# Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe?

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) in USA through Ensemble Kalman Filter (EnKF) [24] (using both synthetic and real case experiments), concluded that: “Assimilation of actual surface soil moisture data had limited success in the upper layers only and was generally unsuccessful in improving stream flow prediction mainly due to the SWAT decoupling between surface and root-zone layer that limits the ability of the EnKF to update the soil moisture states of deeper layers”. Brocca et al. [17], in a small catchment in central Italy, assimilated the Advanced SCATterometer (ASCAT, [11]) SM observations into two layer continuous hydrological model obtaining a great improvement in discharge prediction particularly for the floods occurring during dry to wet transition periods. The authors explored the sensitivity of the assimilation of both surface and root zone satellite SM observations to the model structure via two different assimilation experiments: (i) assimilation of the surface SM observations in the upper layer of the hydrological model, and, (ii) assimilation of the root zone SM observations (obtained by the application of the Exponential filter, [25]) into the lower layer of the model. They showed that the second solution provides much better results because of the larger impact of the root zone SM on runoff simulation for the investigated basin and of the weak and highly non-linear linkage between the SM states of the two layers which prevent the EnKF from updating the state of the deeper layer when the surface layer is assimilated.

^{2}are considered for which high-quality hydro-meteorological hourly observations are available in the period 2000–2013.

## 2. Materials

#### 2.1. Study Area

^{2}to 2040 km

^{2}and the mean catchment elevation ranges between 350 and 604 m a.s.l. The catchments located in the western part, Nestore and Chiani, are characterized by low slopes, and very similar soil and land use, whereas Marroggia lies in the Apennine reliefs, with higher elevations and slopes (Table 1). The climate is Mediterranean with mean annual precipitation of about 800 mm. Higher monthly precipitation values are generally observed during the autumn–winter period when floods caused by widespread rainfall normally occur. Mean annual temperature ranges from around 12–13 °C. Snowfall represents a low percentage of precipitation and is unusual and ephemeral at altitudes below 500 m a.s.l.

**Table 1.**Physical parameters of the selected catchments (A = area, P = annual precipitation amount, El = mean elevation, Sl = mean slope) along with the most important calibrated model parameters in the period 2000–2009 (W

_{max}= maximum water storage, K

_{s}= parameter of drainage, K

_{c}= parameter of evapotranspiration, η = lag time parameter of Equation (1)) and the time averaged model error standard deviation ${\overline{\text{\sigma}}}_{m}$ # SM-OBS4 pixels represents the number of the satellite pixels falling inside the catchment area, SM-OBS4 noise is the spatial average of noise SM information provided as ancillary data with SM-OBS4 product while T refer to value of the characteristic time length of the Exponential filter. α

_{1}, α

_{2}, α

_{3}represent the coefficients used to multiply the value of the parameters for obtaining their model error standard deviation, while σ

_{p}is the rainfall error standard deviation.

Catchment | TV-PF | NE-MA | CHI-MO | MA-AZ | NI-MI |
---|---|---|---|---|---|

A (km^{2}) | 2040 | 725 | 457 | 258 | 137 |

P (mm) | 818 | 739 | 724 | 835 | 830 |

El (m) | 521 | 350 | 404 | 604 | 452 |

Sl. (%) | 26 | 17 | 19 | 29 | 25 |

Land Use (%) | |||||

Woods | 53.6 | 37.7 | 49.5 | 55.7 | 65.1 |

Croplands | 9.4 | 3.8 | 4.7 | 4.6 | 7.9 |

Grasslands | 35.2 | 53.5 | 43.8 | 35.8 | 26.6 |

Urban areas | 1.7 | 5.0 | 2.0 | 3.9 | 0.4 |

Hydrologic Soil Group—Soil Conservation Service (%) | |||||

High infiltration rate | 5.0 | 1.7 | 0.6 | 9.4 | 3.2 |

Moderate infiltration rate | 19.5 | 17.4 | 19.9 | 11.1 | 12.4 |

Low infiltration rate | 74.4 | 81.0 | 79.4 | 75.6 | 84.4 |

Very low infiltration rate | 1.0 | 0.0 | 0.1 | 3.9 | 0.0 |

Parameters of the Rainfall—Runoff Model | |||||

W_{max} (mm) | 497 | 380 | 388 | 327 | 372 |

Ks (mm/h) | 20.8 | 28.8 | 29 | 40 | 21.8 |

Kc (mm/h) | 0.87 | 0.84 | 0.66 | 1.03 | 0.89 |

η (-) | 0.59 | 0.94 | 1.18 | 0.37 | 1.51 |

${\overline{\text{\sigma}}}_{m}$ (%) | 4 | 4.4 | 2 | 3.3 | 5 |

α_{1} (%) | 40 | 40 | 80 | 50 | 80 |

α_{2}, α_{3} (%) | 30 | 10 | 30 | 20 | 30 |

${\text{\sigma}}_{p}$ (mm) | 0.75 | 0.5 | 0.25 | 0.75 | 0.25 |

Satellite Data | |||||

# SM-OBS4 pixels | 12 | 5 | 1 | 1 | 1 |

SM-OBS4 noise (%) | 11 | 9.5 | 8 | 13.5 | 9.3 |

T (days) | 48 | 87 | 67 | 62 | 68 |

#### 2.2. In Situ Data

#### 2.3. Satellite Data

## 3. Methods

#### 3.1. Hydrological Model

^{2}), and η a parameter to be calibrated.

_{max}, the saturated hydraulic conductivity, K

_{s}, the parameter controlling the fraction of drainage that transforms in subsurface runoff, υ, the pore size distribution index, m, the correction coefficient for the potential evapotranspiration, K

_{c}, the lag-area relationship parameter η, the initial abstraction coefficient, λ, and the parameter a of the relationship between modelled SM and the S of the SCS-CN method.

#### 3.2. Ensemble Kalman Filter

**Y**(t) the vector of system states at time step t

_{k}obtained via a generic model and

**Z**

_{k}the observation vector at time t

_{k}, then, the optimal updating of

**Y**

_{k}, can be expressed as

_{th}ensemble member, respectively,

**H**

_{k}is the observation operator that maps the model states to the observations,

**v**

_{k}is a synthetically generated error added to the observation

**Z**

_{k}and represents the uncertainties of the observation process that is assumed to be a mean-zero Gaussian random variable with variance

**R**

_{k}[53], and

**K**

_{k}is the Kalman gain:

#### 3.3. Filtering and Rescaling Techniques

_{k}is the surface SM observed by the satellite sensor at time t

_{k}and SWI

_{k}is the Soil Wetness Index representing the profile averaged saturation degree at time t

_{k}. The gain G

_{k}at time t

_{k}is given by (in a recursive form):

#### 3.4. Model Error Representation and Observation Error

**K**can significantly affect the results of the assimilation. As remarked in the Introduction, the main sources of uncertainty in hydrologic models are the errors in the forcing data, the model structure and the incorrect specification of model parameters. A common way to represent these errors is by adding unbiased synthetic noise to forcing datasets (precipitation and evapotranspiration), model state variables and/or model parameters.

_{p}, while for temperature a zero-mean normally distributed additive error was chosen with temperature standard deviation equal to σ

_{T}. For the perturbation of model parameters, we first carried out a sensitivity analysis (not shown) in order to select for modelled SM the most sensitive parameters. Then, these parameters were perturbed with a normally distributed additive error with zero mean. In particular, only three parameters were selected: W

_{max}, K

_{s}and K

_{c,}for which the relative standard deviations were expressed as percentage α of the absolute value of the parameter, i.e., σ

_{Wmax}= α

_{1}W

_{max}, σ

_{Ks}= α

_{2}K

_{s}, and σ

_{Kc}= α

_{3}K

_{c}. The model error estimation was performed by varying the values of the percentages α

_{i}(i = 1,2,3) along with σ

_{p}(σ

_{T}was assumed constant) in a way that two ensemble verification measures (Test #1 and Test #2 onward) commonly used in meteorology [29] were satisfied. That is, if the ensemble spread sp is large enough, the temporal mean of the ensemble skill <sk> should be similar to the temporal average of the ensemble spread <sp>

_{k}, Q

_{obs,k}is the observed discharge at time t

_{k}, T

_{p}is the length of the time period, while <·>is the mean operator. Assuming σ

_{T}constant, from different values of α

_{i}(i = 1,2,3), σ

_{p}and σ

_{T}we obtained different ensembles and different values, f

_{1}(α

_{1,}α

_{2,}α

_{3,}σ

_{p}) and f

_{2}(α

_{1,}α

_{2,}α

_{3,}σ

_{p}) of Test #1 and Test #2, respectively. Then, the optimal selection of α

_{i}(i = 1,2,3), σ

_{p}was carried out by picking up the minimum of the following function:

_{p}was performed during 2000–2009, then the same perturbations were used during the validation period for generating the ensemble.

_{obs}, were chosen ranging from 0.5%–20%. Moreover, as a reference we calculated the variance of rescaled SWI for VM, LR and CDF schemes and take the ratio between ${\sigma}_{obs}^{2}$ and ${\sigma}_{SWI}^{2}$. In particular, as in [27], we considered an upper bound of the rescaled observation error for each catchment, and tested a selection of error variances within the bound. The rationality behind this is that if we express the rescaled observation ($SW{I}_{ASCAT}^{R}$ as the sum of the “true” rescaled observation $\left\{SW{I}_{ASCAT}^{R}\right\}$ and the rescaled observation error..), and we assume error orthogonality, we can express the variance of the rescaled observation as ${\sigma}_{SW{I}_{ASCAT}^{R}}^{2}={\sigma}_{\left\{SW{I}_{ASCAT}^{R}\right\}}^{2}+{\sigma}_{{\epsilon}_{ASCAT}^{R}}^{2}$ where ${\sigma}_{{\epsilon}_{ASCAT}^{R}}^{2}$ represents the term R (from here onward not in bold since in the paper configuration it is a scalar) in Equation (3). Under this assumption ${\sigma}_{SW{I}_{ASCAT}^{R}}^{2}$ can be considered an upper bound for R. Specific settings for the model parameter errors and observation errors are discussed ahead in Section 4.2.

#### 3.5. Performance Indexes

_{obs}) against (i) the discharge time series obtained during the calibration and the validation period, Q

_{c}and Q

_{v}; (ii) the time series obtained by the mean of the different discharge ensemble members of the open loop simulations, (Q

_{ol}) and (iii) against the mean of the different updated discharge ensemble members obtained in assimilation mode (Q

_{a}).

_{c}, Q

_{v}, Q

_{ol}and Q

_{a}(Q

_{sim}in Equation (11)) and Q

_{obs}:

_{a}. NS was calculated for both the entire time series and for a number of selected events. The event selection was carried out by extracting the events with a continuous rainfall characterized by a total rainfall larger than 10 mm, and no rainfall in the preceding day. Only for discharges related to the selected events, we also calculated the error in volume by the following equation:

_{obs}with the open loop (Q

_{a}= Q

_{ol}) and with respect to the validation (Q

_{a}= Q

_{v}).

_{NS(logQ)}, Δ

_{ANSE}between the results obtained after and prior the assimilation. In Equation (14), ε is arbitrarily chosen as a small fraction of the inter-annual mean discharge (e.g., ${\overline{Q}}_{obs}/40$) and is introduced to avoid problems with nil observed or simulated discharges.

## 4. Results

#### 4.1. Model Calibration and Validation

^{®}). The calibrated parameters (only W

_{max}, K

_{c}, K

_{s}and η) are shown in Table 1 while the results in terms of NS of the calibration are reported in Table 2. A general good behaviour (in calibration) can be seen in the model for all the catchments.

_{max}and K

_{c}while different values of K

_{s}and η were obtained for MA-AZ. The results obtained in validation—we are referring to a single deterministic run using the calibrated parameters of the previous step—provide relatively good performance with NS always above 0.6 (an example of the discharge time series in validation for TV-PF during 2013 is shown in Figure 2b). The analysis of the results was carried out also by calculating the performance of the model on a number of selected flood events (Table 3) extracted from the time series as specified in Section 3.5. The results for validation are generally satisfactory (NS > 0.7 and error in volume lower than 30%) except for TV-PF and NI-MI. The poor performance of the model in these two cases was mainly determined by a significant mismatch existing between the model simulation and the observed discharge for the most important flood event which occurred in November 2012 (see the results for TV-PF in Figure 2c). Indeed, in this case, a leave overtopping occurred prior to the measurement section determining a flood peak much lower than expected (i.e., there was a significant reduction of the river discharge upstream to the measurement section) and, as a consequence, a strange shape of the flood hydrograph formed.

**Figure 2.**Results of the data assimilation experiment for Tiber River at Ponte Felcino using LS as RT and an observation error equal to 7%. (

**a**) Plots the satellite SM time series along with the ensemble forecast and analysis (5%–95% percentiles). In purple, it is also shown the Kalman gain. (

**b**) Plots a small part of the discharge time series: the plot of the entire time series is not shown because of problems of visualization. In the panel, Q

_{obs}is the observed discharge, Q

_{v}is the discharge obtained in validation, Q

_{ol}is the ensemble mean and Q

_{a}is the updated discharge obtained in assimilation. (

**c**) Plots the discharge values for the selected flood events.

**Table 2.**Results of the calibration-validation procedures and of the data assimilation experiment for the five selected catchments. NS

_{c}is the Nash Sutcliffe efficiency index obtained in calibration from 2000–2009, NS

_{v}refers to the same index in validation during 2010–2013, while NS

_{ol}is the Nash Sutcliffe calculated in the same validation period on the ensemble mean. On the right part of the table, σ

_{obs}refers to the observation error for which the data assimilation provides the best performance in terms of Nash-Sutcliffe (NS

_{a}). Eff

_{v}and Eff

_{ol}refer to the results in terms of efficiency in the validation and in the ensemble mean, respectively. Gray cells in the table denote a deterioration with respect to the open loop simulations.

NS_{c} | NS_{v} | NS_{ol} | NS_{a} | Eff_{v} (%) | Eff_{ol} (%) | σ_{obs} | ||
---|---|---|---|---|---|---|---|---|

TV-PF | VM | 0.79 | 39.64 | 35.86 | 0.05 | |||

LR | 0.80 | 0.65 | 0.67 | 0.80 | 42.33 | 38.72 | 0.05 | |

CDF | 0.75 | 29.53 | 25.11 | 0.05 | ||||

NE-MA | VM | 0.91 | 29.30 | 31.56 | 0.20 | |||

LR | 0.88 | 0.87 | 0.87 | 0.91 | 28.72 | 31.00 | 0.20 | |

CDF | 0.90 | 23.49 | 25.93 | 0.20 | ||||

CHI-MOR | VM | 0.87 | 24.64 | 31.66 | 0.09 | |||

LR | 0.76 | 0.83 | 0.81 | 0.88 | 26.03 | 32.93 | 0.07 | |

CDF | 0.87 | 21.09 | 28.44 | 0.05 | ||||

MA-AZ | VM | 0.70 | 2.06 | −13.30 | 0.20 | |||

LR | 0.77 | 0.69 | 0.74 | 0.71 | 3.67 | −11.44 | 0.20 | |

CDF | 0.70 | 3.35 | −11.81 | 0.20 | ||||

NI-MI | VM | 0.79 | 39.58 | 41.67 | 0.03 | |||

LR | 0.85 | 0.65 | 0.64 | 0.79 | 39.27 | 41.37 | 0.05 | |

CDF | 0.77 | 34.23 | 36.50 | 0.03 |

**Table 3.**Results of the data assimilation experiment for the five selected catchments on the selected flood events (number of events N

_{ev}). NS

_{val}is the Nash Sutcliffe efficiency index calculated on the selected flood events from 2000–2009, NS

_{ol}refers to the same index calculated on the selected flood events on the ensemble mean, σ

_{obs}refers to the observation error (the same of Table 2) while NS

_{a}is the Nash-Sutcliffe efficiency index calculated after data assimilation on the selected flood events. Eff

_{v}and Eff

_{o}

_{l}refer to the results in terms of efficiency with respect to the validation and to the ensemble mean, respectively, calculated for the selected flood event. Gray cells in the table denote a deterioration with respect to the open loop simulations.

NS_{v} | Err_{vol} (%) | NS_{ol} | NS_{a} | Err_{vol(a)} (%) | Eff_{v} (%) | Eff_{ol} (%) | σ_{obs} | N_{ev} | |||
---|---|---|---|---|---|---|---|---|---|---|---|

TV-PF | VM | 0.64 | −2.56 | 52.55 | 50.18 | 0.05 | 16 | ||||

LS | 0.25 | 26.09 | 0.29 | 0.67 | −5.49 | 56.08 | 53.89 | 0.05 | 16 | ||

CDF | 0.56 | 2.84 | 41.53 | 38.61 | 0.05 | 16 | |||||

NE-MA | VM | 0.91 | 14.23 | 37.09 | 38.71 | 0.20 | 16 | ||||

LS | 0.85 | 19.45 | 0.85 | 0.91 | 15.14 | 36.69 | 38.32 | 0.20 | 16 | ||

CDF | 0.90 | 16.04 | 32.83 | 34.56 | 0.20 | 16 | |||||

CHI-MOR | VM | 0.87 | −1.18 | 27.11 | 37.54 | 0.09 | 24 | ||||

LS | 0.83 | 1.69 | 0.8 | 0.88 | −1.64 | 28.02 | 38.32 | 0.07 | 24 | ||

CDF | 0.87 | −1.27 | 22.05 | 33.21 | 0.05 | 24 | |||||

MA-AZ | VM | 0.71 | −7.31 | 7.69 | −34.14 | 0.2 | 17 | ||||

LS | 0.68 | −0.1 | 0.78 | 0.72 | −6.83 | 10.83 | −29.57 | 0.2 | 17 | ||

CDF | 0.71 | −5.25 | 8.51 | −32.95 | 0.2 | 17 | |||||

NI-MI | VM | 0.75 | −9.65 | 55.56 | 57.98 | 0.03 | 30 | ||||

LS | 0.44 | −3.81 | 0.41 | 0.75 | −12.83 | 54.5 | 56.98 | 0.05 | 30 | ||

CDF | 0.7 | −9.85 | 46.16 | 49.09 | 0.03 | 30 |

#### 4.2. Ensemble Generation and Data Assimilation Experimental Setup

_{1}between 30 and 80% along with α

_{2}and α

_{3}between 0% and 30%. At the same time, σ

_{p}varied between 0.25 and 1, while σ

_{T}was assumed constant and equal to 3 °C. Figure 3 shows the value of the function F of Equation (10) in the α

_{1}− σ

_{p}domain for different values of α

_{2}, α

_{3}for NE-MA catchment (the other catchments lead to the same conclusions and are not shown for brevity). It can be seen that there is a problem of equifinality in which different combinations of error parameters lead to a similar value of F. The main responsible of this behavior is α

_{1}which controls the perturbation of the storage parameter W

_{max}. In order to make a selection, we ran the same assimilation experiments by using different optimal and close-optimal solutions (e.g., 2/3 solutions for each catchment) obtaining very similar results with some small differences in some cases. It is likely that the model-non-linearity plays a role in this case and allows obtaining similar model error covariance and in turn similar results. Finally, since a choice has to be made (e.g., think to the application of the DA at operational level), we selected the best combination of the error parameters as described in Section 3.4. Such values for all the catchments are shown in Table 1. In addition, it has to be stressed that the selection of the quadruplet was made during the calibration period, and hence, this does not guarantee that the quadruplet is optimal also during the validation phase (2010–2013). This eventuality was tested for all catchments and it was found that the tests are close to the required values except in some cases (e.g., NE-MA yields 0.68 vs. 1 for test #1 and 0.63 vs. 0.71 for test #2). Another issue that might potentially affect the methodology of the selection of the best error parameters is the reliability of the stream flow observations. Indeed, there is the assumption that their random error is much lower than the modelling error. Although the quality of the observations is very high—since they were successfully tested and cross-verified by many other papers in the past (e.g., [17,40,63])—we cannot guarantee this is always true. The above results suggest the complexity of the issue, which would require a separate and detailed analysis specifically addressed to the problem of the estimation of the model error covariance.

**Figure 3.**Contour plot of the function F of Equation (10) as a function of the standard deviation of the precipitation σ

_{p}, the percentage α

_{1}of the perturbation of the maximum water storage W

_{max}, and the percentages α

_{2}, α

_{3}of the parameters of drainage, Ks and evapotranspiration Kc, respectively (period 2000–2009, catchment NE-MA). The optimal value of these standard deviations is identified by the red cross and corresponds to the minimum value of the function F representing the error made in the identification of the optimal value of the tests. It can be clearly seen a problem of equifinality in the figure with darker blue areas (smaller F) covering a large part of the domain.

_{k}(the error representing the uncertainties of the observation process with variance R and hereafter as σ

_{obs}) was made variable between 0.5% and 20% (i.e., 0.005, 0.01, 0.03, 0.05, 0.07, 0.09, 0.12, 0.15, 0.18, 0.2) and the corresponding R was then compared against the variance of the rescaled SWI for different RTs as explained in Section 3.4. Assuming that the range of volumetric soil moisture variability is equal to 0.33 [1], these values correspond in volumetric terms to a range variable between 0.002 and 0.06 m

^{3}/m

^{3}and are in the range of those found in the area by [31].

#### 4.3. Data Assimilation Experiment

_{a}between 30% and 40%) obtained for σ

_{obs}ranging between 0.03 and 0.07. NE-MA shows similar improvements but only after σ

_{obs}= 0.09. The same efficiency index as a function of the ratio between the variance of the error and the rescaled observation ${\sigma}_{obs}^{2}/{\sigma}_{SW{I}^{R}}^{2}$ (top axis of the panels) show similar results with TV-PF, CHI-MOR and NI-MI having higher performance with ${\sigma}_{obs}^{2}/{\sigma}_{SW{I}^{R}}^{2}$ between 0.1 or less, and 0.5. Consistently, NE-MA shows improvements for ${\sigma}_{obs}/{\sigma}_{SW{I}^{R}}$ larger than 0.5 and best Eff for values of ${\sigma}_{obs}^{2}/{\sigma}_{SW{I}^{R}}^{2}$ greater than one. It has to be pointed out that the latter results violate the assumption made in Section 3.4, which assumes the variance of the rescaled observation as an upper bound value of the variance of the observation error; hence, making this assumption may not lead to an optimal solution. For MA-AZ, Eff

_{a}is always lower than zero although it increases by increasing the observation error.

**Figure 4.**Efficiency index calculated with respect to the open loop simulation for the five catchments for the three RTs as a function of the observation error. σ

_{obs}is the observation error standard deviation, ${\sigma}_{obs}^{2}$ is the variance observation error, ${\sigma}_{SW{I}^{R}}^{2}$ is the variance of the rescaled observation. Values below zero (black line) denote a deterioration of the results.

_{a}, and Eff calculated by using Q

_{ol}and Q

_{v}. It can be seen that except for CHI-MO the optimal observation error does not change too much from one RT to another and lower NS and Eff are generally obtained with CDF.

_{NS(logQ)}, Δ

_{ANSE}) obtained in the NS

_{(logQ)}and ANSE indexes with respect to the open loop simulation for the three RTs considering the optimal choice of observation error (the same presented in Table 2). The results are plotted in Figure 5 and show significant improvement for both indexes only for NI-MI. For TV-PF, DA succeeds only for high flows and show contrasting results between the different RTs. MA-AZ always provides poor results while CHI-MO and NE-MA have a general consistent behavior. Overall, the improvement for high flows is more consistent.

**Figure 5.**Differences (Δ

_{NS(logQ)}, and Δ

_{ANSE}) between performance scores NS

_{(logQ)}and ANSE obtained prior and after the assimilation of SM for the five selected catchments. While (

**a**) NS

_{(logQ)}is well suited for highlighting the performance in the reproduction of low flows, (

**b**) ANSE is used for characterizing the agreement of high flows. The related observation errors are the same as selected in Table 2.

**Figure 6.**Pattern of the Normalized Root Mean Squared error (NRMSE) and variance of the rescaled Soil Water Index (rescaled with LR technique), ${\sigma}_{SW{I}^{R}}^{2}$ for the five selected catchments calculated with a time window of 90 days. Values above the red horizontal line (NRMSE = 1) denote deteriorations. Periods of increased ${\sigma}_{SW{I}^{R}}^{2}$ generally correspond with improvements except for MA-AZ.

#### 4.5. Discussion

_{s}, and a much quicker response (smaller η) with respect to the catchments located in the western part of the study area (NE-MA, CHI-MO, NI-MI) while TV-PF shows an intermediate behavior. In particular, the larger K

_{s}for MA-AZ is somehow consistent with the higher infiltration rate value (i.e., MA-AZ is located in the Apennines relief with high permeable rocks, see Table 1) while the smaller η is likely due to the difficulty of the model to reproduce the larger baseflow component for this catchment (also noted for TV-PF).

_{obs}—RT) have been found to lead to an enhancement of the performances. The reason for the poor assimilation results of MA-AZ might be due to three main causes. First, the expected poor quality of the satellite observations (the catchment is located in a mountainous area where ASCAT may suffer from topography issues)—this problem is confirmed by the higher SM-OBS4 soil moisture noise with respect to the other catchments as shown in Table 1. Second, an overestimation of the model error covariance, which prevents the filter from obtaining an improvement in the range of the chosen observation errors. Finally, and most likely, it might be due to the runoff generation mechanism, which is different from the other catchments. Indeed, the higher permeability of MA-AZ catchment determines that water stored in the soil is less retained by surface tension (i.e., gravity is dominant) and water is released in large quantities to the subsurface leading to a larger contribution of base flow and subsurface runoff. This contribution is not negligible with respect to the total runoff in this catchment and is much less controlled by SM variation at the surface (i.e., where we have information of SM from the satellites). On the other hand, catchments located in the western part of the Umbria Region are characterized by less permeable soils with higher retention properties and show larger sensitivity to surface SM. This second hypothesis was tested though a synthetic experiment (not shown) which showed that the efficiencies obtainable for the other catchments were much larger than those obtainable for MA-AZ. Although DA provides positive results for most of the catchments, the improvements also contain a number of contradictions, which are highlighted below.

_{a}, Table 2) for the three RTs, we obtained an improvement for all catchments except MA-AZ and a general lower performance for the CDF technique. The reason for the lower performance of CDF might be due to the small sample size, (i.e., the length of the time series) where the CDF technique was calibrated. Similar results were found by [34] in the Murray Darling Basin in Australia who analyzed the impact of different RTs on the DA and showed sub-optimal performance of the CDF due to the relatively short two-year data record. As mentioned earlier, we have to stress the existence of other rescaling techniques (see [57,65] for further details); however, we found that the ones selected in this study are the most used in DA of SM in rainfall runoff modelling. Therefore, we prefer to focus our analysis by using them, and pursue the matter in a future study specifically addressed to analyzing the effect of the RT on the DA.

_{(logQ)}) highlights significant improvements for TV-PF for high flows but smaller and even negative scores for low flows. NE-MA, CHI-MO and NI-MI have consistent performances for low and high flows as well as MA-AZ for which the scores are always negative. Overall, a general lower performance is obtained with the CDF technique for high flow conditions, while for low flows CDF demonstrates an unexpected good behavior for TV-PF and provides similar results to the other techniques for the other catchments. As before, this might be due to the larger number of SM values associated to low flow conditions with respect to those in high flow conditions that are used for calibrating the CDF parameters. The above considerations suggest that simpler rescaling techniques (e.g., VM) can be considered equally valid (or better), and, in most of the cases, preferable due to the simplicity of their implementation.

Factors | What Has Been Done | Findings |
---|---|---|

Model error | We performed a sensitivity analysis and calibrated the perturbation of the parameters and of the rainfall for calculating the optimal value of the ensemble statistical indexes | The results are good but we observed a problem of equifinality in which different perturbations lead to same values of the ensemble statistical indexes. |

Catchment area, topography and soil type | We compared the performance of the assimilation for different catchments characterized by different areas (140–2000 km^{2}) and soil type | We did not observe any effect of the catchment area but catchment specific characteristics may prevent positive results of the DA |

Rescaling technique | We compared the performance of the assimilation for three different RTs (LR, VM, CDF) | We obtained a uniform pattern of performance of the DA for LR, VM and CDF. We concluded that simple techniques may be equally valid as easier to implement |

Observation error | We chose different observation errors and tested their optimality in the DA experiments | We obtained that adjacent and similar catchments have very different optimal observation errors, therefore its appropriate choice may strongly depend on a correct model error estimation |

Flood magnitude | We explored the performance of the DA for low and high flows | We found larger improvements for high flow conditions. |

Seasonality | We performed a seasonal analysis and compared it against the SM temporal variability | We obtained that DA performance during the year that has a relation with the SM temporal variability. Thus, we advise that this parameter must be taken into consideration when analyzing possible effects of seasonality in the DA of SM. |

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Massari, C.; Brocca, L.; Tarpanelli, A.; Moramarco, T.
Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe? *Remote Sens.* **2015**, *7*, 11403-11433.
https://doi.org/10.3390/rs70911403

**AMA Style**

Massari C, Brocca L, Tarpanelli A, Moramarco T.
Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe? *Remote Sensing*. 2015; 7(9):11403-11433.
https://doi.org/10.3390/rs70911403

**Chicago/Turabian Style**

Massari, Christian, Luca Brocca, Angelica Tarpanelli, and Tommaso Moramarco.
2015. "Data Assimilation of Satellite Soil Moisture into Rainfall-Runoff Modelling: A Complex Recipe?" *Remote Sensing* 7, no. 9: 11403-11433.
https://doi.org/10.3390/rs70911403