The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

On behalf of Mr. Koichiro Matsuura, Director-General of UNESCO, it is my great pleasure to welcome you all to this international scientific conference. Drylands are often considered fragile ecosystems, yet they have a remarkable resilience to stress. They are home to unique and well-adapted plant and animal species that we need to conserve. Some of the world’s greatest cultures and belief systems have originated in drylands. On the other hand, desertification and land degradation in drylands often result in poverty and cause environmental refugees to abandon their homes. These problems can only be addressed in a holistic manner, based on sound scientific research and findings. Solutions to the problems of dryland degradation need to be communicated as widely as possible through education at all levels. These are many reasons why UNESCO – within its mandate of science, education, culture and communication – took the intiative to organize this conference. And we are glad that so many partners have responded to our call. UNESCO considers this conference as its main contribution to the observance of the International Year of Deserts and Desertification in 2006. We have deliberately chosen the title ‘The Future of Drylands’ as we feel it is time to redefine our priorities for science, education and governance in the drylands based on 50 years of scientific research in arid and semi-arid zones. In fact UNESCO has one of the longest traditions, within the UN system, of addressing dryland problems from an interdisciplinary, scientific point of view. In 1955, the ‘International Arid Land Meetings’ were held in Socorro, New Mexico (USA). They were organized by the American Association for the Advancement of Science (AAAS), sponsored by UNESCO and supported by the Rockefeller Foundation. One important output of the International Arid Land Meetings was a book entitled The Future of Drylands, edited by Gilbert F. White and published in

United Nations Educational, Scientific and Cultural Organization (UNESCO)

The Prediction in Ungauged Basins (PUB) initiative of the International Association of Hydrological Sciences (IAHS), launched in 2003 and concluded by the PUB Symposium 2012 held in Delft (23–25 October 2012), set out to shift the scientific culture of hydrology towards improved scientific understanding of hydrological processes, as well as associated uncertainties and the development of models with increasing realism and predictive power. This paper reviews the work that has been done under the six science themes of the PUB Decade and outlines the challenges ahead for the hydrological sciences community.Editor D. KoutsoyiannisCitation Hrachowitz, M., Savenije, H.H.G., Bloschl, G., McDonnell, J.J., Sivapalan, M., Pomeroy, J.W., Arheimer, B., Blume, T., Clark, M.P., Ehret, U., Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V., Hughes, D.A., Hut, R.W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P.A., Uhlenbrook, S., Wagener, T., Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec, C., 2013. A d...

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A decade of Predictions in Ungauged Basins (PUB)—a review

Despite significant recent advancements, global hydrological models and their input databases still show limited capabilities in supporting many spatially detailed research questions and integrated assessments, such as required in freshwater ecology or applied water resources management. In order to address these challenges, the scientific community needs to create improved large-scale datasets and more flexible data structures that enable the integration of information across and within spatial scales; develop new and advanced models that support the assessment of longitudinal and lateral hydrological connectivity; and provide an accessible modeling environment for researchers, decision makers, and practitioners. As a contribution, we here present a new modeling framework that integrates hydrographic baseline data at a global scale (enhanced HydroSHEDS layers and coupled datasets) with new modeling tools, specifically a river network routing model (HydroROUT) that is currently under development. The resulting ‘hydro-spatial fabric’ is designed to provide an avenue for advanced hydro-ecological applications at large scales in a consistent and highly versatile way. Preliminary results from case studies to assess human impacts on water quality and the effects of dams on river fragmentation and downstream flow regulation illustrate the potential of this combined data-and-modeling framework to conduct novel research in the fields of aquatic ecology, biogeochemistry, geo-statistical modeling, or pollution and health risk assessments. The global scale outcomes are at a previously unachieved spatial resolution of 500 m and can thus support local planning and decision making in many of the world's large river basins. Copyright © 2013 John Wiley & Sons, Ltd.

Global river hydrography and network routing: baseline data and new approaches to study the world's large river systems

. Current global precipitation (P) datasets do not take full advantage of the complementary nature of satellite and reanalysis data. Here, we present Multi-Source Weighted-Ensemble Precipitation (MSWEP) version 1.1, a global P dataset for the period 1979–2015 with a 3-hourly temporal and 0.25° spatial resolution, specifically designed for hydrological modeling. The design philosophy of MSWEP was to optimally merge the highest quality P data sources available as a function of timescale and location. The long-term mean of MSWEP was based on the CHPclim dataset but replaced with more accurate regional datasets where available. A correction for gauge under-catch and orographic effects was introduced by inferring catchment-average P from streamflow (Q) observations at 13 762 stations across the globe. The temporal variability of MSWEP was determined by weighted averaging of P anomalies from seven datasets; two based solely on interpolation of gauge observations (CPC Unified and GPCC), three on satellite remote sensing (CMORPH, GSMaP-MVK, and TMPA 3B42RT), and two on atmospheric model reanalysis (ERA-Interim and JRA-55). For each grid cell, the weight assigned to the gauge-based estimates was calculated from the gauge network density, while the weights assigned to the satellite- and reanalysis-based estimates were calculated from their comparative performance at the surrounding gauges. The quality of MSWEP was compared against four state-of-the-art gauge-adjusted P datasets (WFDEI-CRU, GPCP-1DD, TMPA 3B42, and CPC Unified) using independent P data from 125 FLUXNET tower stations around the globe. MSWEP obtained the highest daily correlation coefficient (R) among the five P datasets for 60.0 % of the stations and a median R of 0.67 vs. 0.44–0.59 for the other datasets. We further evaluated the performance of MSWEP using hydrological modeling for 9011 catchments ( http://www.gloh2o.org .

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MSWEP: 3-hourly 0.25° global gridded precipitation (1979–2015) by merging gauge, satellite, and reanalysis data

In this paper, a hydrologic/hydrodynamic modeling of the Amazon River basin iscpresented using the MGB-IPH model with a validation using remotely sensed observations. Moreover, the sources of model errors by means of the validation and sensitivity tests are investigated, and the physical functioning of the Amazon basin is also explored. The MGBIPH is a physically based model resolving all land hydrological processes and here using a full 1-D river hydrodynamic module with a simple floodplain storage model. Riverfloodplain geometry parameters were extracted from the SRTM digital elevation model, and the model was forced using satellite-derived rainfall from TRMM3B42. Model results agree with observed in situ daily river discharges and water levels and with three complementary satellite-based products: (1) water levels derived from ENVISAT altimetry data; (2) a global data set of monthly inundation extent; and (3) monthly terrestrial water storage (TWS) anomalies derived from the Gravity Recovery and Climate Experimental mission. However, the model is sensitive to precipitation forcing and river-floodplain parameters. Most of the errors occur in westerly regions, possibly due to the poor quality of TRMM 3B42 rainfall data set in these mountainous and/or poorly monitored areas. In addition, uncertainty in river-floodplain geometry causes errors in simulated water levels and inundation extent, suggesting the need for improvement of parameter estimation methods. Finally, analyses of Amazon hydrological processes demonstrate that surface waters govern most of the Amazon TWS changes (56%), followed by soil water (27%) and ground water (8%). Moreover, floodplains play a major role in stream flow routing, although backwater effects are also important to delay and attenuate flood waves.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/wrcr.20067

Large‐scale hydrologic and hydrodynamic modeling of the Amazon River basin

Daily hydrological modeling in the Amazon basin using TRMM rainfall estimates

Recent developments in hydrological modelling of river basins are focused on prediction in ungauged basins, which implies the need to improve relationships between model parameters and easily-obtainable information, such as satellite images, and to test the transferability of model parameters. A large-scale distributed hydrological model is described, which has been used in several large river basins in Brazil. The model parameters are related to classes of physical characteristics, such as soil type, land use, geology and vegetation. The model uses two basin space units: square grids for flow direction along the basin and GRU—group response units—which are hydrological classes of the basin physical characteristics for water balance. Expected ranges of parameter values are associated with each of these classes during the model calibration. Results are presented of the model fitting in the Taquari-Antas River basin in Brazil (26 000 km2 and 11 flow gauges). Based on this fitting, the model was the...

https://www.tandfonline.com/doi/pdf/10.1623/hysj.52.5.878

The MGB-IPH model for large-scale rainfall—runoff modelling

Large scale hydrologic and hydrodynamic modeling using limited data and a GIS based approach

In planning routes for roads and canals, topography is often a significant constraint. Among the infinite number of possible trajectories between two points, the selected path should be a good approximation to the one with the least cost, and should avoid extremes of slopes. In the case of a canal, the number of uphill reaches of the trajectory should be minimised. This paper presents a least-cost-path algorithm developed to find the best path given the topography, the start and end-points of the linear feature (canal or road) and a function relating slope, distance and cost. The algorithm is based on dynamic programming techniques adapted to solve problems on the grid, or raster structure usually used in Geographical Information Systems. The algorithm was programmed and used to solve hypothetical problems. Although real cost functions were not used, the results were coherent and showed the algorithm's capabilities.

Walter Collischonn

Papers

Large‐scale hydrologic and hydrodynamic modeling of the Amazon River basin

Daily hydrological modeling in the Amazon basin using TRMM rainfall estimates

The MGB-IPH model for large-scale rainfall—runoff modelling

Large scale hydrologic and hydrodynamic modeling using limited data and a GIS based approach

A direction dependent least-cost-path algorithm for roads and canals