Top PDF Could operational hydrological models be made compatible with satellite soil moisture observations?

Could operational hydrological models be made compatible with satellite soil moisture observations?

Could operational hydrological models be made compatible with satellite soil moisture observations?

Abstract Soil moisture is a significant state variable in flood forecasting. Nowadays more and more satellite soil moisture products are available, yet their usage in the operational hydrology is still limited. This is because the soil moisture state variables in most operational hydrological models (mostly conceptual models) are over-simplified – resulting in poor compatibility with the satellite soil moisture observations. A case study is provided to discuss this in more detail, with the adoption of the XAJ model and the Soil Moisture and Ocean Salinity (SMOS) level-3 soil moisture observation to illustrate the relevant issues. It is found that there are three distinct deficiencies existed in the XAJ model that could cause the mismatch issues with the SMOS soil moisture observation: i) it is based on runoff generation via the field capacity excess mechanism (interestingly, such a runoff mechanism is called the saturation excess in XAJ while in fact it is clearly a misnomer); ii) evaporation occurs at the potential rate in its upper soil layer until the water storage in the upper layer is exhausted, and then the evapotranspiration process from the lower layers will commence – leading to an abrupt soil water depletion in the upper soil layer; iii) it uses the multi-bucket concept at each soil layer - hence the model has varied soil layers. Therefore, it is a huge challenge to make an operational hydrological model compatible with the satellite soil moisture data. The paper argues that this is possible and some new ideas have been explored and discussed.
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Error distribution modelling of satellite soil moisture measurements for hydrological applications

Error distribution modelling of satellite soil moisture measurements for hydrological applications

19 analysis and uncertainty analysis. In addition, more detailed studies such as the spatial and temporal dependence analysis should be conducted in the future. Studies are also needed to consider soil moisture information from other satellite missions over a wider range of catchment conditions with different hydrological models in order to find generalisation patterns of the error distribution models (this is especially important for ungauged catchments). However this is a huge task that cannot be achieved by a single study. The key mission for this paper is to attract attention by the hydrological community on this important issue which has been largely neglected, so that a great deal of hydrological models, satellite soil moisture observations and various catchments could be further explored by the community. We hope this study will raise the awareness on the importance of satellite soil moisture error distribution modelling so that such useful data source could be fully utilised in future hydrological modelling.
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Calibration of a large scale hydrological model using satellite based soil moisture and evapotranspiration products

Calibration of a large scale hydrological model using satellite based soil moisture and evapotranspiration products

Although there is still room for further research, this study showed that globally available Earth observations, such as evapotranspiration or soil moisture, can be used to further parameterize large-scale hydrological models providing rea- sonable discharge estimates at the regional or basin scales. In principle, these calibration approaches can be applied and investigated in other basins without or with limited in situ ground hydro-meteorological data (ungauged basins), to not only estimate discharge, but also to improve the understand- ing of the hydrological processes in the basin. Results sug- gested the potential of using other satellite products for hy- drological modelling studies, including soil moisture prod- ucts such as AMSR-E (Njoku et al., 2003) and SMOS (Kerr et al., 2001), evapotranspiration products such as SEBAL (Bastiaanssen et al., 1998) and MOD16 (Nishida, 2003), total water storage products such as GRACE (Tapley et al., 2004), etc. The spatial information of these satellite-based products could be used in a different way than the one explained in this study. For example, a calibration scenario based on a pixel-by-pixel, instead of basin-average, comparison of sur- face soil moisture and actual evapotranspiration model esti- mates and observations could further improve discharge es- timates. This calibration approach would have to take into account the spatial variability of the variables over the basin. Previous studies investigated how to incorporate spatial in- formation into hydrological models using innovative spatial
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Satellite soil moisture observations:

applications in the UK and India: report of pump priming project

Satellite soil moisture observations: applications in the UK and India: report of pump priming project

This study focused on soil moisture (SM), a major fundamental variable in global hydrological cycles, which has a huge range of potential applications including agricultural drought and flood forecasting, improving irrigation efficiency, risk mapping (e.g. disease, landslides) and integration into land surface models to improve predictions. As part of this Pump Priming Project a review of the current state of knowledge in the application of satellite-based SM products in the UK and India was carried out, providing valuable new information to aid future India-UK collaborations. Following this, a survey of current and potential end-users of satellite soil moisture data was carried out to identify future opportunities and barriers to uptake of EO-based products. This Project also explored the potential for using new technologies (i.e. low-cost sensors) for validating EO products, as an improvement on current sparse in situ measurements which fail to adequately represent SM variability. Low-cost weather stations and soil moisture sensors were constructed and deployed in India as a proof-of-concept study. During the field campaign in India, preliminary findings of the study were disseminated to researchers at University of Delhi and the Banaras Hindu University, Varanasi. This was an opportunity to get feedback from current satellite soil moisture users in India, and these discussions have been included into this report. Hence, the Project also facilitated cross-fertilization of ideas between researchers in the UK and India and identified future opportunities for collaboration.
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Hydrological evaluation of satellite soil moisture data in two basins of different climate and vegetation density conditions

Hydrological evaluation of satellite soil moisture data in two basins of different climate and vegetation density conditions

Accurate soil moisture information is very important for real-time lood forecasting. Although satellite soil moisture observations are useful information, their validations are generally hindered by the large spatial diference with the point-based measurements, and hence they cannot be directly applied in hydrological modelling. his study adopts a widely applied operational hydrological model Xinanjiang (XAJ) as a hydrological validation tool. Two widely used microwave sensors (SMOS and AMSR-E) are evaluated, over two basins (French Broad and Pontiac) with diferent climate types and vegetation covers. he results demonstrate SMOS outperforms AMSR-E in the Pontiac basin (cropland), while both products perform poorly in the French Broad basin (forest). he MODIS NDVI thresholds of 0.81 and 0.64 (for cropland and forest basins, resp.) are very efective in dividing soil moisture datasets into “denser” and “thinner” vegetation periods. As a result, in the cropland, the statistical performance is further improved for both satellites (i.e., improved to NSE = 0.74, RMSE = 0.0059 m and NSE = 0.58, RMSE = 0.0066 m for SMOS and AMER-E, resp.). he overall assessment suggests that SMOS is of reasonable quality in estimating basin-scale soil moisture at moderate-vegetated areas, and NDVI is a useful indicator for further improving the performance.
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Potential and limitations of multidecadal satellite soil moisture observations for selected climate model evaluation studies

Potential and limitations of multidecadal satellite soil moisture observations for selected climate model evaluation studies

While both models show also significant positive corre- lations in the tropical areas with dense vegetation like the Amazon or Congo basins, the ECVSM does not show any significant correlations in these areas with either of the model datasets. This was expected, as the remote sensing signal is perturbed by dense vegetation and the microwave sig- nal is lacking any soil moisture information in these areas (Jeu et al., 2008; Dorigo et al., 2010). The global mean cor- relations between soil moisture anomalies of ECVSM and JSBACH (ERA-interim) are ρ = 0.41 ± 0.2 (ρ = 0.36 ± 0.19) while the anomaly correlation between the model simula- tions is higher (ρ = 0.64 ± 0.2). Thus, in areas where the mi- crowave signal is in general sensitive to soil moisture dynam- ics, the ECVSM dataset shows reasonable agreement with the two simulated soil moisture datasets for both, absolute values as well as for the soil moisture anomalies. A more detailed comparison of the soil moisture statistics of the dif- ferent datasets will be made in the following by analyzing the soil moisture percentile distribution.
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Additional Value of Using Satellite-Based Soil Moisture and Two Sources of Groundwater Data for Hydrological Model Calibration

Additional Value of Using Satellite-Based Soil Moisture and Two Sources of Groundwater Data for Hydrological Model Calibration

The Soil Moisture Active Passive (SMAP) mission has been developed by NASA as one of the first Earth observation satellites in return for the National Research Council’s Decadal Survey. SMAP analyses global measurements of soil moisture present at the Earth’s surface, thus allowing to make indirect observations of soil moisture and thaw/freeze state from space to make considerably improved estimates of energy, water and carbon transfers between the atmosphere and the land. Correct characterization of these transfers is highly dependent on the accuracy of numerical atmosphere models that are used in weather prediction and climate projections. Measurement of soil moisture can be applied directly to flood assessment and drought monitoring. It is useful in estimating global water and energy fluxes at the land surface. Since April 2015, Soil Moisture Active Passive (SMAP) mission of NASA has been successfully monitoring near-surface soil moisture, by mapping the globe between the latitude bands of 85.044◦N/S in 2-3 days, depending on location [52– 55]. In this research, daily data of soil moisture with a resolution of 36x36 km is used.
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The Relevance of Soil Moisture by Remote Sensing and Hydrological Modelling

The Relevance of Soil Moisture by Remote Sensing and Hydrological Modelling

Papers by [59, 60] present a modification scheme to improve conventional conceptual hydrological models to better utilise the satellite soil moisture observations. XAJ model is used as a representative hydrological model in their studies. As a result, the amended XAJ model is as effective as its original form in flow modelling, but represents more logically realistic soil water processes. In addition, a term called the holding excess runoff has been introduced to illustrate the computational runoff mechanism in the XAJ and other similar models, which helps to clarify the difference between the runoff in reality and the modelled runoff. Another term called Soil Moisture Deficit to Saturation (SMDS) is proposed to replace the conventional Soil Moisture Deficit (SMD). The study shows that SMDS is hydrologically more realistic than SMD based on general soil water movement principles. The methods discussed in [59, 60] are only a first step towards a comprehensive soil moisture modification procedure. Therefore, more studies with longer time periods, a larger number of catchments should be carried out in the future. 7. The need for new soil moisture products development
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Error distribution modelling of satellite soil moisture measurements for hydrological applications

Error distribution modelling of satellite soil moisture measurements for hydrological applications

4 be considered as the only benchmark. For example, Dorigo et al. (2010) used three independent satellite soil moisture datasets to derive their error characterisations (albeit only summary statistics such as RMSE are derived) without using ground based estimates (the so called ‘triple collocation error estimation’). The reason is explained by the authors as ‘a spatially coherent assessment of the quality of the various globally available datasets is often hampered by the limited availability over space and time of reliable in-situ measurements.’ As Wagner, (2008) has explained that ‘there is no universal remote sensing method (= sensor + algorithm) that satisfies all user requirements’, an excellent performance of the soil moisture data in one application field may have a poor performance in another field. For example, in climate change modelling, the global climate models usually have spatial resolutions in hundreds of kilometres, so a soil moisture product suitable for such applications may not be optimal for studies in crop growth monitoring in agriculture, and vice versa. Since this study aims at hydrological modelling applications, the benchmark is based on the effective catchment soil moisture data estimated from a well-known operational hydrological model Xinanjiang (XAJ).
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Multi-Temporal Evaluation of Soil Moisture and Land Surface Temperature Dynamics Using in Situ and Satellite Observations

Multi-Temporal Evaluation of Soil Moisture and Land Surface Temperature Dynamics Using in Situ and Satellite Observations

Abstract: Soil moisture (SM) is an important component of the Earth’s surface water balance and by extension the energy balance, regulating the land surface temperature (LST) and evapotranspiration (ET). Nowadays, there are two missions dedicated to monitoring the Earth’s surface SM using L-band radiometers: ESA’s Soil Moisture and Ocean Salinity (SMOS) and NASA’s Soil Moisture Active Passive (SMAP). LST is remotely sensed using thermal infrared (TIR) sensors on-board satellites, such as NASA’s Terra/Aqua MODIS or ESA & EUMETSAT’s MSG SEVIRI. This study provides an assessment of SM and LST dynamics at daily and seasonal scales, using 4 years (2011–2014) of in situ and satellite observations over the central part of the river Duero basin in Spain. Specifically, the agreement of instantaneous SM with a variety of LST-derived parameters is analyzed to better understand the fundamental link of the SM–LST relationship through ET and thermal inertia. Ground-based SM and LST measurements from the REMEDHUS network are compared to SMOS SM and MODIS LST spaceborne observations. ET is obtained from the HidroMORE regional hydrological model. At the daily scale, a strong anticorrelation is observed between in situ SM and maximum LST (R ≈ − 0.6 to − 0.8), and between SMOS SM and MODIS LST Terra/Aqua day (R ≈ − 0.7). At the seasonal scale, results show a stronger anticorrelation in autumn, spring and summer (in situ R ≈ − 0.5 to − 0.7; satellite R ≈ − 0.4 to − 0.7) indicating SM–LST coupling, than in winter (in situ R ≈ +0.3; satellite R ≈ − 0.3) indicating SM–LST decoupling. These different behaviors evidence changes from water-limited to energy-limited moisture flux across seasons, which are confirmed by the observed ET evolution. In water-limited periods, SM is extracted from the soil through ET until critical SM is reached. A method to estimate the soil critical SM is proposed. For REMEDHUS, the critical SM is estimated to be ∼ 0.12 m 3 /m 3 , stable over the study period and consistent between in situ and satellite observations. A better understanding of the SM–LST link could not only help improving the representation of LST in current hydrological and climate prediction models, but also refining SM retrieval or microwave-optical disaggregation algorithms, related to ET and vegetation status.
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Correcting satellite precipitation data and assimilating satellite-derived soil moisture data to generate ensemble hydrological forecasts within the HBV rainfall-runoff model

Correcting satellite precipitation data and assimilating satellite-derived soil moisture data to generate ensemble hydrological forecasts within the HBV rainfall-runoff model

Abstract: An implementation of bias correction and data assimilation using the ensemble Kalman filter (EnKF) as a procedure, dynamically coupled with the conceptual rainfall-runoff Hydrologiska Byråns Vattenbalansavdelning (HBV) model, was assessed for the hydrological modeling of seasonal hydrographs. The enhanced HBV model generated ensemble hydrographs and an average stream-flow simulation. The proposed approach was developed to examine the possibility of using data (e.g., precipitation and soil moisture) from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Satellite Application Facility for Support to Operational Hydrology and Water Management (H-SAF), and to explore its usefulness in improving model updating and forecasting. Data from the Sola mountain catchment in southern Poland between 1 January 2008 and 31 July 2014 were used to calibrate the HBV model, while data from 1 August 2014 to 30 April 2015 were used for validation. A bias correction algorithm for a distribution-derived transformation method was developed by exploring generalized exponential (GE) theoretical distributions, along with gamma (GA) and Weibull (WE) distributions for the different data used in this study. When using the ensemble Kalman filter, the stochastically-generated ensemble of the model states generally induced bias in the estimation of non-linear hydrologic processes, thus influencing the accuracy of the Kalman analysis. In order to reduce the bias produced by the assimilation procedure, a post-processing bias correction (BC) procedure was coupled with the ensemble Kalman filter (EnKF), resulting in an ensemble Kalman filter with bias correction (EnKF-BC). The EnKF-BC, dynamically coupled with the HBV model for the assimilation of the satellite soil moisture observations, improved the accuracy of the simulated hydrographs significantly in the summer season, whereas, a positive effect from bias corrected (BC) satellite precipitation, as forcing data, was observed in the winter. Ensemble forecasts generated from the assimilation procedure are shown to be less uncertain. In future studies, the EnKF-BC algorithm proposed in the current study could be applied to a diverse array of practical forecasting problems (e.g., an operational assimilation of snowpack and snow water equivalent in forecasting models).
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Temporal variation of soil moisture over the Wuding River basin assessed with an eco hydrological model, in situ observations and remote sensing

Temporal variation of soil moisture over the Wuding River basin assessed with an eco hydrological model, in situ observations and remote sensing

Physically process-based models are thus used to ob- tain reliable prediction of long-term SM. So far several SM datasets have been produced using different land surface pro- cess models. However most of the models have simple SM schemes (e.g., Liu et al., 2003) or are forced with monthly average, which made the simulated SM results not agree well with the observations (Chen et al., 1997; Entin et al., 1999; Schlosser et al., 2000). Soil moisture is an important ele- ment in hydrological cycle which is closely related to wa- ter and energy transfer between soil, vegetation, and atmo- sphere. It has been shown that much of the global warming so far was at night (Karl et al., 1991, 1993; Folland et al., 1992; Stenchikov and Robock, 1995; Robock et al., 2000). So at least models with diurnal cycle are needed to correctly simulate SM. The SM may also be characterized by auto- correlation in time, which means that the lagged effects in inputs or losses can be important as much as those occurring at the time that the impacts are actually observed (Hamlet et al., 2007). A physically process-based model with detailed information about soil-vegetation-atmosphere water and en- ergy transfer is needed to correctly simulate long term SM time series for trend analysis.
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Error distribution modelling of satellite soil moisture measurements for hydrological applications

Error distribution modelling of satellite soil moisture measurements for hydrological applications

19 analysis and uncertainty analysis. In addition, more detailed studies such as the spatial and temporal dependence analysis should be conducted in the future. Studies are also needed to consider soil moisture information from other satellite missions over a wider range of catchment conditions with different hydrological models in order to find generalisation patterns of the error distribution models (this is especially important for ungauged catchments). However this is a huge task that cannot be achieved by a single study. The key mission for this paper is to attract attention by the hydrological community on this important issue which has been largely neglected, so that a great deal of hydrological models, satellite soil moisture observations and various catchments could be further explored by the community. We hope this study will raise the awareness on the importance of satellite soil moisture error distribution modelling so that such useful data source could be fully utilised in future hydrological modelling.
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Assessment of soil moisture fields from imperfect climate models with uncertain satellite observations

Assessment of soil moisture fields from imperfect climate models with uncertain satellite observations

Reciprocally, the degree of disagreement between the two products may be viewed as a measure of the uncertainty associated with the data. In regions where both products agree in particular over large spatial distances, the values are likely to represent actual soil moisture characteristics (de Jeu et al., 2008). This information can be used in an evaluation scheme where both model and observation data are known to be in error. Such schemes have recently gained popu- larity in hydrological studies (Beven, 2006) and an adap- tation is used here to assess the acceptability of both cli- mate models. It is clear that other satellite products avail- able at similar scales, such as global precipitation (e.g. Hong et al., 2004) or/and evaporation data (e.g. Bastiaanssen et al., 2005; Cleugh et al., 2007), might be used within similar acceptability schemes. Given the rather limited availability of global-scale spatially distributed hydrological parameters and the simplicity as well as difficulties with which current climate models reproduce spatially averaged seasonal hydro- logical behaviour, we believe that assessing the acceptability of models to adequately reproduce monthly changes in spa- tial heterogeneity of near-surface soil moisture saturation is a fair test to evaluate surface hydrological response.
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Improved large scale hydrological modelling through the assimilation of streamflow and downscaled satellite soil moisture observations

Improved large scale hydrological modelling through the assimilation of streamflow and downscaled satellite soil moisture observations

sensed observations of key water cycle variables. Higher- resolution satellite data contain information at finer spatial resolution and could be used to correct for suboptimal model performance at these finer resolutions. Multiple studies have used data assimilation techniques to obtain the best possi- ble estimate of the hydrological system status, merging the strengths of hydrological modelling and observations and mitigating their respective weaknesses (Moradkhani, 2008; Clark et al., 2008; van Dijk et al., 2014). Among the sequen- tial and variational data assimilation methods, the ensemble Kalman filter (Evensen, 2003) has arguably emerged as the most popular choice for assimilation into land surface and hydrological models. The various individual components of the water cycle, such as surface water (Vrugt et al., 2006; Rakovec et al., 2012), soil moisture (van Dijk et al., 2014; Wanders et al., 2014a), snow water (Sun et al., 2004; Morad- khani, 2008) and groundwater (Zaitchik et al., 2008; Tang- damrongsub et al., 2015), which influence the hydrological system in different ways, can be assimilated into the model.
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Correction of real time satellite precipitation with satellite soil moisture observations

Correction of real time satellite precipitation with satellite soil moisture observations

Precipitation is perhaps the most important variable in con- trolling energy and mass fluxes that dominate climate and particularly the terrestrial hydrological and ecological sys- tems. Precipitation estimates, together with hydrologic mod- els, provide the foundation for understanding the global en- ergy and water cycles (Sorooshian, 2004; Ebert et al., 2007). However, obtaining accurate measurements of precipitation at regional to global scales has always been challenging due to its small-scale, space–time variability, and the sparse networks in many regions. Such limitations impede precise modeling of the hydrologic responses to precipitation. There is a clear need for improved, spatially distributed precipita- tion estimates to support hydrological modeling applications. In recent years, remotely sensed satellite precipitation has become a critical data source for a variety of hydrologi- cal applications, especially in poorly monitored regions such as sub-Saharan Africa due to its large spatial coverage. To date, a number of fine-scale, satellite-based precipitation es- timates are now in operational production. One of the most frequently used is the Tropical Rainfall Measuring Mission Multi-satellite Precipitation Analysis (TMPA) product (Huff- man et al., 2007). Over the 17-year lifetime since the launch of the Tropical Rainfall Measuring Mission (TRMM) in 1997, a series of high-resolution (0.25 ◦ and 3-hourly), quasi-
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SM2RAIN–ASCAT (2007–2018): global daily satellite rainfall data from ASCAT soil moisture observations

SM2RAIN–ASCAT (2007–2018): global daily satellite rainfall data from ASCAT soil moisture observations

For estimating the rainfall rate, Eq. (1) is applied only dur- ing rainfall periods, and, hence, some of the components of the equation can be considered as negligible. For instance, the actual evapotranspiration rate during rainfall is quite low due to the presence of clouds and, hence, the absence of solar radiation. Similarly, the surface runoff rate, i.e. the water that does not infiltrate into the soil and flows at the surface to the watercourses, is much lower than the rainfall rate, mainly if Eq. (1) is applied at a coarse spatial resolution (20 km), i.e. with satellite soil moisture data. Indeed, most of the water becomes runoff flowing in the subsurface, and also the part that does not infiltrate, due to for instance impervious land cover or soil, may re-infiltrate downstream within a pixel at a 20 km scale. We have indirectly tested this hypothesis by counting the number of days the ASCAT soil moisture prod- uct is higher than the 99.5 percentile for 2 (or more) consecu- tive days in the period 2007–2018. We have indirectly tested this hypothesis by counting the number of days the ASCAT soil moisture product is higher than the 99.5 percentile for 2 (or more) consecutive days in the period 2007–2018. We have found that the number of consecutive days in which the soil is saturated is equal to 4 d (median value on a global scale) over 12 years, with 90 % of the land pixels with val- ues lower than 12 d (i.e. 1 d yr −1 ). The occurrence of higher values is limited to very few areas in the tropical forests and over the Himalayas (see Fig. A2).
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Information Theoretic Evaluation of Satellite Soil Moisture Retrievals

Information Theoretic Evaluation of Satellite Soil Moisture Retrievals

those of in-situ datasets), particularly over areas with moderate vegetation. The SMAP retrievals also demonstrate high information content relative to other retrieval products, with higher levels of complexity and reduced entropy. Finally, a joint evaluation of the entropy and complexity of remotely sensed soil moisture products indicates that the information content of the AMSR-E, AS- CAT, SMOS and AMSR2 retrievals is low, whereas SMAP retrievals show better performance. The use of information theoretic assessments is effective in quantifying the required levels of improve- ments needed in the remote sensing soil moisture retrievals to enhance their utility and information content.
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Improving operational flood ensemble prediction by the  assimilation of satellite soil moisture: comparison between  lumped  and semi distributed schemes

Improving operational flood ensemble prediction by the assimilation of satellite soil moisture: comparison between lumped and semi distributed schemes

Studies from the first group evaluate the prediction im- provement of the same variable that is updated in the as- similation scheme (SM). Improvements in streamflow pre- dictions investigated by studies in the second group are not exclusively influenced by better representation of SM. The potential improvement of streamflow predictions in the latter case is constrained by the particular runoff mechanisms op- erating within a catchment. Accordingly, even when a model structure and parametrisation are capable of representing the runoff mechanisms, improving streamflow prediction by re- ducing error in soil moisture depends on the error covariance between these two components. This error covariance (which in the model space will be defined by the representation of the different sources of uncertainty) may become marginal when the errors in streamflow come mainly from errors in rainfall input data (Crow and Ryu, 2009). This physical con- straint is case specific and determines the potential skill of SM-DA for improving streamflow prediction. To understand and assess this skill, further studies focusing on the im-
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Multivariate hydrological data assimilation of soil moisture and groundwater
head

Multivariate hydrological data assimilation of soil moisture and groundwater head

The ensemble is generated by adding an appropriate model error to the deterministic model. Similarly, given the prede- fined model error, a single random model realization is gen- erated to be the “true” model. Note that the “true” model here is only an assumption of reality. The model error is defined by perturbing both model forcing (precipitation and potential evapotranspiration) and selected model parameters (Zhang et al., 2015). The ensemble runs freely from 1 December 1969 to 1 January 1973 as a warm-up period. During the warm- up period, each ensemble member starts with the same initial condition but has different model trajectories because of dif- ferent forcing and parameter values. It is important to gener- ate an ensemble with a realistically large spread, so that the model uncertainty can be fully represented by the ensemble. The synthetic observations to be assimilated are generated from the “true” model. Given the true realization, by adding measurement errors to observed model variables at a given time and location, a set of synthetic observations can be pro- duced. Both groundwater head and soil moisture (depths of 5 and 25 cm) are extracted from the same 35 locations as the actual head observations (Fig. 1). The observation noise for each variable is assumed to be white Gaussian, with a homo- geneous and constant standard deviation of 0.15 m for head and 5 % for the soil volumetric water content. Due to the fact that groundwater head has a much slower dynamic compared to the unsaturated flow, we assimilate head with weekly fre- quency and soil moisture with daily frequency.
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