In the present study, we focus on the assimilation of satellite observations for Surface Soil Moisture (SSM) in a hydrological model. The satellite data are produced in the framework of the EUMETSAT project H-SAF and are based on measurements with the Advanced radar Scatterometer (ASCAT), embarked on the Meteorological Operational satellites (MetOp). The product generated with these measurements has a horizontal resolution of 25 km and represents the upper few centimeters of soil. Our approach is based on the Ensemble Kalman Filter technique (EnKF), where observation and model uncertainties are taken into account, implemented in a conceptual hydrological model. The analysis is carried out in the Demer catchment of the Scheldt River Basin in Belgium, for the period from June 2013–May 2016. In this context, two methodological advances are being proposed. First, the generation of stochastic terms, necessary for the EnKF, of bounded variables like SSM is addressed with the aid of specially-designed probability distributions, so that the bounds are never exceeded. Second, bias due to the assimilation procedure itself is removed using a post-processing technique. Subsequently, the impact of SSM assimilation on the simulated streamflow is estimated using a series of statistical measures based on the ensemble average. The differences from the control simulation are then assessed using a two-dimensional bootstrap sampling on the ensemble generated by the assimilation procedure. Our analysis shows that data assimilation combined with bias correction can improve the streamflow estimations or, at a minimum, produce results statistically indistinguishable from the control run of the hydrological model.

Sources of errors in model estimations are generally of two kinds, input data errors (including initialization) and model errors. One method to decrease deviations of the estimated model states from observations is to optimally “assimilate” observed data of relevant model variables into the model. Data assimilation has a long history as a modeling tool, and in the present article, we will focus on applications to hydrology, with emphasis on soil moisture and streamflow.

Soil moisture is a variable that plays an important role in a hydrological system by regulating several water exchanges and energy fluxes. There are many monitoring networks for soil moisture around the world [

Satellite observations can ensure today complete coverage of large areas and provide a representation of the soil state at regular time intervals. Specifically, as an alternative to ground-based measurements, great efforts have been made in the past two decades to develop soil moisture products from microwave signals with the launch of several instruments on board satellite missions [

Each satellite mission carrying such instruments has been designed to satisfy certain technical requirements, e.g., regarding spatial coverage, resolution and scanning frequency. Therefore, significant differences can be expected between the technical specifications of satellite data and the corresponding requirements of several applications in Earth systems, e.g., modeling of the atmosphere and of the hydrological cycle. In fact, many studies have investigated the potential to improve river discharge estimations by using satellite data in hydrological models. This is a complex task, and the outcome depends on the model used, the spatiotemporal scales, the method of using the data (direct use or assimilation) and the quality and availability of the satellite data. For example, [

Several other studies exist investigating potential benefits of assimilating soil moisture data, e.g., [

Another frequently-encountered problem is the difference, or bias, in the mean value and variability between different sources of SSM data (satellite retrievals and model integrations in our context). This bias can pose significant obstacles to the use of the information contained in satellite measurements for any kind of application, including data assimilation, and has to be removed. Different methods to remove such bias have been explored in the literature, in particular linear regression, mean and variance matching and Cumulative Distribution Function (CDF) matching [

Estimating an appropriate error for soil moisture observations, used in data assimilation, is still an open problem. One choice is to compare the satellite data with ground-based observations (validation) [

The ensemble Kalman filter is a data assimilation method used in geosciences [

The existence of bounds for the assimilated variable gives rise to another problem as well. In the ensemble Kalman filter, the generation and use (as perturbations) of stochastic terms from a normal distribution are generally required. Obviously, repeated application of such perturbations on a bounded variable, like soil moisture, will often drive out of their bounds the values that are already near them. This is another source of biases in the estimations, especially in the most extreme cases (very dry or very wet conditions, speaking of soil moisture). A technique based on variable standard deviation was introduced in [

In the present study, our goal is to assimilate satellite data for surface soil moisture in the SCHEME hydrological model and to assess the effects of this assimilation in terms of streamflow. The satellite data for soil moisture that we use here are derived from active microwave measurements with the ASCAT sensor on board the MetOp [

In our approach, surface soil moisture is properly treated as a bounded variable. In particular, the perturbations needed for the ensemble Kalman filter are generated from truncated normal distributions. This ensures that no soil moisture value exceeds the bounds after the application of perturbations. We use truncated distributions in order to generate perturbations for the precipitation, as well, which is thought of as the forcing of the hydrological model. In this case, the perturbations are applied multiplicatively; therefore, truncated log-normal distributions are used. Of course, precipitation is not bounded in theory from the top, and simple log-normal sampling would suffice. The reason for this unusual, at first sight, choice is that it will ensure that the precipitation values that will be generated by applying such perturbations will remain within the climatological margins.

We tackle in the following way the issue of bias, induced by non-linear processes in conjunction with the use of stochastic terms. Initially, a full data assimilation run is performed. Then, another run is performed in which only perturbations are applied to precipitation, that is the model states are not updated by the Kalman equation. The streamflow ensemble generated by this run is carrying only the bias of the process because there is no assimilated information. The deviation of its mean from the control simulation for the streamflow is then used in order to remove the bias from the full data assimilation ensemble. The introduction and use of truncated probability distributions in a data assimilation scheme and the post-processing technique explained above are the two main advances proposed here.

The article is organized as follows. In

The SCHEME hydrological model (SCHEldt-MEuse, from the names of the two major rivers of Belgium), used for our simulations, is the distributed version of the IRMB hydrological model [

The SCHEME model is optimized for river basins up to 20,000

The SCHEME model structure comprises 9 different land covers with a snow accumulation and melting module. The land cover types are represented by the appropriate variable fractions on each grid cell. Sub-grid soil properties are also indirectly taken into account through a regionalization procedure. The actual evapotranspiration is calculated on the basis of the water intercepted by the vegetation and the water content of two soil layers, as well as the Potential Evapotranspiration (PET) according to the Penman formula. The time step of the model is equal to one day. Surface water is simulated with a unit hydrograph, and the underground water is represented with two reservoirs. The streamflow produced on each grid cell is routed to the outlet with a 1D submodel based on the width function of the river network [

Let us recall briefly from [

If instead

Overall, in the SCHEME model, the soil water content and runoff calculation is based on simple water balance considerations. In other studies, while analogous principles are used for soil moisture, the runoff is estimated using the Soil Conservation Service Curve Number [

The parameters of the SCHEME model have been calibrated based on data from a variety of catchments in the Scheldt and the Meuse River Basins from the period 1981–1988. The calibration technique combines elements from the approach in [

The capacity of the upper soil layer is one of the parameters of the model that are optimized and regionalized. Its value is in the range of 5–28 mm in the Scheldt River Basin and corresponds to a soil depth of several centimeters. The saturation of this conceptual reservoir is put into correspondence with the soil wetness index of the satellite product.

Our data assimilation approach is based on the ensemble Kalman filter technique [

The general principles of the EnKF can be described as follows. We restrict our interest in finite dimensional systems described by ordinary differential equations. If

In discrete form, Equation (

Let

During assimilation, the model states are adjusted using information from the observations of the variable

Under these conventions, the updated state

In Equation (

In our case, there is only one variable to assimilate, SSM from satellite observations. Therefore, the assimilation problem is one-dimensional, and all of the matrices involved are simply real numbers. We will consider as true model state

One particular feature of soil moisture is that it is bounded between the values 0 and 100. Therefore, during assimilation in an EnKF context, applying Gaussian noise on SSM will often violate this constraint, especially for values near the bounds. This is a long-standing problem that was, to our knowledge, not adequately addressed so far. A method using the variable standard deviation for the error distribution is proposed in [

We notice here that

A truncated variable will be used in our context in the following way. Let us consider an SSM value, for example

We need such additive truncated variables in order to generate the variance

We work similarly with truncated log-normal distributions, which are used to generate multiplicative factors. These factors constitute an implementation of the uncertainty in interpolated precipitation, which is one of the input fields in the SCHEME model. In existing literature, this uncertainty is represented as a rule by full range log-normal distributions [

The ensemble Kalman filter can be used, by its design, in non-linear systems without the need for developing a linearization scheme, like for example in the case of the extended Kalman filter. This has the potential to considerably simplify the study. On the other hand, it became at some point clear that the stochastic terms generated by the filter generally induce bias in the estimations when non-linear processes take place [

It is possible to implement a correction method for this bias in order to make evident the net effect of the assimilation procedure. Such a method has been proposed in [

In the SCHEME model, the calculation of moisture at the top layer of the soil is carried out as follows. Let

This simple condition on the range of

The notation convention is the same for all of the ensembles

The reason to examine the effect of precipitation perturbations only is that among the three transformations that affect directly the soil moisture variable

The bias correction method proposed in this section presents some analogies with the method of [

Our study is carried out for the catchment of Demer, located in the central-eastern part of Belgium. This catchment covers an area of

The main land use in the Demer catchment consists of crops (46%), meadows (29%) and forests (18%). The remaining 7% is inhabited. The elevation ranges between 17 and 173 meters, with a mildly hilly profile in the south. The length of the main river is

A rain gauge network from the Royal Meteorological Institute of Belgium (approximately one station per

In the same reference period (1966–1995), the mean temperature is

The study period is 1 June 2013–31 May 2016. The satellite data we use for this period come from the EUMETSAT Satellite Application Facility on Support to Operational Hydrology and Water Management (project H-SAF,

For assimilation purposes, we use the large-scale surface soil moisture product SM-OBS-1(or H07). This product is generated from MetOp scatterometer data (ASCAT) at a coarse resolution (

We also use the H-SAF product SM-DAS-2 (or H14) for comparisons with the SCHEME model data at the root zone level. This product is generated in the ECMWF Land Data Assimilation System by assimilating ASCAT SSM data (essentially the H07 product that we discussed previously). In this case, the data assimilation process is based on the extended Kalman filter [

Before assimilating the SSM data from H07, a bias correction is applied on them in order to determine the true state in Equation (

As mentioned in

The model error term

For the generation of the term

In an analogous way, the perturbations for precipitation (

The precipitation input and the results of simulations with the SCHEME model are graphically represented in

The effect of the assimilation is very obvious at the level of the soil moisture. Regarding the upper layer of the soil, the ensemble generally follows the satellite values. The situation is very different in the lower soil layer, where no assimilation is taking place, but the moisture values are calculated by the SCHEME model after assimilating satellite data at the upper layer. The results of the reference simulation are the only basis for quantitative comparisons that we have for this layer of the soil. In some cases, we observe large deviations between the ensemble members and the reference simulation (e.g., autumn and winter in

For the streamflow, we have two cases, one ensemble obtained by applying the assimilation procedure (DA) and another one obtained by correcting the previous ensemble for bias (DA-BC), according to the method described in

In the corresponding figures, the ensemble averages are also depicted together with the control simulation of the model and the streamflow observations. The differences between these time series are quantified using well-established synoptic statistical measures such as bias, Absolute bias (A-bias), root mean square error (RMSE), correlation (R) and Nash–Sutcliffe Efficiency coefficient (NSE). The calculations are carried out at seasonal and annual time scales. The results of such synoptic statistics for all possible combinations of data and time periods are shown in

Finally, in order to assess the significance of the differences in the scores, we calculate the 95% confidence intervals of the ensemble average scores by using a bootstrap approach. More precisely, each ensemble is randomly sampled in two ways, once in its members and once more in time. We consider the difference between the scores of the control simulation and of the ensemble average as statistically significant if the control value lies outside of the confidence interval.

The qualitative features of the results for the streamflow, seasonal and annual, as well, depend on the period considered. For example, for the year June 2013–May 2014, the average of the DA ensemble yields better annual scores than the reference simulation. The situation is reversed in the year June 2014–May 2015, while in the final period from June 2014–May 2015, the ensemble average becomes again better than the control simulation. However, the differences between the scores are small, and this motivates the use of the statistical significance test mentioned before.

On the other hand, the average of the DA-BC ensemble exhibits more consistent performance in time. For example, its annual scores are all better than the scores of the control simulation in the three years studied here. Like in the case of the DA ensembles, the differences in the scores are small and their significance is checked with the calculation of confidence intervals.

The results of statistical significance analysis using bootstrap replications are presented in

In this implementation of the ensemble Kalman filter, we can see in a clear way the manifestation of bias due to the use of stochastic perturbations in a nonlinear process. This bias can have unpredictable effects on model performance and can mask the net result of the adjustment applied to the model states through the Kalman equation.

In the three-year period that we study in this article, there are cases of large differences between the control simulation and the ensemble averages for the streamflow during shorter periods of time. For example, from 20 February 2014–6 May 2014, the average of the DA ensemble is a much better approximation of the observations than the control simulation. This is clearly seen in

Another typical case is from 20 September 2014–10 November 2014 (

The previous situations demonstrate the need to reduce the biases arising in EnKF where non-linear processes take place. The general idea here is to identify the sources of bias and, subsequently, to filter out their effect by running again the model while keeping active the perturbations, which are responsible for bias generation, but without assimilating any data.

It is clear also, at least for this case study, that soil moisture assimilation has a limited impact on the streamflow calculated by the model. This is not surprising because streamflow is mainly determined by precipitation. The assimilation of soil moisture would have more potential in cases where the model does not estimate correctly the water content of the soil, especially in cases with significant amounts of rainfall and saturated soils. Such indications exist also for the SCHEME model in the period that we study here. For example, we see in

The moisture variations of the lower soil layer is another point that warrants further investigation. There are systematic differences between the control simulation and the output of the EnKF, which are larger in autumn and the beginning of winter. The origin of such deviations is in part the bias generated by the precipitation perturbations through the nonlinearities of the model and in part the assimilation itself, which transmits the satellite signal from the surface to the lower soil layer through the processes encompassed in the model, with the largest contribution coming from the latter. The lack of any soil moisture measurements for the lower layer prevents at this point a thorough analysis. However, H-SAF provides a root zone soil moisture product, SM-DAS-2 (H14). In order to compare the estimations of H14 and those of the SCHEME model, we can only rescale both in the interval [0,100], because the units are different. Therefore, no proper quantification of the differences could be made in soil moisture units. Nevertheless, visual inspection of the graphs that we provide in

The purpose of this study is to explore the possibilities to improve streamflow estimation from a hydrological model by assimilating soil moisture data. Our analysis leads to improvements of certain aspects of the ensemble Kalman filter for bounded variables used in nonlinear processes.

The ensemble version of the Kalman filter relies on the repetitive generation of stochastic terms, which are used in order to perturb the ensemble members and calculate state corrections. In the existing literature, this leads systematically to biases, because the perturbations do not in principle preserve the bounds of a variable like the soil moisture. Here, we propose a natural solution to this problem based on truncated probability distributions, which can be applied to the case of any bounded variable.

Another problem is the generation of bias in the model output when such perturbations are applied to a variable that is used in nonlinear processes (soil moisture in our case). The solution proposed here is to identify the source of bias and to isolate its effect by running the model in ensemble mode without assimilating any data, but keeping the perturbations that cause the bias generation. The ensemble obtained in this way can be used to remove the nonlinear processes bias from the full assimilation ensemble.

The combination of the previous steps leads to very consistent data assimilation results. In summary, the streamflow estimations after data assimilation in the SCHEME hydrological model and bias correction are in many cases better than the control simulation of the model in a statistically-significant way. In the remaining situations, these estimations are statistically identical to the control.

Our results point out that the EnKF could be also used as a diagnostic tool to detect weaknesses in a model and to improve its performance. The case of March 2014 reported previously is indicative of such situations. It suggests that further investigation is required regarding the optimization of the SCHEME model parameters that control the seasonal streamflow contribution, especially in spring.

Extending the domain of hydrological simulations into other catchments will provide new insight regarding the spatial features of our data assimilation approach assisted by bias correction. Ultimately, a more extensive use of satellite data could be considered in this context.

This article is based on work supported by EUMETSAT in the framework of the H-SAF project. Discharge data are provided by the Hydrological Information Centre of the Flemish Region. Credit for the topographic data in

P. Baguis carried out the data processing and analysis, developed the data assimilation methodology and wrote the paper. E. Roulin proposed the main idea, offered guidance to complete the work and contributed to the editing of the manuscript and to the discussion and interpretation of the results.

The authors declare no conflict of interest.

The following abbreviations are used in this manuscript:

_{2}doubling on the water cycle and on the water balance—A case study for Belgium

_{2}doubling on the water balance—A case study in Switzerland

Diagram of the SCHEME model. Model parameters: (1)

Bias for the surface soil moisture product H07, based on data from June 2009–May 2013. The original raw data are also shown.

Probability distribution of surface soil moisture values, based on simulation data with the SCHEME model, from January 1966–December 1995. The bins subdivide the interval formed by the whole dataset into ten equal parts.

Probability distribution of surface soil moisture standard deviation values, based on simulation data with the SCHEME model, from January 1966–December 1995. The bins subdivide the standard deviation intervals corresponding to each soil moisture class into ten equal parts.

Hydrological data and model output for the period June 2013–May 2014. From top to bottom: precipitation, soil moisture in the upper layer, soil moisture in the lower layer, streamflow with data assimilation only and streamflow with data assimilation and bias correction.

Hydrological data and model output for the period June 2014–May 2015. From top to bottom: precipitation, soil moisture in the upper layer, soil moisture in the lower layer, streamflow with data assimilation only and streamflow with data assimilation and bias correction.

Hydrological data and model output for the period June 2015–May 2016. From top to bottom: precipitation, soil moisture in the upper layer, soil moisture in the lower layer, streamflow with data assimilation only and streamflow with data assimilation and bias correction.

Streamflow for the period 20 February 2014–6 May 2014.

Streamflow for the period 20 September 2014–10 November 2014.

Areal average for the lower soil layer moisture of the SCHEME model and the H-SAF product H14, over three successive years (1 June 2013–31 May 2016). The SCHEME model output is given originally as the degree of saturation (%), while H14 is in volumetric units (m^{3}/m^{3}). A rescaling has been applied in both time series for this comparison.

Synoptic statistics for streamflow with and without bias correction in the ensemble, 1 June 2013–31 May 2016. The unit for bias, Absolute bias (A-bias) and RMSE is

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Reference simulation | −0.077 | 0.130 | 0.176 | 0.938 | 0.848 |

Ensemble mean DA | 0.062 | 0.111 | 0.171 | 0.943 | 0.856 |

Ensemble mean DA-BC | −0.039 | 0.114 | 0.159 | 0.946 | 0.876 |

Synoptic statistics for streamflow with and without bias correction in the ensemble, 1 June 2013–31 May 2014. The unit for bias, A-bias and RMSE is

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Reference simulation | |||||

Annual | −0.094 | 0.116 | 0.138 | 0.940 | 0.769 |

Summer 2013 | −0.074 | 0.087 | 0.107 | 0.817 | 0.359 |

Autumn 2013 | −0.075 | 0.096 | 0.119 | 0.958 | 0.856 |

Winter 2013–2014 | −0.101 | 0.147 | 0.170 | 0.946 | 0.763 |

Spring 2014 | −0.126 | 0.136 | 0.147 | 0.706 | −1.310 |

Ensemble mean DA | |||||

Annual | 0.017 | 0.068 | 0.105 | 0.952 | 0.866 |

Summer 2013 | −0.020 | 0.059 | 0.090 | 0.788 | 0.539 |

Autumn 2013 | 0.017 | 0.062 | 0.077 | 0.971 | 0.939 |

Winter 2013–2014 | 0.056 | 0.087 | 0.141 | 0.959 | 0.836 |

Spring 2014 | 0.019 | 0.065 | 0.099 | 0.764 | −0.060 |

Ensemble mean DA-BC | |||||

Annual | −0.068 | 0.099 | 0.121 | 0.947 | 0.821 |

Summer 2013 | −0.075 | 0.089 | 0.109 | 0.808 | 0.332 |

Autumn 2013 | −0.053 | 0.078 | 0.094 | 0.968 | 0.909 |

Winter 2013–2014 | −0.043 | 0.117 | 0.150 | 0.945 | 0.816 |

Spring 2014 | −0.100 | 0.111 | 0.125 | 0.721 | −0.672 |

Synoptic statistics for streamflow with and without bias correction in the ensemble, 1 June 2014–31 May 2015. The unit for bias, A-bias and RMSE is

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Reference simulation | |||||

Annual | −0.052 | 0.133 | 0.192 | 0.927 | 0.831 |

Summer 2014 | 0.001 | 0.165 | 0.239 | 0.930 | 0.739 |

Autumn 2014 | −0.043 | 0.091 | 0.126 | 0.758 | 0.508 |

Winter 2014–2015 | −0.054 | 0.158 | 0.215 | 0.926 | 0.840 |

Spring 2015 | −0.109 | 0.119 | 0.167 | 0.928 | 0.729 |

Ensemble mean DA | |||||

Annual | 0.102 | 0.149 | 0.224 | 0.920 | 0.770 |

Summer 2014 | 0.189 | 0.208 | 0.326 | 0.935 | 0.512 |

Autumn 2014 | 0.145 | 0.156 | 0.185 | 0.786 | −0.056 |

Winter 2014–2015 | 0.035 | 0.146 | 0.212 | 0.929 | 0.846 |

Spring 2015 | 0.038 | 0.085 | 0.121 | 0.935 | 0.857 |

Ensemble mean DA-BC | |||||

Annual | −0.005 | 0.125 | 0.189 | 0.930 | 0.837 |

Summer 2014 | 0.036 | 0.170 | 0.252 | 0.932 | 0.707 |

Autumn 2014 | 0.007 | 0.079 | 0.111 | 0.791 | 0.623 |

Winter 2014–2015 | 0.007 | 0.153 | 0.216 | 0.925 | 0.839 |

Spring 2015 | −0.073 | 0.097 | 0.141 | 0.927 | 0.806 |

Synoptic statistics for streamflow with and without bias correction in the ensemble, 1 June 2015–31 May 2016. The unit for bias, A-bias and RMSE is

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Reference simulation | |||||

Annual | −0.084 | 0.141 | 0.193 | 0.944 | 0.867 |

Summer 2015 | −0.043 | 0.125 | 0.160 | 0.777 | 0.461 |

Autumn 2015 | −0.074 | 0.094 | 0.125 | 0.886 | 0.667 |

Winter 2015–2016 | −0.195 | 0.221 | 0.272 | 0.950 | 0.802 |

Spring 2016 | −0.019 | 0.125 | 0.184 | 0.909 | 0.773 |

Ensemble mean DA | |||||

Annual | 0.065 | 0.116 | 0.164 | 0.959 | 0.904 |

Summer 2015 | 0.083 | 0.099 | 0.166 | 0.826 | 0.413 |

Autumn 2015 | 0.038 | 0.081 | 0.113 | 0.881 | 0.729 |

Winter 2015–2016 | 0.006 | 0.137 | 0.177 | 0.958 | 0.917 |

Spring 2016 | 0.140 | 0.151 | 0.190 | 0.949 | 0.758 |

Ensemble mean DA-BC | |||||

Annual | −0.045 | 0.118 | 0.160 | 0.957 | 0.909 |

Summer 2015 | −0.035 | 0.116 | 0.154 | 0.780 | 0.498 |

Autumn 2015 | −0.059 | 0.089 | 0.117 | 0.889 | 0.711 |

Winter 2015–2016 | −0.103 | 0.169 | 0.210 | 0.956 | 0.883 |

Spring 2016 | 0.021 | 0.096 | 0.143 | 0.939 | 0.862 |

Statistical significance of the differences between the scores of the ensemble averages and the corresponding scores of the reference simulation for streamflow, 1 June 2013–31 May 2016.

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Ensemble mean DA | Y+ | Y+ | N | N | N |

Ensemble mean DA-BC | Y+ | Y+ | Y+ | N | Y+ |

Statistical significance of the differences between the scores of the ensemble averages and the corresponding scores of the reference simulation for streamflow, 1 June 2013–31 May 2014.

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Ensemble mean DA | |||||

Annual | Y+ | Y+ | Y+ | N | Y+ |

Summer 2013 | Y+ | Y+ | N | N | N |

Autumn 2013 | Y+ | Y+ | Y+ | N | N |

Winter 2013–2014 | Y+ | Y+ | N | N | N |

Spring 2014 | Y+ | Y+ | Y+ | N | Y+ |

Ensemble mean DA-BC | |||||

Annual | Y+ | Y+ | Y+ | N | N |

Summer 2013 | N | N | N | N | N |

Autumn 2013 | Y+ | Y+ | Y+ | N | N |

Winter 2013–2014 | Y+ | Y+ | N | N | N |

Spring 2014 | Y+ | Y+ | Y+ | N | N |

Statistical significance of the differences between the scores of the ensemble averages and the corresponding scores of the reference simulation for streamflow, 1 June 2014–31 May 2015.

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Ensemble mean DA | |||||

Annual | Y- | N | Y- | N | Y- |

Summer 2014 | Y- | N | N | N | Y- |

Autumn 2014 | Y- | Y- | Y- | N | Y- |

Winter 2014–2015 | Y+ | N | N | N | N |

Spring 2015 | Y+ | Y+ | Y+ | N | Y+ |

Ensemble mean DA-BC | |||||

Annual | Y+ | N | N | N | N |

Summer 2014 | N | N | N | N | N |

Autumn 2014 | Y+ | N | N | N | N |

Winter 2014–2015 | Y+ | N | N | N | N |

Spring 2015 | Y+ | N | N | N | N |

Statistical significance of the differences between the scores of the ensemble averages and the corresponding scores of the reference simulation for streamflow, 1 June 2015–31 May 2016.

Bias | A-Bias | RMSE | R | NSE | |
---|---|---|---|---|---|

Ensemble mean DA | |||||

Annual | Y+ | Y+ | Y+ | Y+ | Y+ |

Summer 2015 | Y- | N | N | N | N |

Autumn 2015 | Y+ | N | N | N | N |

Winter 2015–2016 | Y+ | Y+ | Y+ | N | Y+ |

Spring 2016 | Y- | Y- | N | N | N |

Ensemble mean DA-BC | |||||

Annual | Y+ | Y+ | Y+ | N | Y+ |

Summer 2015 | N | N | N | N | N |

Autumn 2015 | N | N | N | N | N |

Winter 2015–2016 | Y+ | Y+ | Y+ | N | Y+ |

Spring 2016 | Y0 | Y+ | Y+ | N | N |

Synoptic statistics for streamflow with and without SSM assimilation, 20 February 2014–6 May 2014. The unit for bias, A-bias and RMSE is

Ref. Simulation | Ens. Mean DA | Ens. Mean DA-BC | |
---|---|---|---|

Bias | −0.141 | −0.010 | −0.105 |

A-Bias | 0.141 | 0.044 | 0.106 |

RMSE | 0.150 | 0.056 | 0.114 |

R | 0.871 | 0.881 | 0.892 |

NSE | −1.364 | 0.660 | −0.382 |

Synoptic statistics for streamflow with and without SSM assimilation, 20 September 2014–10 November 2014. The unit for bias, A-bias and RMSE is

Ref. Simulation | Ens. Mean DA | Ens. Mean DA-BC | |
---|---|---|---|

Bias | −0.024 | 0.184 | 0.024 |

A-Bias | 0.070 | 0.184 | 0.067 |

RMSE | 0.085 | 0.205 | 0.082 |

R | 0.801 | 0.827 | 0.825 |

NSE | 0.607 | −1.277 | 0.636 |