Conditioning of coefficient matrices of Ordinary Kriging

The solution of a set of linear equations is central to Ordinary Kriging. Computers are commonly applied because of the amount of data and work involved. There has, until recently, been little attention devoted toward the conditioning of kriging matrices. This article considers implications of conditioning upon numerical stability, instead of on robustness which has been the main focus of past work. The effect of properties of the stationary covariance matrix on the conditioning of the kriging matrix is discussed. The relationship between the covariance and autocorrelation functions allows some conclusions about the conditioning of covariance matrices, based on past work in deconvolution. The conditioning of some coefficient matrices of stationary kriging, defined in terms of either the semivariogram or the covariance, is examined.     

Influence of long‐period filter cut‐off on elastic spectral displacements

The effect of the long‐period filter cut‐off, T_c, on elastic spectral displacements is investigated using a strong ground‐motion database from Europe and the Middle East. The relation between the filter and oscillator responses is considered to observe the influence of T_c for both analogue and digital records, and the variations with site classification, magnitude, filter order and viscous damping. Robust statistics are derived using the re‐processed European data to generalize the effects of the long‐period filter cut‐off on maximum oscillator deformation demands as a function of these seismological and structural features. Statistics with a 95% confidence interval are derived to suggest usable period ranges for spectral displacement computations as a function of T_c. The results indicate that the maximum period at which spectral displacements can be confidently calculated depend strongly on the site class, magnitude and filter order. The period range where reliable long‐period information can be extracted from digital accelerograms is twice that of analogue records. Copyright © 2006 John Wiley & Sons, Ltd.     

Environmental influences on the yield of spring Barley in England and Wales

Using data on crop yields and soil conditions derived from reports of the Soil Survey of England and Wales, and incorporating a variety of climatic and topographic data, relationships were identified between the yield of spring barley and edaphic and climatic conditions. Yields are highest on fine loamy and silty soils and on freely to imperfectly drained soils. Multiple regression analysis indicated that yields are related to sand contents, drainage conditions and available water capacity of the soil, potential summer soil moisture deficit and annual accumulated temperature.     

Lagrangian measurements and modelling of fluid advection in the inner surf and swash zones

New laboratory and field data are presented on fluid advection into the swash zone. The data illustrate the region of the inner surf zone from which sediment can be directly advected into the swash zone during a single uprush, which is termed the advection length. Experiments were conducted by particle tracking in a Lagrangian reference frame, and were performed for monochromatic breaking waves, solitary bores, non-breaking solitary waves and field conditions. The advection length is normalised by the run-up length to give an advection ratio, A, and different advection ratios are identified on the basis of the experimental data. The data show that fluid enters the swash zone from a region of the inner surf zone that can extend a distance seaward of the bore collapse location that is approximately equal to half of the run-up length. This region is about eight times wider than the region predicted by the classical swash solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. Journal of Fluid Mechanics 16, 113–125], as illustrated by Pritchard and Hogg [Pritchard, D., Hogg, A.J., 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52, 1–23]. Measured advection ratios for periodic waves show no significant trend with Iribarren number, consistent with self-similarity in typical swash flows. The data are compared to recent characteristic solutions of the non-linear shallow water wave (NLSW) equations and both finite difference and finite volume solutions of the NLSW equations.     

Magmatic Evolution of the La Pacana Caldera System, Central Andes, Chile: Compositional Variation of Two Cogenetic, Large-Volume Felsic Ignimbrites

La Pacana is one of the largest known calderas on Earth, andis the source of at least two major ignimbrite eruptions witha combined volume of some 2700 km³. These ignimbrites have stronglycontrasting compositions, raising the question of whether theyare genetically related. The Toconao ignimbrite is crystal poor,and contains rhyolitic (76–77 wt % SiO₂) tube pumices.The overlying Atana ignimbrite is a homogeneous tuff whose pumiceis dacitic (66–70 wt % SiO₂), dense (40–60% vesicularity)and crystal rich (30–40 % crystals). Phase equilibriaindicate that the Atana magma equilibrated at temperatures of770–790°C with melt water contents of 3·1–4·4wt %. The pre-eruptive Toconao magma was cooler (730–750°C)and its melt more water rich (6·3–6·8 wt% H₂O). A pressure of 200 MPa is inferred from mineral barometryfor the Atana magma chamber. Isotope compositions are variablebut overlapping for both units (⁸⁷Sr/⁸⁶Sr_i 0·7094–0·7131;¹⁴³Nd/¹⁴⁴Nd 0·51222–0·51230) and are consistentwith a dominantly crustal origin. Glass analyses from Atanapumices are similar in composition to those in Toconao tubepumices, demonstrating that the Toconao magma could representa differentiated melt of the Atana magma. Fractional crystallizationmodelling suggests that the Toconao magma can be produced by30% crystallization of the observed Atana mineral phases. Toconaomelt characteristics and intensive parameters are consistentwith a volatile oversaturation-driven eruption. However, thelow H₂O content, high viscosity and high crystal content ofthe Atana magma imply an external eruption trigger. KEY WORDS: Central Andes; crystal-rich dacite; eruption trigger; high-silica rhyolite; zoned magma chamber     

Seasonal climate patterns and their influence on calibration of the Hargreaves-Samani equation

Abstract

Annual patterns in climate parameters were studied to evaluate how these influence the quality of reference evapotranspiration (ETo) estimates obtained from the Hargreaves-Samani (HS) equation, since the method only uses the measured temperature directly. The work evaluates how these patterns can be used to improve the HS ETo estimates. Ten-year moving averages from a set of California Irrigation Management Information System (CIMIS) stations were used to evaluate the relationships between solar radiation (R_s), temperature (T) and ETo. The results indicate that T treads behind solar radiation and its value peaks some 25 days later. Thus, the main irrigation season in the Mediterranean climate (1 May–30 September) can be divided into three phases: increasing R_s and T; decreasing R_s with increasing T; and decreasing R_s and T. Non-univocal annual cycles were observed between R_s and T, ETo and R_s, and ETo and T. These annual patterns result in important seasonal changes in the ratio between the HS and Penman-Monteith (FAO PM) ETo estimates. The changes are particularly important during the irrigation season, where the FAO PM initially calculates greater ETo values than the HS methodology, and from the end of May to early September, where the HS equation overestimates the ETo values (by 17 mm, or 3%). These patterns obtained from 2000–2009 data were used to calibrate and improve HS ETo estimates at new sites for the 2010–2011 period. Calibration based on the proposed seasonal region-wide FAO PM/HS ETo ratios improved both the bias (decreased from 0.40 to 0.36 mm d^-1) and r² (increased from 0.67 to 0.87) of the ETo estimates for the irrigation season. The proposed methodology can be easily applied to other regions, even when the existing weather stations are sparse.

Editor Z.W. Kundzewicz     

The hydrological response of soil surfaces to rainfall as affected by cover and position of rock fragments in the top layer

Rainfall experiments have been conducted in the laboratory in order to assess the hydrological response of top soils very susceptible to surface sealing and containing rock fragments in different positions with respect to the soil surface. For a given cover level, rock fragment position in the top soil has an ambivalent effect on water intake and runoff generation. Compared to a bare soil surface rock fragments increase water intake rates as well as time of runoff concentration and decrease runoff volume if they rest on the soil surface. For the same cover level, rock fragments reduce infiltration rate and enhance runoff generation if they are well embedded in the top layer. The effects of rock fragment position on infiltration rate and runoff generation are proportional to cover percentage. Micromorphological analysis and measurements of the saturated hydraulic conductivity of bare top soils and of the top layer underneath rock fragments resting on the soil surface reveal significant differences supporting the mechanism proposed by Poesen (1986): i.e. runoff generated as rock flow or as Horton overland flow can (partly) infiltrate into the unsealed soil surface under the rock fragments, provided that they are not completely embedded in the top layer. Hence, rock fragment position, beside other rock fragment properties, should be taken into account when assessing the hydrological response of soils susceptible to surface sealing and containing rock fragments in their surface layers. A simple model, based on the proportions of bare soil surface, soil surface occupied by embedded rock fragments, and soil surface covered with rock fragments resting on the soil surface, describes the runoff coefficient data relatively well.