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

Nature And Properties Of Soils

Assessing the impacts of climatic and, in particular, land use changes on rates of soil erosion by water is the objective of many national and international research projects. However, over the last decades, most research dealing with soil erosion by water has concentrated on sheet (interrill) and rill erosion processes operating at the (runoff) plot scale. Relatively few studies have been conducted on gully erosion operating at larger spatial scales. Recent studies indicate that (1) gully erosion represents an important sediment source in a range of environments and (2) gullies are effective links for transferring runoff and sediment from uplands to valley bottoms and permanent channels where they aggravate off site effects of water erosion. In other words, once gullies develop, they increase the connectivity in the landscape. Many cases of damage (sediment and chemical) to watercourses and properties by runoff from agricultural land relate to (ephemeral) gullying. Consequently, there is a need for monitoring, experimental and modelling studies of gully erosion as a basis for predicting the effects of environmental change (climatic and land use changes) on gully erosion rates. In this respect, various research questions can be identified. The most important ones are: (1) What is the contribution of gully erosion to overall soil loss and sediment production at various temporal and spatial scales and under different climatic and land use conditions? (2) What are appropriate measuring techniques for monitoring and experimental studies of the initiation and development of various gully types at various temporal and spatial scales? (3) Can we identify critical thresholds for the initiation, development and infilling of gullies in different environments in terms of flow hydraulics, rain, topography, soils and land use? (4) How does gully erosion interact with hydrological processes as well as with other soil degradation processes? (5) What are appropriate models of gully erosion, capable of predicting (a) erosion rates at various temporal and spatial scales and (b) the impact of gully development on hydrology, sediment yield and landscape evolution? (6) What are efficient gully prevention and gully control measures? What can be learned from failures and successes of gully erosion control programmes? These questions need to be answered first if we want to improve our insights into the impacts of environmental change on gully erosion. This paper highlights some of these issues by reviewing recent examples taken from various environments.

Gully erosion and environmental change: importance and research needs

応用水文 = Applied hydrology

The production of topographic datasets is of increasing interest and application throughout the geomorphic sciences, and river science is no exception. Consequently, a wide range of topographic measurement methods have evolved. Despite the range of available methods, the production of high resolution, high quality digital elevation models (DEMs) requires a significant investment in personnel time, hardware and/or software. However, image-based methods such as digital photogrammetry have been decreasing in costs. Developed for the purpose of rapid, inexpensive and easy three-dimensional surveys of buildings or small objects, the ‘structure from motion’ photogrammetric approach (SfM) is an image-based method which could deliver a methodological leap if transferred to geomorphic applications, requires little training and is extremely inexpensive. Using an online SfM program, we created high-resolution digital elevation models of a river environment from ordinary photographs produced from a workflow that takes advantage of free and open source software. This process reconstructs real world scenes from SfM algorithms based on the derived positions of the photographs in three-dimensional space. The basic product of the SfM process is a point cloud of identifiable features present in the input photographs. This point cloud can be georeferenced from a small number of ground control points collected in the field or from measurements of camera positions at the time of image acquisition. The georeferenced point cloud can then be used to create a variety of digital elevation products. We examine the applicability of SfM in the Pedernales River in Texas (USA), where several hundred images taken from a hand-held helikite are used to produce DEMs of the fluvial topographic environment. This test shows that SfM and low-altitude platforms can produce point clouds with point densities comparable with airborne LiDAR, with horizontal and vertical precision in the centimeter range, and with very low capital and labor costs and low expertise levels. Copyright © 2012 John Wiley & Sons, Ltd.

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Topographic structure from motion: a new development in photogrammetric measurement

Ephemeral gully erosion is a common type of water erosion in the loamy soils formed on the Miocene Marls of southern Navarra. A study has been conducted to describe the different types of ephemeral gullies and to determine their origin, evolution and importance as sediment sources. Three main types were identified according to their origin: classic ephemeral gullies formed within the same field where runoff starts, drainage ephemeral gullies collecting the runoff from another upstream area, and discontinuity ephemeral gullies due to some abrupt slope change in the landscape. During 2 consecutive years of normal precipitation, ephemeral gully erosion has caused significant soil losses, locally over 2.66 kg m−2 yr−1, which is above tolerable levels. In each year, one short and intense rainfall event has been responsible for almost all soil losses from ephemeral gullies. The main cause of gully formation is the lack of any proper waterway for conveying water excess. Conventional tillage practices provoked gully occurrence, while the maintenance of stubble or vegetation cover completely prevented their formation. Although farmers refill gullies every year, they reappear at the same position if no preventive measures are taken. Early winter has been the most critical period for gully formation, when the soil is wetter and the surface cover is scarce. But a strong summer thunderstorm also caused severe gully erosion in unprotected soils. Two simple topographic indices based on the area and the slope of the watersheds are useful to describe total soil losses.

Ephemeral gully erosion in southern Navarra (Spain)

This work was possible by the financial support of: a) the Department of Education and
Culture of the Government of Navarre, with a graduate and postdoctoral fellowship
awarded to the fourth author; b) by the financial support of the Department of Education
and Culture of the Government of Navarre, through the Research Project Characterization of soil erosion in cultivated areas of Navarra; c) by the financial
support of the Spanish Ministry of Science and Technology, through the Research
Project REN2003-03028/HID. This material is based upon work supported by the U. S.
Department of Agriculture, under Agreement No. 58-6408-0-F137.

Accuracy of methods for field assessment of rill and ephemeral gully erosion

Runoff, erosion, and water quality of agricultural watersheds in central Navarre (Spain)

The formation of ephemeral gullies can significantly increase soil losses from agricultural lands and severely
impact farm productivity, yet few data exist on the physical characteristics of actively eroding gullies. The objectives of
the current study were to examine the time variation of gully morphology and sediment load in response to a range of
overland flow discharges and the impact of soil moisture content and soil density on erosion rates. Preformed ephemeral
gullies were constructed at field scale in a large experimental channel using the same cohesive soil but at two different
moisture contents and bulk densities. For the bed with relatively high soil moisture content and bulk density, clear-water
flows caused low rates of erosion, detachment-limited flows prevailed, and bed degradation was uniform along the flume.
For the bed with relatively low soil moisture content and bulk density, comparable clear-water flows caused high rates of
erosion, both detachment-limited and transport-limited flows prevailed, and bed degradation was greater in the upstream
reaches. In both experiments, erosion caused the gullies to incise, to significantly increase gully bottom width, and to
steepen gully sidewalls. These results compare favorably with field studies of ephemeral gullies, and the hydraulics and
sediment transport processes observed are similar to those reported for actively eroding rills.

Characteristics of actively eroding ephemeral gullies in an experimental channel

Although there is much evidence of intense soil erosion in cultivated areas of Navarre (Spain), information on it is currently scarce. Rill and ephemeral gully volumes can be used as a guide to minimum erosion rates. With the main purpose of determining the annual soil loss rates in cultivated areas of central Navarre, a detailed assessment of rainfall and of rill and gully erosion was made in 19 small catchments from October 1999 to September 2001. Seventeen of them were randomly selected, and were cultivated with winter cereals, vineyards or sunflowers. The other two catchments were selected to represent partially uncultivated lands abandoned for ten years. Channel cross-sections were measured by using a 1-m-wide micro-topographic profile meter, describing 632 cross-sections and processing information from 31 600 pins. Erosive events happened every year in the three study areas. For cereal catchments, soil losses occurred in only one or two rainfall events each year, usually at the end of autumn and in some summers, with high erosion rates (0·20–11·50 kg m−2 a−1). In vineyards, soil losses occurred several times per year, and in any season. This is attributed to the small percentage of surface covered by the crop throughout the year. Again, high erosion rates were found (0·33–16·19 kg m−2 a−1), with ephemeral gully erosion causing more loss than rill erosion. No-till is proposed as an effective conservation measure. From this large data set, it can be stated that rill erosion and ephemeral gully erosion are widespread in Mediterranean regions, and that much more attention should be paid to the problem. Abandoned fields showed very high erosion rates (16·19 kg m−2 a−1 on average), suggesting that the abandonment of marginal lands without implementing any erosion control can lead to severe erosion rates. Copyright © 2005 John Wiley & Sons, Ltd.

Javier Casalí

Papers

Ephemeral gully erosion in southern Navarra (Spain)

Accuracy of methods for field assessment of rill and ephemeral gully erosion

Runoff, erosion, and water quality of agricultural watersheds in central Navarre (Spain)

Characteristics of actively eroding ephemeral gullies in an experimental channel

Assessing soil erosion rates in cultivated areas of Navarre (Spain)