyse discharge records from key gauging stations in the Rhine Basin upstream gauge Basel. We use Moderate Resolution Imaging Spectrometer (MODIS) snow cover maps to validate our model results. The main goal is to better understand the impact of rising temperatures on alpine snowpacks. We focus on the timing, magnitude and elevation of snowmelt events and assess how changes in snowmelt translate into changes in river runoff.

STUDY AREA AND DATA
The study area is the Rhine Basin upstream gauge Basel. The basin covers a total area of 3.59 × 10 4 km² and an elevation range of almost 4,000 m ( Figure 1). Gauge Basel is located at 294 m a.s.l. The southern parts of the basin are of highalpine character. The highest mountain peaks reach up to elevations above 4,000 m a.s.l. In winter, precipitation is often solid and accumulates in temporary snowpacks.
Depending on the elevation, areas are covered by snow for weeks or even months. A considerable fraction of runoff originates from snowmelt (Stahl et al. ). In general, elevation is an important factor determining local climatic conditions, vegetation and land use. The basin also encompasses large parts of the Swiss Plateau, hilly to flat areas north of the alpine ridge, which mostly cover elevations between 300 and 1,000 m a.s.l. In recent decades, temperatures in the Swiss Alps have been rising at a very fast pace   (Matiu et al. , ). All data analysis was carried out using the free software R 3.6.1 (R Core Team ).
MeteoSwiss and WSL conduct monitoring and analysis programmes for the snowpack in Switzerland at numerous locations. In this study, we focus on a few selected stations.
Selected records of snow depth stand out by their length and cover a broad range of elevations, i.e. 555-2,691 m a.s.l. To examine changes in river runoff, we exert a nested catchment approach in the two main branches of the Rhine River network: the Aare branch (left in Figure 1) and the Rhine branch including Lake Constance (right in Figure 1).   Within the project 'EDgE -End-to-end Demonstrator for improved decision making in the water sector in Europe' by Copernicus, these data were further refined to a 5 km grid using external drift kriging (EDK). EDK addresses altitude effects and provides input data for hydrological modelling at high spatial resolutions (e.g. Zink

METHODS
Our analysis is based on the combination of both observed and modelled data. We analyse changes in snowpacks and snowmelt dynamics and assess the effect of changes in snowpacks on the timing and magnitude of snowmelt-induced runoff. An in-depth analysis of discharge data and governing flood drivers complements the investigations (Figure 2).

Snow observations
To get a first insight into observed changes in snowpacks, we display snow observations as raster graphs and determine the mean annual cycle for snow depth and accumulation/ melt rates for two time windows : 1958-1987 and 1988-2017. We select the time windows in order to have two (1,404 m a.s.l) and used as radiation input. Values of air pressure, relative humidity, wind speed and cloud coverage are currently assumed to be constant with values of 1,000 hPa, 70%, 1 m/s and 50%, respectively.
As a first step, we validate the model setup and modifications using measured temperature and precipitation records from meteorological stations and a default parameter set for daily data from two sites in the German low mountain ranges (Kneis ). After ascertaining flawless model operation, we re-calibrate model parameters (see Supplementary Table B1) using the particle swarm optimisation algorithm from the R-package 'ppso' (https://github.com/ TillF/ppso). This calibration aims to improve model performance by customising parameters to the alpine setting.
We employ 5,000 model runs and assess model performance Next, we use the resulting parameters and gridded datasets of temperature and precipitation (available for the time frame 1950-2014) to perform snow simulations for the entire study area upstream gauge Basel. The temperature grid used to drive the simulations was obtained by downscaling from 5 to 1 km resolution using a lapse rate-based approach. The lapse rates, i.e. changes of temperature with elevation, were determined every day individually based on In the following, we aggregate results into 50 m elevation bands and calculate annual cycles of mean average and trends in SWE, SWE area volume totals and accumulation/melt rates. Accumulation/melt rates are calculated as the difference in SWE volume between two consecutive days. In addition, we assess mean annual cycles and trends for temperature and precipitation.
Trends are determined using the Theil-Sen trend estimator (Theil ; Sen ; Bronaugh & Werner ) after applying a 30-day moving average filter. Grid points showing a continuous accumulation of snow over the simulation period were classified as 'glacier points' and not included in this analysis (2.75% of the data points). To validate our modelling approach, we calculate annual average snow cover durations and compare with satellite-based snow cover maps. With regard to snow simulations, areas are considered covered by snow when SWE is equal to or exceeds 2 mm. All points classified as 'water body' in more than 90% of the MODIS maps were treated as lake surfaces and not included in the analysis.

Snowmelt as flood-driver
Interested in snowmelt as a flood-generating process, we calculate the total snowmelt within a 14-day moving window for all 50 m elevation bands from modelling results, i.e. snowmelt rates, and determine the annual maximum (max14) thereof and assess the two characteristics timing (T-max14) and magnitude (M-max14). In addition, we determine the mean elevation of defined max14 within a 30-day moving window (E-max14). To assess changes over time, we compare max14 characteristics between the two 30-year time frames 1954-1983 and 1984-2013. We also calculate the timing and magnitude of max14 on the catchment scale (T-max14-C and M-max14-C) for the total snow volume in the basin. We assess trend magnitude and significance of these variables using the Theil-Sen trend estimator and the Mann-Kendall trend test (Mann ; Kendall ).
To improve our understanding of the interplay between snowmelt-induced runoff and rainfall-induced runoff with regard to the annual maximum runoff events, we take a closer look at the 3-day sums of precipitation and 14-day sums of modelled snow accumulation/melt and visualise these variables along with observed discharge measured at gauge Basel. We differentiate between solid and liquid precipitation following the temperature threshold obtained during model calibration (see Supplementary Table B1). In  1951-1982, 1983-2014, 1919-1967 and 1968-2016

Snow observations
Seasonal snowpack characteristics are subject to strong inter-annual variability (Figure 3(a)). In recent decades , seasonal snowpacks are diminished at all stations compared to 1958-1988 (Figure 3(b)). Our results indicate that accumulation is reduced. The maximum snow depth is often already reached earlier in the year.
For stations above 1,000 m, a pattern of increased melt rates at the beginning of the snowmelt period and a reduction in maximum melt rates show up (Figure 3(c)).
Snowpacks have already thawed completely earlier in the year. Changes in measured snow depth only are an indication of changes in water stored in the snow cover.
During the compaction of a snowpack, for example, snow depth can decrease, while water content stays the same.  At the catchment scale, SWE depth and snow cover duration increase with elevation ( Figure 5(a)). The total SWE volume is distributed more uniformly along the elevation range, as the areal fraction an elevation band covers decreases with elevation ( Figure 1 and 5(c)). Similar to results from snow observations, the simulations indicate that SWE depth and volume is reduced in recent decades, particularly before and during the melt season ( Figure 5(b) and 5(d)). We detect a decline also in snow accumulation for elevation bands below approximately 2,000 m. Annual averages and trends in snowmelt/accumulation rates, i.e. snow volume changes between two consecutive days, are depicted in Figure 5   ( Figure 8(a)). According to the model results, a part of the precipitation input is solid and stored in temporary snowpacks (23%). Our results indicate that the runoff event is exclusively rain-fed, and no snowmelt is contributing. In the year 1978/1979, the annual runoff maximum is recorded in June. Rainfall-induced runoff overlaps with high baseflow due to snowmelt from high elevations (Figure 8   decreases from 12 to 7. Absolute contributions of snowmelt/ rainfall tend to decrease/increase (Figure 9(b)).

Discharge
Seasonal snowpacks are an important factor redistributing runoff from winter to summer at all gauges investigated ( Figure 10). Runoff seasonality is most pronounced in the alpine part of the catchment (Figure 10(f) and 10(g)).
A strong weekly pattern of reservoir operations for hydropower production with higher runoff during weekdays than on the weekend is imprinted at gauge Diepoldsau since the 1960s ('dashed pattern' in Figure 10(g)).
In the Rhine branch including Lake Constance, our results hint at a decrease in runoff during summer Detected changes go along with results from Musselman et al.
(), who indicate that a 'shallower snowpack melts earlier, and at lower rates, than deeper, later-lying snow-cover' and 'that the fraction of meltwater volume produced at high snowmelt rates is greatly reduced in a warmer climate'.
According to our analysis, rising temperatures do not just decrease the maximum melt rates, we identify a threefold effect: snowmelt becomes weaker, occurs earlier and originates from higher elevations (Figure 7(c)). If we refer to a fixed location (e.g. at an observational site), we can detect the shift forward in time. Conversely, if looking at a fixed time of year, the location of the melt event (i.e. contributing elevation bands) moves upward the elevation range (Figure 12(a)).

Snowmelt as flood-driver
In the Rhine Basin upstream gauge Basel, both snowmelt and precipitation seem to be important flood-drivers. Even moderate precipitation events can cause the annual runoff and 38% of the total basin relief. They refer to the elevations contributing most to a runoff event as the 'critical zone'.

Role of precipitation
The analysis of the annual runoff maximum of the hydrological year 1969-1970 indicates, in an exemplary way, how precipitation alone can cause high runoff values ( Figure 8(a)). According to our analysis, no snowmelt is contributing to the runoff peak. On the contrary, part of the precipitation is solid and stored in temporary snowpacks.
The accumulation of snow reduces the effective

Model performance and limitations
We are confident that our modelling approach enables investigations of snow cover changes. Temporal dynamics and absolute values have been reproduced for the stations, patterns realistically generated on the catchment scale.
Elevation-dependent differences in snowpack characteristics are represented well. However, our modelling approach includes several assumptions and simplifications that require caution and limit the explanatory value of our simulations. In the framework of our snow model, we do not address changes in incoming solar radiation. Instead, the simple mean annual cycle we use as input inter alia does not supply information on recent regional brightening effects

CONCLUSIONS
We analyse snow and discharge observations and simulate the Alpine snow cover in order to get a better understanding of how changes in snowmelt timing translate into changes in river runoff. The focus of the study is the Rhine River Basin upstream gauge Basel. We are confident that the physically based snow model setup used represents the snow cover dynamics in the basin well. However, several assumptions and simplification advice caution, most importantly the lapse rate-based approaches, applied to downscale gridded temperature input, simple seasonal cycle used as radiation input and the neglect of snow redistribution processes.
Our results point at strong decreases in seasonal snow- This study represents a further step towards understanding how changes in alpine snowpacks translate into changes in river runoff. Future studies need to further investigate the proposed hypotheses describing elevation-dependent compensation effects. Investigations using meso-scale hydrological modelling frameworks in combination with satellite dataderived snow cover maps seem predestined for such a task.