Hydrological forecasts constitute an important tool in water resource management, especially in the case of impending extreme events. This study investigates the potential predictability of soil moisture and streamflow in Switzerland using a conceptual model including a simple water balance representation and a snow module. Our results show that simulated soil moisture and streamflow are more predictable (as indicated by significantly improved performance compared to climatology) until lead times of approximately 1 week and 2–3 days, respectively, when using initial soil moisture information and climatological atmospheric forcing. Using also initial snow information and seasonal weather forecasts as forcing, the predictable lead time doubles in case of soil moisture and triples for streamflow. The skill contributions of the additional information vary with altitude; at low altitudes the precipitation forecast is most important, whereas in mountainous areas the temperature forecast and the initial snow information are the most valuable contributors. We find furthermore that the soil moisture and streamflow forecast skills increase with increasing initial soil moisture anomalies. Comparing the respective value of realistic initial conditions and state-of-the-art forcing forecasts, we show that the former are generally more important for soil moisture forecasts, whereas the latter are more valuable for streamflow forecasts. To relate the derived predictabilities to respective soil moisture and streamflow memories investigated in other publications, we additionally illustrate the similarity between the concepts of memory and predictability as measures of persistence in the last part of this study.
 Hydrologic forecasts constitute an important tool for decision makers in water resource management [Yao and Georgakakos, 2001; Hamlet et al., 2002; Modarres, 2007; Berthet et al., 2009]. Especially in case of impending extreme events such as floods and droughts, they may help to plan mitigation measures. Many studies focusing on streamflow prediction have pointed out the potential of applied streamflow forecasting [Wood et al., 2002; Koster et al., 2010a; Mahanama et al., 2012]. Also, operational streamflow forecasting systems have been established by meteorological services. Similar benefits can be expected from drought forecasting and early warning. In addition, drought forecasting could also help predicting the occurrence of heat waves [Lorenz et al., 2010; Hirschi et al., 2011; Mueller and Seneviratne, 2012].
 In contrast to streamflow, soil moisture has received only little attention so far in the context of hydrological forecasting [Calanca et al., 2011], despite its importance for agriculture and its well-known persistence characteristics [Robock et al., 2000; Koster and Suarez, 2001; Seneviratne et al., 2006; Orth and Seneviratne, 2012]. This is probably due to the scarcity of measurements available to validate models and forecasts.
 This study therefore focuses on the predictability of both streamflow and soil moisture. We thereby investigate and compare the respective contributions of initial conditions versus seasonal weather forecasts in impacting forecast skills of the two quantities. The use of weather and/or climate model predictions in hydrological forecasts has become more popular in recent years, and several studies illustrated their possible added value [Wood et al., 2002; Block et al., 2009; Fundel et al., 2013].
 Performing reforecasts, we investigate the potential skill of soil moisture and streamflow forecasts in 22 Swiss catchments and evaluate the importance of initial conditions (soil moisture and snowpack) versus that of different meteorological variables obtained from seasonal weather forecasts. For this purpose we use a conceptual hydrological model calibrated with streamflow measurements, which has been validated with measurements of soil moisture, streamflow, and evapotranspiration [Koster and Mahanama, 2012; Orth et al., 2013]. Despite its simplicity, it is able to reproduce observed temporal and spatial hydrological patterns in Central Europe [Orth et al., 2013] with a similar performance to that of a state-of-the-art hydrological model such as PREVAH [Viviroli et al., 2009].
 Another focus of this study is the link between the concepts of predictability and memory. Given that many previous studies either focus on forecast skill [e.g., Koster et al., 2010b; van den Hurk et al., 2012] or memory characteristics [e.g., Koster and Suarez, 2001; Seneviratne et al., 2006; Orth and Seneviratne, 2012], we illustrate the connection between these concepts and point out their similarity.
2.1 Simple Water-Balance Model
 We use in this study a conceptual simple water balance model introduced by Koster and Mahanama  and later refined by Orth et al. , based on the water balance equation:
where wnis the total soil moisture content at the beginning of time step n and Pn, En, and Qn are precipitation, evapotranspiration, and runoff, respectively, accumulated between time step n and n+△t. We employ here a refined model version for daily time steps [Orth et al., 2013], which also includes a more exact computation of soil moisture through an implicit form of equation (1). As in Orth et al. , we run the model in this study with a time step of 1 day (△t=1d).
 In the simple water balance model, normalized runoff and evapotranspiration (referred to as ET in the following) are simple polynomial functions of soil moisture. ET is normalized by net radiation, which results in the following equation:
where Rn is the mean net radiation of time step n, λ is the latent heat of vaporization, and ρw is the density of water (in kg/m3). Furthermore, β0, γ, and csare constant catchment-specific model parameters (see section 2.1.2). cs denotes the water holding capacity of the soil and is used to normalize the absolute soil moisture content, γ determines the shape of the function, and β0ensures that not all net radiation is necessarily transformed into ET, as plant transpiration may also be limited by other factors than radiation.
 Similarly to ET, runoff normalized by precipitation is assumed to be a function of soil moisture only:
where αand τ are further catchment-specific model parameters (see section 2.1.2). The shape of this function is determined by α. As in Orth et al. , we distinguish between runoff and streamflow to account for the transport of subsurface runoff to streambeds and for the traveling time of surface runoff to the stream gauge site. Hence, streamflow is computed from the simulated runoff with an imposed delay:
where τdenotes the delay time scale (in days) that determines the streamflow Fn+t at time n+t which is caused by the runoff Qnat time n. To ensure that all runoff is converted into streamflow, the integral of equals 1 as t→∞. Note that we use the notation F for streamflow instead of S [Orth et al., 2013] to distinguish it from snow, which is newly introduced to the model (see section 2.1.1).
 The model is always applied on catchment scale, such that the related quantities are averages over a whole catchment. To derive an initial soil moisture content for a particular catchment, we run the model during the first 5 years (spin-up) using 90% of the fitted water holding capacity as initial soil moisture content. The mean soil moisture value on 31 December (computed from all 5 years) is then used to initialize the actual model run.
 Examples of functions (2) and (3) are illustrated in Figure 1 together with a histogram indicating the soil moisture distribution in different seasons (except for winter, which is not considered in this study). The fitted functions show increasing (normalized) ET and runoff with increasing soil moisture. The sensitivity of runoff to soil moisture, as indicated by the slope of the respective function, increases toward wetter conditions until all precipitation is converted into runoff. Because a wetter soil can store less water, its ability to dampen runoff is limited. For ET, on the contrary, the sensitivity increases toward drier conditions, as plants tend to react more strongly when water is in short supply. The responses of runoff and ET to precipitation and radiation, respectively, vary seasonally due to soil moisture changes. For example, in spring when the soil is wet, runoff is very sensitive to soil moisture and a higher fraction of precipitation is transformed into runoff, whereas in summer when the soil is drier, there is less (normalized) runoff, which is also less sensitive to soil moisture. Even if the fraction of radiation transformed into ET decreases from spring to summer, the response of ET to radiation does not vary as much with soil moisture as the runoff response in this example.
2.1.1 Introduction of Snow
 To better adapt the simple model for cold conditions, we introduce an expansion in order to account for snow. This leads to an improved model performance (not shown) in winter (even if we do not explicitly consider winter time in the forecasting experiments), and furthermore in spring when snow melt occurs. For this purpose we employ a simple degree-day approach [see Hock, 2003, for an overview], meaning that snowpack dynamics depend on precipitation and temperature only. The snow depth is computed as follows:
where Sn is the mean snow water equivalent (in mm) of day n, Tn is the respective mean daily temperature in °C, and fmis a catchment-specific degree-day melt factor, expressed in mm K−1. This factor is a new model parameter which is fitted together with the other parameters as described in section 2.1.2. The melting process depends linearly on temperature, and the strength of the relationship is determined by the melt factor. The accumulation or melting of snow according to (5) alters the precipitation that is used to force the model:
 This means that no precipitation reaches the soil when the temperature is below 1°C, instead, snow is accumulated. If the temperature exceeds this threshold and snow exists, the observed precipitation is increased by snow melt that depends on the melt factor and on temperature. We select an arbitrary threshold of 1°C (which is kept constant throughout this study) because we use 2 m-temperature in this study. This threshold slightly exceeds 0°, because precipitation falls usually as snow as the temperature in the higher atmosphere is colder. Different thresholds (±0.5 K) lead to similar model results in terms of soil moisture and streamflow (not shown).
 To derive an initial snow water equivalent for a particular catchment, we first run the snow module over the whole time period starting with zero snow. We then compute a climatology from all years except the first and use the climatological value of 1 January to initialize the snow module in the next run. The modified precipitation obtained in this run is then used to force the model. Further discussion and validation of the modeled snow depth is provided in section 4.1.
2.1.2 Parameter Fitting
 The dependencies in the model are captured through equations (2)–(4) and characterized by the respective parameters therein. Additionally, a newly introduced parameter controls the dependency of snow melt on temperature. All parameters are fitted for each catchment separately using respective streamflow measurements. The fitting is done with an optimization procedure [see Orth et al., 2013, for details] that allows to identify the parameter set that yields the best agreement between modeled and observed streamflow measured by their correlation. We use here the correlation as an evaluation metric, as the model should capture the hydrological dynamics instead of, e.g., the absolute amount of streamflow or soil moisture. Indeed, the hydrological dynamics determine the memory and the predictability of the considered system, which are our focus in this study. We use the same parameter bounds and accuracies (step widths in the optimization procedure) as in Orth et al. , and for fm we use 0mmK−1as a lower bound (because negative melting would not make sense) and 0.2 mmK−1as step width. Note that we use precipitation and radiation observations (equations (2) and (3)) to run the model in all applications, including this optimization procedure (and also in general).
 Even if only streamflow information is used to fit the parameters (in combination with precipitation and radiation used to run the model), Orth et al.  show that the simple model is able to reproduce realistic soil moisture dynamics compared to observations. This ability and its simplicity make the model well suited for our study as we focus especially on soil moisture and streamflow.
 To fit the parameters, we use data from the time period 1984–1992. For an independent validation of the modeled streamflow, we computed the correlation between modeled and observed values during the time period 1993–2007 as listed in Table 2. We consider here the Spearman rank correlation, as streamflow values are not normally distributed. The rather high correlations in all catchments show that the parameter fitting was successful and that the model is able to capture the hydrological dynamics in an independent time period that was not used for calibration.
2.2 Forecasting Methodology
 We perform reforecasts of soil moisture and streamflow during the time period 1993–2007 (see section 3), such that the model calibration runs that use data from an earlier time period (1984–1992) are independent from the forecast runs. The forecasts are deterministic, have a maximum lead time of 32 days (as the European Centre for Medium-Range Weather Forecasts (ECMWF) forcing forecasts described in section 3), are computed with a daily time step, and are initialized weekly from March until October in order to focus on the growing season. All forecasts consist of five ensemble members (one control run and four perturbed forecasts).
2.2.1 Determination of Forecast Skill
 All soil moisture forecasts are validated against a synthetic soil moisture “truth” (hereafter referred to as “true” soil moisture). As we do not have actual observations, we instead use the model output obtained with observed forcing data as synthetic truth. Streamflow forecasts are evaluated in the same way as for soil moisture (i.e., against synthetic truth data), such that we can compare the results of both quantities. The validation of the forecasts against a modeled synthetic truth allows us to assess potential predictabilities of soil moisture and runoff. It should be noted that the forecasting skill with respect to actual observations is lower, as it suffers from inconsistencies between model and observations (see section 4.2.1 for a comparison of potential and actual streamflow forecast skill). Note moreover that potential predictability is a model-dependent estimate; nevertheless, we use this concept in this study because (i) there is no comprehensive observational soil moisture data set available that we could use to validate the soil moisture forecasts and (ii) the simple water balance model has been found to perform reasonably well in comparison with observations at selected sites [Orth et al., 2013]. Furthermore, we validate the forecasts of precipitation, temperature, and net radiation (see section 3) against respective observations in all catchments.
 To compute the forecast skill for a particular half-monthly time period and lead time, we consider all forecasts with this particular lead time within the respective period or in the preceding or following 2 weeks. We consider these additional periods to derive a more representative estimate. The length of 2 weeks each is an arbitrary choice, using 1 or 3 weeks has almost no impact on the results. The anomalies of the ensemble means of all considered forecasts are evaluated against the anomalies of the synthetic truth using the R2 of a least squares regression as a measure of skill. We use anomalies in this context (derived by subtracting the seasonal cycle) to yield the skill beyond climatology. The determination of skill is illustrated exemplarily in Figure 2 for two different forecasting experiments (see section 2.2.2). As the forecasts are initialized weekly and the considered time period is about 6 weeks long (including the 2 weeks before and after the half-monthly period), there are 6 weeks × 15 years = 90 points for each forecasting experiment in this example to determine the skill.
2.2.2 Forecasting Experiments
 To study the importance of different contributors to soil moisture and streamflow predictability, we perform several forecasting experiments for both soil moisture and streamflow. An overview of the various experiments is provided in Table 1. To assess the respective contributions of information on initial soil moisture and initial snow depth, we either use their climatologies or their actual values (synthetic truths, see section 2.2.1) in the different experiments. To determine the respective contributions of the atmospheric forcing variables (precipitation, net radiation, and temperature), we use either forecasts issued by the European Centre for Medium-range Weather Forecasting (ECMWF) as described in section 3 or climatologies based on available observations. Each of these forecasts consists of five ensemble members, and we use the respective ensemble mean to force our experiments. Note that this implies that we disregard information contained in the spread of the ensemble members; however, as discussed in the next paragraph, this has no significant impact on our results. Due to a lack of observations of initial soil moisture, we use the synthetic truth as reference instead (as described above). Although snow depth observations are available, for consistency, we follow the same procedure for initial snow depth (because the synthetic soil moisture truth used as reference to evaluate forecasts is based on modeled snow depth).
“Obs.” refers to observed values (synthetic truth), “clim.” means climatological values (values from other years), and “ECMWF” denotes atmospheric forcing forecasts (VarEPS) issued by the ECMWF.
 The respective climatological values of the initial conditions and the forcing on a particular day are computed as the mean from observed values of that day in all considered years. As this means, for example, that there is precipitation on every day of the forecast when using the climatology, we also tested another methodology. We performed each soil moisture and streamflow forecast with five ensemble members, for which we used the observed forcings from five other, randomly chosen, years in case of a climatological forcing, or the five ensemble members of the respective ECMWF forecast (in contrast to the ensemble mean as highlighted above). The forecast skill was computed using the respective soil moisture and streamflow ensemble mean. However, this methodology leads to qualitatively similar results as the simpler and more straightforward methodology outlined above (not shown). Hence, for simplicity, the latter approach was used in this study.
 As listed in Table 1, experiment 1 is the most basic. It uses the synthetic initial soil moisture truth and climatological values for all other variables. In experiment 2, we additionally use the synthetic initial snow cover truth instead of its climatology to assess its impact through a comparison to results from experiment 1. This experiment therefore assesses the predictability that results from all considered initial conditions. In experiments 3–5, we evaluate the contributions of the different forcing forecasts in addition to the skill resulting from the “true” initial conditions. Experiment 6 uses all these information sources to determine the maximum potential predictability. In contrast to all other experiments, experiment 7 uses climatological initial conditions instead of true values, combined with all forcing forecasts. Similarly to the analysis performed by Wood and Lettenmaier , this allows us to evaluate the importance of the forcing forecasts alone versus the importance of the initial conditions (as determined in experiments 1 and 2) by comparing the respective forecast skills.
 Figure 3 illustrates for a particular forecast initialization date the ability of the soil moisture and streamflow forecasts of experiments 1, 6, and 7 to capture the dry conditions in the 2003 hot summer [e.g., Schär et al., 2004; Zappa and Kan, 2007; Seneviratne et al., 2012] in a particular catchment. The forecasts of experiment 1 are shown in blue. As described above, the initial soil moisture is the same as in the synthetic truth (black dashed line) for that experiment. The forecast does not capture the streamflow evolution and the further drying of the soil, even though the information from the observed initial soil moisture allows the simulation to capture the below-average conditions throughout the forecasting period. The spread between the forecast and respective observations increases quickly with lead time, suggesting only weak skill. Experiment 6 (red lines) captures the observed soil moisture and streamflow evolution during approximately the first week of the forecasting period. This clearly highlights the added value of the ECMWF forcing forecasts, even if the increase in skill decays with lead time as illustrated by the red lines diverging from the soil moisture and streamflow observations at longer lead times. The green lines illustrate experiment 7. When the forecasted ECMWF forcing is applied, the green line in the soil moisture forecast initially slightly approaches the synthetic truth, reducing the error imposed by the climatological initial conditions. This effect seems to be weak, suggesting a limited value of the forcing forecast if it is applied without realistic initial conditions. The evolution of streamflow is well captured during the first days, even if the forecasted streamflow is too high as a result of the overestimated soil moisture (equation (3)). After about 1 week when the forcing forecasts contribute no more to the soil moisture and streamflow forecasts, the green lines also diverge from the observations.
 Figure 4 provides another example of the forecasts in the same catchment in the wet summer of 2007. The green forecast performs clearly better than the blue forecast and almost as well as the red forecast indicating that for capturing upcoming wet conditions, the forcing forecasts are more important than the initial conditions.
2.3 Computation of Memory
 We compute persistence of soil moisture and streamflow in order to show the similarities between memory and predictability. As introduced by Koster and Suarez , and also analyzed in, e.g., Seneviratne et al. , Seneviratne and Koster , Orth and Seneviratne  and Orth et al. , we compute memory as an interannual correlation. For this purpose, the memory at day n of the year is computed as the correlation between the values at day n of all considered years and the values at day n+tlag of all considered years. To compute a representative memory estimate for soil moisture for a particular half-monthly period, we apply the following equation (as introduced by Orth and Seneviratne ):
 As in equations (1)–(3), wndenotes soil moisture at the beginning of day n of the year, and is accordingly the soil moisture of day n+tlag. The first day of the half-monthly period is tstartand the last day is tend. Several soil moisture memory estimates during this period are computed with a moving time window of length tlag starting 15 days prior to tstart and moving forward until 15−tlagdays after tend. The trimmed average of these particular soil moisture memories (avoiding the 10% lowest and 10% highest correlations) is then a representative estimate for the soil moisture memory of the respective half-monthly period. Streamflow memory is computed in the same way.
 We apply the simple water balance model in 22 near-natural catchments located across Switzerland, i.e., catchments with negligible human impact on streamflow. Characteristics of these catchments are listed in Table 2 and their locations are shown in Figure 10 together with the corresponding mean soil moisture and streamflow forecasting skills discussed in section 4.2.2. As mentioned earlier, the considered time period in the forecasting experiments is 1993–2007 (while the calibration period is 1984–1992, see section 2.1.2).
Table 2. Overview of Characteristics of Catchments Considered in the Forecasting Experimentsa
(m Above Sea Level)
Versus Modeled Streamflow
The column on the right provides the Spearman correlations between the modeled and observed streamflow during the forecasting period 1993–2007.
Ova Da Cluozza
Ova Dal Fuorn
Riale di Calneggia
 To run the model, we need catchment-averaged observations of net radiation (equation (2)), precipitation (equation (3)), and temperature (equations (5) and (6)). For this purpose we use precipitation and temperature measurements from the Swiss weather service (MeteoSwiss) taken at stations located within and close to our considered catchments. Applying an inverse-distance weighting, these data are used to derive representative estimates of the two quantities for each particular catchment. Note that this weighting only considers horizontal distances and no differences in elevation. Nevertheless, the quality of the interpolated catchment estimates is expected to be satisfactory, as the station network is very dense (http://www.meteoschweiz.admin.ch/web/de/klima/ messsysteme/boden.Par.0049.DownloadFile.tmp/karteniederschlagsmessnetz.pdf [accessed on 30 August 2013]). As MeteoSwiss is usually not measuring net radiation, we use satellite-derived measurements from the NASA/GEWEX SRB project (http://eosweb.larc.nasa.gov/PRODOCS/srb/table_srb.html [checked on 10 December 2012]). The respective coordinates of the employed satellite-derived radiation for each catchment are listed in Table 2. Given the resolution of the satellite, the grid cells of the data set cover a relatively large area of 1° × 2°, but nevertheless, they compare well with point-scale measurements as reported by Orth et al. . Therefore, we assume that the radiation data is also representative for the scale of our considered catchments. To fit the model parameters for each catchment as described in section 2.1.2, we use respective stream-gauge measurements from 1984 to 1992 provided by the Swiss Federal Office for the Environment (FOEN) in connection with the forcing data discussed above.
 To validate the snow cover simulated by the new extension of the model described in section 2.1.1, we use catchment-averaged observations derived from a gridded data set (Joerg-Hess et al., 2013, in preparation). The data set uses snow data from different station networks run by MeteoSwiss and the Institute for Snow and Avalanche Research (SLF). The measured snow depths are converted into snow water equivalents (SWE) using the parametric snow density model of Jonas et al.  and are then interpolated on a 1 km × 1 km grid. The gridded SWE data are further calibrated with data from new stations operating only since 2001, thereby combining information from a denser network with that from the existing long-term stations.
 Forecasts of precipitation, net radiation, and temperature as used in some forecasting experiments (section 2.2.2) are provided by the ECMWF. The forecasts are produced as reforecasts using the ensemble prediction system VarEPS ([Vitart et al., 2008], http://www.ecmwf.int/products/changes/vareps/ [checked on 10 December 2012]) with the same 2011 model version over our considered time period. They are initialized weekly, consist of five ensemble members, and have a lead time of 32 days. The forcing forecasts for each specific catchment were derived with respect to its location from a 0.5° × 0.5° grid. We calibrate the forecasts for each particular catchment by subtracting a constant mean bias of temperature and net radiation from all forecasts in all months and at all lead times. This mean bias is computed from a comparison of the 1 day lead forecast with respective observations for March through October in all considered years. Also, precipitation forecasts were adapted in a similar way, but instead of subtracting a mean bias (which could lead to negative values), we multiply the forecasted precipitation with a constant mean calibration factor to yield the same mean annual precipitation as observed.
 In this section we first show validation results of the newly introduced snow module. Then, we illustrate results of the various forecasting experiments averaged over (i) all considered catchments and (ii) over all considered months. Thereafter, we identify the most important contributor(s) to soil moisture and streamflow forecast skill. Furthermore, we study the dependency of these skills on initial soil moisture anomalies, and we illustrate the general importance of realistic initial soil moisture information. In a last step, we point out the conceptual similarity between forecast skills and memories.
4.1 Validation of Simulated Snow
 As described in section 2.1.1, we add a snow module to the applied simple water balance model. It includes a threshold of 1°C, below which precipitation is assumed to fall as snow; this threshold is applied in all considered catchments. Figure 5 provides a validation of the simulated SWE against catchment-averaged observations (see section 3). We compare modeled and observed monthly averaged SWE for all catchments in all considered years for each month between December and March, resulting in 15 years × 22 catchments = 330 points per plot. We find generally a good correlation, especially between January and March, during which explained fractions of variance exceed 0.8, although the snow module displays an overall tendency to underestimate SWE (all slopes smaller than 1). The especially low slope for December suggests a delayed buildup of the modeled snowpack. The increase of the slope from 0.65 to 0.77 between March and April indicates a delayed melting of the simulated snowpack. This delayed evolution of the modeled SWE may be a consequence of the simplicity of the snow module which only uses temperature and precipitation information (equations (5) and (6)) but not radiation. Low net radiation in December supports the accumulation of snow, whereas comparatively high radiation in April accelerates the melting. The nonconsideration of radiation may also explain the general underestimation of SWE, even between January and March where R2 values are high, because modeled melting occurs only based on temperature and is not limited by energy availability; it could therefore be overestimated.
 However, despite the simplicity of the snow module, we find an overall satisfactory agreement between modeled and observed SWE in terms of correlation. We tested the incorporation of radiation information into the snow module but found only a small improvement of the simulated snow (not shown), likely because the simpler version of the model already performs well and because other factors such as wind, precipitation intensity, and ground heat flux also play a role. Hence, the small improvement did not justify the added complexity. It should be noted that we only focus here on the spring, summer, and autumn seasons. Follow-up studies considering winter would therefore likely benefit from an improved representation of snow dynamics.
 Although the simulated soil moisture, streamflow, and ET are impacted by the newly introduced snow module, a comparison of the model performance with that of the earlier model version [Orth et al., 2013] not including the snow model revealed only minor changes (not shown). In tests, we found that soil moisture and streamflow are especially impacted by snow melt (and less importantly also by buildup of snow) at the beginning of our considered period in March, April, and May. The memory of these quantities is slightly increased as the accumulation and melting of snow smooths the water input, particularly in high-altitude catchments.
4.2 Forecasting Soil Moisture and Streamflow
4.2.1 Skills Averaged Over All Catchments
 As described in section 2.2.2 and summarized in Table 1, we perform several forecasting experiments to characterize the general predictability of soil moisture and streamflow and the importance of various contributors to forecasting skill. The results are illustrated in Figures 6 and 7 for experiments 1–6 (from top to bottom) for half-monthly periods between March and October and for lead times between 1 and 32 days, averaged over all 22 catchments. The skills are computed as described in section 2.2.1 with respect to the synthetic truths of soil moisture and streamflow. Therefore, the displayed skills should be viewed as potential forecast skills.
 Considering the skill derived only from (synthetically) true initial soil moisture (top row of figures) we find clear differences between soil moisture and streamflow predictability. Soil moisture forecasts show high skill until about 2 and 1.5 weeks in spring and summer, respectively, and until approximately 1 week otherwise. On the other hand, streamflow forecast skill vanishes after 2–3 days and displays no seasonal cycle. Using initial snow information and ECMWF forcing forecasts (experiment 6, bottom row of figures) provides a substantial gain in forecast skill of both soil moisture and streamflow. With that additional information, soil moisture forecasts show high skill up to 2 weeks during most of the year, which means a doubling of the lead time with relatively high skill compared to experiment 1. In spring, predictability is high until about 3 weeks, hence, 1 week longer than in experiment 1, which also underlines the added value of the additional information used here. Streamflow forecasts are also significantly improved and display skill until approximately 1 week, which corresponds to a tripling of the lead time until which streamflow is more predictable compared to experiment 1. Furthermore, we find a weak seasonal cycle in streamflow forecasting skill with a maximum in spring and a minimum in late summer.
 Considering the results of experiments 2–5 in Figures 6 and 7, we evaluate the additional skill gained by introducing each single contributor at a time. Besides initial soil moisture, we find that the ECMWF precipitation forecast is clearly the most important contributor to the predictability of soil moisture and streamflow. Focusing on streamflow, we find that also initial snow information and correspondingly temperature forecasts in early spring contribute some additional skill. Radiation forecasts are not found to add skill for streamflow forecasting. Focusing on soil moisture, we find only small contributions of initial snow information and forecasts of radiation and temperature, compared to the skill improvement resulting from the precipitation forecast.
 Whereas the skills displayed in Figures 6 and 7 are potential forecast skills, Figure 8 illustrates respective results for streamflow expressed as actual skills (a corresponding analysis is not possible for soil moisture as there are no observations available). This means that the streamflow forecasts are validated against observations instead of the modeled synthetic truth (see section 2.2.1). The results are qualitatively similar: As in Figure 7, we find the highest skill in experiment 6 when using all available sources of information and we can also clearly identify precipitation as the most important contributor of skill. The actual forecast skills for all shown experiments are lower than the respective potential skills due to the necessarily limited ability of any model to represent reality; they are slightly higher than half the respective potential skill which fits roughly with the explained fraction of variance between modeled and observed streamflow, which is about 0.6–0.8 for most catchments. Note that the qualitative similarity between the actual and potential forecast skills is not surprising because as discussed earlier in section 2.1.2, the model is capable of capturing the hydrological dynamics during the forecasting period in all considered catchments.
 Figure 9 displays the skill of the ECMWF forcing forecasts, also averaged over all catchments. The low contribution of radiation forecasts to soil moisture and streamflow predictability seems to be partly due to its comparatively low skill. However, even if temperature forecasts show higher skill than precipitation forecasts, they are clearly less important for soil moisture and streamflow forecasts as shown above. This is a consequence of the nature of soil moisture and streamflow that is reflected in the model structure where temperature may only impact these two quantities via snow melt, whereas precipitation directly impacts both streamflow and soil moisture. The precipitation forecast shows significant skill until about a 5 day lead time without a clear seasonal cycle. Interestingly, the contribution of these forecasts to soil moisture and streamflow predictability is significant up to much longer lead times of about 10 days in the case of streamflow and even more than 20 days in the case of soil moisture. Furthermore, there is no improvement of soil moisture predictability in the first days of the forecast even if precipitation forecast skill is highest then. These two findings can be explained by the integrative behavior of soil moisture and its impact on streamflow. Thanks to its outstanding memory characteristics (section 1), soil moisture may “remember” the added value of the precipitation forecast. As streamflow depends on soil moisture (via runoff), its forecast also benefits from a better soil moisture forecast. Because of its high memory, soil moisture reacts only slowly to forcing changes, which explains why we find no improvement of the soil moisture predictability in the first days. Moreover, the predictability is already high even without additional information, which limits the potential for further improvements.
4.2.2 Skills Averaged Over All Months
 Similarly to Figures 6 and 7, Figure 10 displays the soil moisture and streamflow forecasting skills computed in experiments 1–6, but averaged over all half-monthly periods between March and October for each catchment. This allows us to assess the spatial distribution of the predictability of soil moisture and streamflow, and of its contributors.
 Generally, we find again that soil moisture forecast skill (Figure 10a) clearly exceeds streamflow forecast skill (Figure 10b) in all experiments. Focusing on soil moisture, we find no obvious spatial pattern of predictability. For low altitude catchments, the heights of the dark blue (representing experiment 3) and white bars (representing experiment 6) are similar, and they exceed the heights of the other bars. This underlines the dominant contribution of the precipitation forecast to the overall forecasting skill as also discussed above. This contribution is less dominant for high altitude catchments. There are catchments like Grande Eau, Dischma, and Ova Dal Fuorn, where all contributions (except the radiation forecast) are similar. For the catchment with highest elevation (Massa) the contribution of the temperature forecast is dominant instead, because the catchment is largely glaciated as shown in Table 2. This pronounced hydrological response to temperature in glaciated catchments has also been shown by Zappa and Kan  for the 2003 summer heat wave.
 The streamflow predictabilities (Figure 10b) show a tendency for higher forecast skills in the high-altitude catchments. Similarly as in Figure 10a, the precipitation forecast is the most important contributor of skill in low altitude catchments, whereas in the Alpine catchments, the contributors are rather of similar importance (again except for the radiation forecast). As for soil moisture predictability in the Massa catchment, the temperature forecast is the most important contributor also for streamflow predictability. Compared with the other considered contributors, information about initial snow tends to be more important for streamflow forecasts than for soil moisture forecasts. In the Dischma and Ova Dal Fuorn catchments, snow initialization is even the most important contributor of skill.
 Considering the results of Figures 10a and 10b, the importance of different contributors to streamflow and soil moisture forecasting skill varies with altitude. This finding is discussed in more detail in the following subsection.
4.2.3 Importance of Contributors to Skills at Different Altitudes
 As discussed in the previous subsection, the contributions of initial snow information and the forcing forecasts to soil moisture and streamflow forecast skills vary with altitude. This is further illustrated in Figure 11. For all catchments, we plot the differences of (potential) soil moisture and streamflow forecast skill averaged from March to October between experiments 2 and 5, respectively, and experiment 1 with respect to catchment altitude. We find that no contribution to skill in any catchment is (significantly) negative, meaning that the different sources of skill tested here never deteriorate the forecast. Focusing on the forecast skill gained thanks to information about initial SWE, we find no added value in low-altitude catchments (<1000 m) and increasingly higher skill gain toward higher altitudes where snow is more abundant and therefore more important. This feature is more pronounced for streamflow than for soil moisture, because snow melt usually occurs when the soil is wet (and the fraction of precipitation running off is high, as shown in Figure 1). Therefore, snow information mainly impacts streamflow (see section 2.1). Interestingly, the soil moisture and streamflow predictabilities in the highest catchment (Massa) do not benefit from initial snow information because there is snow in all seasons in this catchment. As the information about initial snow is valuable because it indicates how much melting can occur before the snow is gone, it does not add any value in this catchment because it is largely glaciated as discussed above.
 We find similar results for the added forecast skill from the temperature forecast, except that for the Massa catchment the added skill is not zero but clearly positive and much larger than in the other catchments. As snow is continuously present, the temperature information is always important in that catchment. This stands in contrast to the results for low-altitude catchments, which are snow-free during most parts of the year and where temperature is thus of little relevance for soil moisture.
 The added forecast skill from the precipitation forecast for both soil moisture and streamflow is strongly related to altitude. It is most valuable in low altitude catchments where precipitation falls mostly as rain, which directly impacts soil moisture and streamflow. In high-altitude catchments, an increasing part of the precipitation in the considered period March–October falls as snow, which has no direct impact on soil moisture and streamflow. This explains the lower importance of the precipitation forecast in high-altitude catchments.
 As already identified in the two previous subsections, Figure 11 underlines the limited importance of the radiation forecast for soil moisture and streamflow predictability. In case of streamflow, it is almost zero in all catchments. In case of soil moisture, we find a small added value in low altitude catchments. Net radiation there impacts soil moisture, as ET is comparatively high and mostly driven by radiation [Orth and Seneviratne, 2013].
4.2.4 Dependency of Skills on Initial Conditions
 In Figure 12 we investigate the dependency of (potential) soil moisture and streamflow forecast skills on the initial soil moisture anomaly. The uppermost row displays the respective forecast skills that are achieved when using information on initial snow content and all ECMWF forcing forecasts (experiment 6; see also Table 1) as already shown in the bottom rows of Figures 6 and 7. In the other three rows, the selection of forecasts is increasingly constrained such that only forecasts with initial soil moisture anomalies of at least , , and , respectively, are considered. Thereby, is the standard deviation of soil moisture at a certain day of the year computed over the soil moisture values of that day from all considered 15 years. Note that the maximum threshold is chosen such that there are still enough forecasts left to compute meaningful forecast skills for each half-monthly period and lead time (see section 2.2.1), namely about a quarter of the originally considered 90 forecasts for each lead time in each period.
 We find that for both soil moisture and streamflow, the predictability improves for more extreme initial conditions compared to the original experiment 6. The improvement is larger for higher thresholds, indicating that larger initial soil moisture anomalies are associated with higher increases in skill. The improvement occurs predominantly in spring, and also in summer and autumn. Soil moisture forecast skill only increases at lead times beyond 1 week, whereas the streamflow forecast skill increases at all considered lead times. The improvement of streamflow predictability varies considerably even between similar lead times and neighboring half-monthly periods. This reflects the strong dependency of streamflow on precipitation (equation (3)), which by nature has a high variability in Central Europe.
 Summarizing the above findings, Figure 12 shows that information about initial soil moisture is especially valuable for hydrological forecasting when it strongly deviates from the climatological mean. This corresponds well with findings of Koster et al. [2010b], who find increased predictability of temperature and precipitation in North America for larger initial soil moisture anomalies. Also, Orth and Seneviratne find increased soil moisture persistence in case of large initial anomalies in the investigated European catchments, which is consistent with this finding.
 In the following subsection, we further point out the importance of initial soil moisture and snow information by comparing its contribution to soil moisture and streamflow predictability with their contribution of the forcing forecast.
4.2.5 Importance of Initial Conditions
 As described in section 2.2.2, experiment 7 (see Table 1) is the only experiment that does not use “true” initial soil moisture, but instead climatological values as illustrated in Figure 3. Comparing the results of this experiment with the results of experiment 2, we can assess the relative importance of realistic initial conditions versus a state-of-the-art forcing forecast for soil moisture and streamflow forecasts.
 Figure 13 displays the soil moisture and streamflow forecast skills of experiments 2 and 7, and the respective difference in the first three columns. We find that generally the initial conditions provide more soil moisture forecast skill than the ECMWF forcing forecasts in all considered months and at all considered lead times. In terms of streamflow, we find the opposite behavior, i.e., the forcing forecasts are more important during most of the considered period. However, during the snow melting season from May to July, the initial conditions are almost equally important for the streamflow forecasts (and even more important at long lead times), as the information on initial snow depth is especially valuable at that time. The fourth and fifth columns of Figure 13 show results of the catchments with maximum and minimum differences between the skills of experiments 2 and 7. Considering the maximum differences, we find that not all catchments display a higher importance of the forcing forecasts versus initial conditions for the resulting skill of the streamflow forecast. For example in the Alpine Ova Dal Fuorn catchment, the initial conditions are more important, especially during the melting season. Similarly, we find from the minimum difference plots that not all catchments display a higher importance of the initial conditions versus the forcing forecast for the soil moisture forecasts. For instance, in the Alp catchment, the forcing forecasts lead to more soil moisture forecast skill than the (synthetically) true initial conditions at lead times between 5 and 15 days in autumn.
 Note that the maximum difference plot for soil moisture illustrating results for the Ova Da Cluozza catchment points to an extremely large skill resulting from true initial conditions, even at long lead times. The reason for this large skill is that the interannual soil moisture variations in this catchment exceed by far the seasonal variations in contrast to all other catchments. Therefore, true initial conditions in this catchment lead to very high soil moisture forecast skills as these are computed from forecasted anomalies from all considered years as discussed in section 2.2.1.
 Concluding this section, we find that a realistic initialization is generally more valuable for the soil moisture forecasts in the considered Swiss catchments than a state-of-the-art meteorological forecast. This is due to the fact that the period until which there is significant skill in the forcing forecasts is too short to “wash out” the offset between true initial soil moisture and the respective climatological value, because variations in soil moisture only cause small differences in streamflow and ET. In other words, the initial soil moisture variability is larger than the soil moisture difference caused by ECMWF versus climatological forcing. For streamflow, however, the forcing forecast (especially its precipitation component) is more important than initial conditions. For soil moisture we can moreover conclude that its predictability only benefits from a state-of-the-art forcing forecast if the initial conditions are realistic as shown especially for precipitation in Figure 6; whereas if the initial conditions are not known, the soil moisture forecast only benefits weakly from a state-of-the-art forcing forecast.
4.3 Predictability Versus Memory
 To assess the links between the concepts of memory and predictability, we investigate here the relationship between these two quantities. Several previous publications investigated either hydrological memory characteristics [Koster and Suarez, 2001; Seneviratne et al., 2006; Seneviratne and Koster, 2012; Orth and Seneviratne, 2012] or predictability [e.g., Koster et al., 2010b; van den Hurk et al., 2012]. While the latter publications postulated a link between memory and predictability, the exact relationship between these two concepts was not evaluated. Figure 14 shows forecast skills of soil moisture and streamflow of experiment 2 (true initial conditions and climatological forcing forecasts), averaged over all months between March and October in each catchment, plotted versus the respective squared memories (computed as described in section 2.3) for lead times of 5 and 20 days. Squaring the memory values is necessary to make it comparable to forecast skills expressed as explained fractions of variance (R2).
 We find very good correspondence between soil moisture forecast skill and soil moisture memory, pointing out a strong relation between the two quantities. This relation is also apparent for streamflow, but slightly weaker. The correspondence tends to be slightly poorer for the shorter lead time.
 In conclusion, we can summarize that even if predictability and memory are different measures of persistence, these two quantities are clearly related.
 In this study we investigated the potential predictability of soil moisture and streamflow in Switzerland using a simple water balance model. We have shown that there is significant skill in soil moisture and streamflow forecasts in the investigated spring, summer and fall seasons in 22 near-natural catchments, underlining the usefulness of such predictions.
 For this purpose we have successfully updated a simple conceptual water balance model [Orth et al., 2013] by including a simple snow module. In this model, streamflow normalized by precipitation and evapotranspiration normalized by net radiation are catchment-specific functions of soil moisture that are determined using observed streamflow. To yield more realistic model results especially during the melting season and in high-altitude catchments, we account for snow using a simple degree-day approach in which snow melting depends linearly on temperature. Using this methodology, we obtain estimates of snow water equivalent that compare well to observations in all considered catchments.
 Only using initial soil moisture, we find high potential forecast skill for soil moisture until approximately 1 week lead time and for streamflow until 2–3 days ahead. Using also information on initial snow cover as well as seasonal forecasts of precipitation, net radiation, and temperature, the lead time predictability doubles in case of soil moisture and even triples for streamflow. These time scales are very important for decision making, for instance for issues such as irrigation or flood protection. Interestingly, even at long lead times where the seasonal forcing forecasts have no skill, they contribute to better soil moisture and streamflow predictability. Their skill at short lead times leads to a longer-lasting improvement of the soil moisture forecast (and therefore, also of the streamflow forecast that depends on the soil moisture content) thanks to the soil moisture memory. This result as well as the time scale of soil moisture predictability correspond well to findings of Calanca et al.  who applied a simple bucket model with probabilistic forcing forecasts to derive soil moisture forecasts in Switzerland.
 Note that the described forecast skills are potential forecast skills as we compare the model forecasts to (modeled) synthetic truths. Using streamflow observations, we find that the actual forecast skill of the simple model in terms of streamflow is only about 60% of the potential skill.
 Comparing the contributions of initial snow information and the respective forcing forecasts to soil moisture and streamflow forecast skill, we find that in low-altitude catchments, the precipitation forecast is clearly the most important contributor to both. Toward higher altitudes more precipitation falls as snow, therefore limiting its impact on soil moisture and streamflow and hence its contribution to forecast skill. In high-altitude catchments (>2000 m) the temperature forecast and the initial snow information are the main contributors, because the melting snowpack is a large source of water impacting soil moisture and streamflow.
 Confirming other studies [e.g., Koster et al., 2011; Orth and Seneviratne, 2012], we find that not all initial soil moisture states are equally informative for hydrological forecasts. The stronger the initial soil moisture content deviates from its climatological mean, the higher is the skill gained in hydrological forecasts using this information.
 We showed furthermore that accurate initial soil moisture and snow information are generally more important for soil moisture forecasts than accurate forcing forecasts because inaccurate initial soil moisture values deteriorate the soil moisture forecasts more strongly and with longer-lasting consequences than a climatological forcing forecast. This result is important for the interpretation of the GLACE-2 study [Koster et al., 2010b, 2011] which compared realistic versus random soil moisture initialization. A state-of-the-art forcing forecast only significantly improves a soil moisture forecast if the initial conditions are known. For streamflow, we find the opposite result; an accurate forcing forecast is generally more important than realistic initial soil moisture values. However, a few catchments show a different behavior in some seasons, i.e., the forcing forecast is more important for the soil moisture forecast and the initial conditions are more important for the streamflow forecast. These are helpful findings as they indicate where emphasis should be put in order to improve the respective hydrological forecasts in the future. Wood and Lettenmaier report similar results for two sites in the western U.S. (only considering streamflow). Even if they do not find a generally dominant source of information, they also find that the relative importance of initial conditions and seasonal forcing forecasts depend on season and location.
 In the last part of our study, we point out the similarities between the concepts of hydrological memory and predictability. Using the computed forecast skills for soil moisture and streamflow, we show that these correspond very well to the respective soil moisture and streamflow memories, which implies that a high memory is generally associated with good predictability.
 We acknowledge the Swiss Federal Office for the Environment (FOEN) for providing streamflow data, the Institute for Snow and Avalanche Research (SLF) for providing snow depth data, and the Swiss weather service (MeteoSwiss) for providing meteorological data. Furthermore, we thank Massimiliano Zappa for his help with the streamflow and snow data, and Christoph Appenzeller, Andreas Fischer, and Randy Koster for helpful discussions. We acknowledge the ECMWF VarEPS reforecast data set (http://www.ecmwf.int/products/changes/vareps/[checked on 10 December 2012]) and we highly appreciate the help of Dani Lüthi with downloading and storing these data. We also acknowledge the NASA/GEWEX SRB project (http://eosweb.larc.nasa.gov/PRODOCS/srb/table_srb.html [checked on 28 September 2012]) for sharing radiation data. We acknowledge funding by the Swiss National Foundation through the NRP61 DROUGHT-CH project, as well as partial support from the EU-FP7 DROUGHT-RSPI project.