Models to predict water chemical cluster variables

This study is an attempt to quantify and rank variables of significance to predict mean values of lake pH and related variables (alkalinity, conductivity, hardness, etc.) in small glacial lakes. The work is based on a new and extensive set of data from 95 Swedish lakes and their catchment areas. Several empirical models based on catchment and lake morphometric parameters have been presented. These empirical models can only be used to predict mean values of these variables for lakes of the same type, and these models based on geological map parameters can evidently not be used for highly time-dependent and site-typical predictions. Various hypotheses concerning the factors regulating the mean values of the cluster variables were formulated and tested. Different statistical tests were used to separate random influences from causal. The most important map parameters were: the percent of rocks and open (=cultivated) land in the so-called near area to the lake [as determined with the drainage area zonation (DAZ) method], mean depth, linked to resuspension and the form and size of lakes, relief of the drainage area and lake area. Each of these variables only provides a limited degree of (statistical) explanation of the variability in mean annual values of pH and the water chemical cluster variables among the lakes. The predictability of some of the models can be markedly improved by accounting for the distribution of the characteristics in the drainage area. The variability in mean annual values of pH (and related variables) from other parameters, such as specific anthropogenic load, etc., may then be quantitatively differentiated from the impact of these geological parameters. This paper also gives a simple method to estimate natural, preindustrial reference values of these water chemical variables from the presented models.     

Relationships between drainage area characteristics and lake water quality

The aim of this work is to quantify some of the complex relationships between drainage area characteristics (such as bedrocks and quaternary deposits) and lake water quality (pH, alkalinity, conductivity, and hardness). Seventysix drainage lakes, mainly oligotrophic, are described with respect to drainage area characteristics, morphometry, and water chemistry. The DAZ (drainage area zonation) method has been used to describe the drainage areas. The method utilizes a weighting system to reduce the impact of land types with increasing distance from the lake. The most significant parameter governing the water chemistry parameters seems to be the percentage of open land (cultivated land and/or meadows) in the drainage areas. High percentage leads to high pH, alkalinity, conductivity, and hardness. The correlations concerning alkalinity and pH are improved using the DAZ method. No significant relationships between bedrock geology of the drainage areas and lake water chemistry have been recorded.     

都昌县水患区滨湖小流域水土流失影响因子特征与治理

以鄱阳湖之滨都昌县境内的小流域为例，论述了区内水土流失控制因子主要有地质构造、岩性、气候和人类活动及水土流失对江湖演变及洪涝灾害的影响，提出了加强小流域水土保持工作的对策。     

Framework for soil suitability evaluation for sewage effluent renovation

Current methods of establishing suitable locations for onsite wastewater treatment systems (OWTS) are inadequate, particularly in light of the numerous cases of onsite system failure and the resulting adverse consequences. The development of a soil suitability framework for assessing soil suitability for OWTS allows a more practical means of assessment. The use of multivariate statistical analysis techniques, including Principal Component Analysis (PCA) and multi-criteria decision aids of PROMETHEE and GAIA, enabled the identification of suitable soils for effluent renovation. The outcome of the multivariate analysis, together with soil permeability and drainage characteristics permitted the establishment of a framework for assessing soil suitability based on three main soil functions: (1) the ability of the soil to provide suitable effluent renovation, (2) the permeability of the soil, and (3) the soils drainage characteristics. The developed framework was subsequently applied to the research area, Gold Coast, Queensland, Australia, and the use of standard scoring functions were utilised to provide a scoring system to signify which soils were more suitable for effluent renovation processes. From the assessment, it was found that Chromosol and Kurosol soils provided the highest level of effluent renovation, closely followed by Ferrosol and Dermosol, Kandosol and Rudosol soil types. Tennosol and Podosol soil types were found to have a significantly lower suitability, with Hydrosol soils proving the least suitable for renovating effluent from OWTS.     

Factors influencing thermokarst lake development in Beiluhe basin,the Qinghai–Tibet Plateau

Thermokarst lake is a significant indicator of permafrost degradation. However, the evaluation of thermokarst lake development is very difficult through physical mechanism analysis because the development is influenced by many factors. In the present study, the factors influencing thermokarst lake development were investigated from the perspective of frozen soil and the geographical environment. The influences of six factors on thermokarst lake development in Beiluhe basin, located in the hinterland of the Qinghai–Tibet Plateau, were analyzed: permafrost type, ground temperature, vegetation type, soil type, hydrogeological type, and slope. Sensitivity coefficients were calculated for these factors using statistical methods. The results show that thermokarst lake development was influenced by the analyzed factors as follows: permafrost > soil type > ground temperature > hydrogeological type. Furthermore, 80.1% of the study area was highly sensitive to thermokarst lake development. Overall, thermokarst lake development in the Beiluhe basin was thoroughly evaluated based on sensitivity factors and an established statistical evaluation method. The method detailed in this paper provides a reference for evaluating the likelihood and severity of thermokarst lake development.     

Holocene climate variability and cultural evolution in the Near East from the Dead Sea sedimentary record

A comprehensive record of lake level changes in the Dead Sea has been reconstructed using multiple, well dated sediment cores recovered from the Dead Sea shore. Interpreting the lake level changes as monitors of precipitation in the Dead Sea drainage area and the regional eastern Mediterranean palaeoclimate, we document the presence of two major wet phases ( 10–8.6 and  5.6–3.5 cal kyr BP) and multiple abrupt arid events during the Holocene. The arid events in the Holocene Dead Sea appear to coincide with major breaks in the Near East cultural evolution (at  8.6, 8.2, 4.2, 3.5 cal kyr BP). Wetter periods are marked by the enlargement of smaller settlements and growth of farming communities in desert regions, suggesting a parallelism between climate and Near East cultural development.     

Deformationsverhalten tektonisch unterschiedlich beanspruchter Carnallitite

Four different stressed carnallite-rocks were microscopically investigated by U-stage and the indicatrix orientation pattern was treated in topotropic analysis (AVA). The investigation involved a young, post-tectonic carnallitite, a layered carnallite-rock and a weakly cataclastic carnallitite, as well as so-called Trümmercarnallitite, and had as its objective observation of changes in fabric orientation.The youngest, uninfluenced carnallitite is a megagrained (handspecimen 3 grains), the other varieties are heterogenous, and respectively middleto finegrained carnallitite.With increasing tectonically strain, the number of grains with similar indicatrix orientation diminishs from that of the wholegrain. Neighbouring grains are shifted more and more and respectively show varying degrees of recristallisation from layered carnallitite up to the cataclastic Trümmercarnallitite.In addition for interpretation the mechanics undulations, kinkbands and rotationcristallisation by twinning were investigated.An attempt is made to explain the mechanism of the deformation.

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Zusammenfassung Vier unterschiedlich beanspruchte Carnallitite wurden mikroskopisch mit dem U-Tisch gemessen und Achsenverteilungsanalysen angefertigt. Ausgehend von einem posttektonisch entstandenen, jüngeren Carnallitit wurden ein gut geschichteter, ein schwach kataklastischer und sog. Trümmercarnallitit auf die Änderung ihrer Gefüge hin untersucht. Der jüngere unbeeinflußte Carnallitit ist riesenkörnig (Handstück 3 Körner), die anderen Varietäten sind heterogen- und mittel- bis kleinkörnig.Mit zunehmender tektonischer Beanspruchung wird die Zahl der Körner kleiner, die ursprünglich ein Großkorn gebildet haben, d. h. die Lage der Indikatrix benachbarter Körner ist stärker verstellt.Zur Feststellung der Mechanismen werden Messungen an Verbiegungen (undulöse Auslöschungen), Knickbändern und die Rotationskristallisation durch Zwillingsbildung untersucht. Es wird der Versuch unternommen, den mechanischen Ablauf der Deformation zu erklären.

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Résumé Quatre roches à carnallite, ayant subi des sollicitations différentes, ont fait l'objet d'une analyse topotropique («Achsenverteilungsanalyse») au moyen de la platine universelle. Ces quatre roches sont des carnallitites respectivement: (1) grenue posttectonique, (2) à rubanement bien exprimé, (3) légèrement cataclastique, (4) dite «Trümmercarnallitite». La roche jeune non affectée (1) est une Carnallitite à grains géants (3 grains pour l'échantillon); les autres sont des roches à granularité hétérogène moyenne à fine.Lorsque la sollicitation tectonique augmente, on voit diminuer le nombre de grains issus d'un même grain originel; en d'autres termes on voit se modifier de plus en plus la position des indicatrices de grains voisins.En outre, il a été procédé à une investigation des extinctions onduleuses, des kink-bands et des macles de déformation. La note présente finalement un essai d'interprétation du mécanisme de la déformation.

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1975-2006年西藏羊卓雍错流域内湖泊水位变化对气候变化的响应

根据1975年地形图、1988年至2006年的TM、CBERS卫星遥感资料和1962-2006年逐年平均气温、降水量、蒸发量、相对湿度、风速和日照时数等气象资料以及1974-2005年的湖泊水位水文资料,对西藏羊卓雍错及其流域内的空姆错、沉错和巴纠错等4个湖泊的水位变化以及对气候变化的响应作了分析.结果表明:该区湖泊面积在近30 a来呈缓慢下降趋势,2005年与1975年相比,分别减少了46.55 km2、1.73km2、0.03 km2、6.01 km2,减少幅度分别为7.2%、4.3%、0.1%、13.6%.其主要原因是,由于羊卓雍错的湖水主要以降水补给为主,在降水增加、气温上升的情况下由于升温引起的湖泊蒸发效应超过降水增加导致的补给影响,是湖泊面积下降的主要原因.     

Modern Sedimentary Characteristics and Environmental Indication Significance of the Cibi Lake

Based on the particle size test results of 36 surface sediment samples from the Cibi Lake, the spatial distribution characteristics and rules of components were discussed by the combination of natural geographical factors with statistical analysis methods in the basin, which provides scientific evidence and basic data for the study of paleoclimate environment in this region. The results show that:\mathrm{①} The samples mainly include clay, silty and sand, among which silty is the main type in the study area and has the widest distribution due to the disturbance caused by groundwater recharge without obvious spatial variation law;\mathrm{②} The clay distribution is somewhat smaller, and its locality affected by the slope alluvial fan is in the northwest and near the center of the lake, where the sedimentary environment is stable and is the best selected location for the borehole core so that the reconstruction of the paleoclimate environment can be carried out;\mathrm{③} Sand is mainly distributed in the southwest corner and near the north shore of the lake, which is influenced by the rivers entering the lake and human activities, and these two locations have a great influence on the source of surface sediment. Therefore, the management of the north and southwest regions should be strengthened to prevent a large number of pollutants from entering the lake;\mathrm{④} The grain size frequency curve shows that the sediments include suspended and saltant components. Besides the formation by their own biochemistry, other materials come from the aeolian sediments in the basin, and the coarse particles transported over a long distance have a great impact on the grain size components. Section CB-1 indicates that transport process and distribution are significantly affected by the southwest monsoon and more attention should be paid to the prevention and control of pollution at the river inlet and upwind area.     

GIS-based analysis of the Stream Length-Gradient Index for evaluating effects of active tectonics: a case study of Enfidha (North-East of Tunisia)

Our study aims at calculating morphometric indices through the recourse to the Digital Elevation Model (DEM) and its attributes (hydrographic networks, watersheds, and reliefs). This quantitative measurement is used for the morphotectonical analysis of the Enfidha area (North-East of Tunisia) in the GIS environment and statistical platform. The Enfidha area is selected to analyze and identify neotectonic morphostructures on basis of the morphological evolution of the landscape. The coastal Enfidha plain is part of the Tunisian Sahel that is marked by its instability and frequent earthquakes that prove the presence of the recent deformation and active subsurface faults. This morphometric modeling in the geological investigation area reflects the morphotectonic spatial evolution in the Quaternary basins areas. Stream length (SL) proposed by Hack (1973) and denominated by Etchebehere et al. (2004) Revista do Instituto de Geociências USP, Série Científica, São Paulo 4(2):43–56 as the RDE index (Relation Declivity Extension) was used for application in the studies of neotectonic approach. RDE index is one of the morphotectonical indices that designates the tectonics anomalies in rivers. The variability in (RDE) values can indicate both a lithology resistance towards erosion and major active subsurface faults or low slope. Our geostatistical method is required to obtain RDE index maps based on lithological filtrations and value interpolations which are calculated in a drainage line network. This method calculates, measures, and validates spatial distribution of hack RDE index through a high statistical accuracy in a quantitative anomalies study. The RDE anomaly maps of the study area mirror the concurrence between anomaly zones, major active subsurface E-W faults, and local geological discontinuities related to neotectonical activities that affect the hydrographic network. This study proves that the RDE index can be especially used to detect the influence of active large-scale faults on the landscape evolution.     

A generic method to organize boundaries of complex polygons for embedded devices

Based on an analysis of drawbacks in the existing graphical display of complex area objects in embedded system, the paper introduces a new method termed as consecutive boundary organization (CBO) which is able to convert a large number of separate polygons belonging to the same area object into a single consecutive stroke fitting for quick display. The working principle of the CBO method is demonstrated in three cases that can typically occur to the real-world concept “lake”: (1) a lake with an island in it, (2) a lake with multiple islands, and (3) the nested lake-island-lake. In spite of complicated inclusion relationships, the CBO method can always construct an integral stroke with neither information loss nor redundancy. Experiments with a real dataset of lakes and islands from North America have proved the feasibility and efficiency of the CBO method. Due to its generic nature, the CBO method can be applied to any other complex area objects with multiple polygons and inclusion levels.     

Empirical estimation of isostatic uplift using the lake-tilting method at lake Fegen and lake S?ven, southwestern Sweden

A nonuniform glacio-isostatic uplift results in differential uplift for different parts of a lake. If the lake outlet is situated in the area with the greatest rate of uplift, then the lake will be continuously transgressed. Ancient lake levels can be estimated by dating transgressed peat at different depths in such a lake. Two lakes in southwestern Sweden have been investigated by this method and the course of glacio-isostatic uplift has been determined empirically. The uplift can be expressed by an exponential function through the following formula

Characteristics of motions in the 2D isosceles three-body problem with unequal masses

We analyze the general 2D isosceles three-body problem for various ratios ? of the mass of the central body to the mass of each of the other two bodies. We set the initial conditions using two parameters: the virial coefficient k and the parameter \(\mu = \dot r/\sqrt {\dot r^2 + \dot R^2 }\), where \(\dot r\) is the relative velocity of the two outer bodies and \(\dot R\) is the velocity of the central body relative to the center of mass of the outer bodies. We compare statistical dependences between evolutionary parameters of triple systems with various values of ?, and analyze the k and μ dependences of the number of crossings of the center of mass of the triple system by the central body and the lifetime of the system. We construct the functions R_max(r_max), where r_max and R_max are the maximum achievable distances between the outer bodies, and between the central body and the center of mass of the outer bodies in the triple system. The parameter ? proves to be the most important parameter of the problem, and determines the relationship between the measures of the regular and stochastic trajectories. However, there exist “seeds” of stochasticity, even at small ?～10^?2. The measure of the stochastic orbits increases with ?; when ?≥10, virtually the entire region of the initial conditions corresponds to stochastic trajectories.     

Phase relations in the system NaAlSi3O8-KAlSi3O8-CaAl2Si2O8-SiO2 at 1 kilobar water vapour pressure

Crystal-melt relations at a water vapour pressure of 1 kilobar have been determined for planes at 3, 5, 7.5, and 10 weight per cent anorthite in the system NaAlSi₃O₈KAlSi₃O₈-CaAl₂Si₂O₈-SiO₂. The ratio of the silicate components in the liquids which are in univariant equilibrium with plagioclase, alkali feldspar, quartz and gas are Ab₃₁Or₂₈Q₃₈An₃ (weight per cent) at 730°±5–10° C, Ab₂₁Or₃₄Q₄₀An₅ at 745°±5–10° C and Ab₁₀Or₃₉ Q_43.5An_7.5 at 780°±10° C. The univariant curve on which the above compositions lieoriginates on the H₂O-saturated Or-An-Q plane at a composition containing less than 10 weight per cent An and terminates within 1.5 weight per cent An of the H₂O-saturated Or-Ab-Q plane. Experimental data for the synthetic system have been used to illustrate a discussion on the partial melting of metasediments and the possible significance of such a process with respect to the genesis of granitic rocks. Data taken from the literature (Winkler and v. Platen, 1960, 1961a) have been used to illustrate that the normative salic composition of a sediment has a strong influence on the composition of any melt which form when such a rock is subjected to high temperatures and pressures.     

Creation and destruction of lower continental crust

Bulk continental crustal composition results from the net mass exchange between crust and mantle. Crustal addition is mainly by the rise of mantle-derived melts into and through the crust at convergent plate margins and (at a lower rate) within plate interiors. Crustal subtraction occurs by subduction of uppermost crust (sediment, continent-derived elements in hydrothermally altered oceanic crust), by subcrustal erosion at convergent margins and by delamination of lowermost crust following densifying gabbro-eclogite phase transformations that result in a crust-mantle density inversion. As the phase transformations only occur at high pressure, tectonic overthickening of the crust (to > 50 km) is required. The lowermost crust at continent-ocean and continent-continent convergent plate margins is more likely to experience these transient overthickening events (compressional orogenies) than is intraplate crust. Correspondingly, the preservation probability of mafic lower crust is greater for intraplate than for plate margin localities. Delamination of mafic lower crust is the main process for removing basic composition rocks from the crust, thereby creating »andesitic« crustal composition. Evidence for lower crustal delamination comes from »geochemically balanced« cross section of compressional belts, and from the high La/Yb ratios, lack of Eu anomalies, and high Sr contents in deep crustallyderived magmas from the base of tectonically over-thickened crust. These crustal magmas are often accompanied by mantle-derived basalts associated with crustal uplift and extension, both related to the coincident delamination of underlying mantle lithosphere.

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Zusammenfassung Die Gesamtzusammenfassung der Kontinentalen Kruste resultiert aus dem Massenaustausch zwischen Kruste und Mantel. Krustenzuwachs erfolgt hauptsächlich beim Aufstieg in und durch die Kruste von aus dem Mantel abstammenden Basalt an konvergierenden Plattengrenzen und zum geringeren Teil Plattenintern. Der Krustenabbau wird erreicht per Subduktion der obersten Kruste, durch subkrustale Erosion an konvergierenden Plattengrenzen (Sedimente, Elemente kontinentaler Herkunft von hydrothermal veränderter ozeanischer Kruste). Dies wird hervorgerufen von der Schichtspaltung der untersten Kruste nach der Verdichtung durch die Gabbro-Eklogit-Phasentransformation, welche in der Krusten-Mantel-Dichte-Inversion resultiert. Da die Phasentransformation nur unter hohen Drücken stattfindet, werden tektonische Mächtigkeitszunahmen der Kruste (> 50 km) benötigt. Die unterste Kruste in Bereichen von konvergierenden Kontinent-Ozean und Kontinent-Kontinent Plattengrenzen unterliegt einer größeren Wahrscheinlichkeit vorübergehende Mächtigkeitszunahmen zu erfahren als platteninterne Kruste. Dementsprechend ist die Erhaltungswahrscheinlichkeit von mafischer unterer Kruste für platteninterne Bereiche größer als für Plattengrenzen. Schichtspaltung von mafischer unterer Kruste ist der Hauptprozeß basisch zusammengesetzte Gesteine aus der Kruste zu entfernen, hierbei wird die Kruste in Richtung »andesitische« Zusammensetzung verändert. Hinweise für Schichtspaltung der unteren Kruste stammen von »geochemisch bilanzierten« Profilen aus druckhaft deformierten Zonen. Weiterhin sprechen dafür hohe La/Yb-Werte, das Fehlen von Eu-Anomalien und hohe Sr-Gehalte, wie sie an der Basis tektonisch verdickter Kruste in Magmen, die aus der tiefen Kruste stammen, gefunden werden. Diese krustalen Magmen werden häufig von Mantelbasalten begleitet, die zu Krustenhebung und Dehnung in Verbindung stehen; beides im Zusammenhang stehend zu der gleichzeitig stattfindenden Schichtspaltung der unterlagernden Mantellithosphäre.

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Résumé La composition d'ensemble de la croûte continentale résulte des échanges entre la croûte et le manteau. L'apport dans la croûte provient en ordre principal de la montée de basalte d'origine mantélique qui s'opère aux bordures des plaques convergentes et, dans une moindre mesure, à l'intérieur des plaques. Le départ hors de la croûte se produit par la subduction de la croûte supérieure (sédiments, éléments dérivés des continents dans la croûte océanique affectée d'altération hydrothermale), par érosion subcrustale le long des marges convergentes et par délamination à la base de la croûte, les transformations de phase gabbro-éclogitiques entraînant une augmentation de densité et une inversion de densité entre croûte et manteau. Comme ces transformations de phases ne se produisent qu'à haute pression, elles impliquent un épaississement tectonique de la croûte (jusqu'à plus de 50 Km). Le domaine probable de tels épaississement est la partie inférieure de la croûte en bordure des plaques convergentes continentocéan ou continent-continent (orogènes de compression), plutôt que la croûte intra-plaque. Inversement, la probabilité de conversion d'une croûte inférieure mafique est plus élevée au milieu des plaques que sur leurs bordures. La délamination de la croûte inférieure est le processus courant d'appauvrissement de la croûte en roches mafiques, avec création d'une composition crustale »andésitique«. Les arguments en faveur de cette delamination sub-crustale sont tirés de profils »géochimiquement équilibrés« dans les ceintures en compression, ainsi que des rapports La/Yb élevés, de l'absence d'anomalie de l'Eu et des hautes teneurs en Sr dans les magmas dérivés de la partie profonde des croûtes tectoniquement épaissies. Ces magmas crustaux sont souvent accompagnés de basaltes d'origine mantélique associés à un soulèvement et à une extension crustale, ces deux processus étant liés à la délamination concommittante de la lithosphère mantélique sousjacente.

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Accompanying seismic refraction investigations along the profile DEKORP 2-North

Seismic refraction measurements were carried out along the DEKORP 2-N reflection line. Traveltime data have been inverted to velocity-depth distributions using x-t-inversion- und ray-tracing-methods. The velocity-model shows alternating layers of high and low velocity. High-velocity values range from 6.0 to 6.6 km/s in the upper crust and from 70 to 8.2 km/s in the lower crust. In low-velocity zones velocities do not exceed 6.25 km/s. The crust/mantle boundary lies in about 28–30 km depth. Correlations exist between the velocity-model of refraction seismics and the line drawing section of reflection seismics.

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Zusammenfassung Entlang dem tiefenseismischen Reflexionsprofil DEKORP 2-Nord wurden seismische Refraktionsmessungen durchgeführt. Die Laufzeitdaten wurden mit Hilfe von x-t-Inversions- und Ray-Tracing-Verfahren in Geschwindigkeits-Tiefen-Verteilungen transformiert. Es treten alternierende Hoch- und Niedriggeschwindigkeitszonen auf. In der oberen Kruste treten hohe Geschwindigkeitswerte im Bereich von 6,0 bis 6,6 km/s auf und in der unteren Kruste Werte von 7,0 bis 8,2 km/s. Die Geschwindigkeitswerte in Niedriggeschwindigkeitszonen überschreiten 6,25 km/s nicht. Die Grenze zwischen Erdkruste und Erdmantel liegt in einer Tiefe von etwa 28 bis 30 km. Es bestehen Übereinstimmungen zwischen dem Geschwindigkeitsmodell der Refraktionsseismik und der Struktur der reflexionsseismischen Sektion.

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Résumé Des mesures en sismique-réfraction ont été effectuées le long du profil de sismique réflexion DEKORP 2-N. On a réalisé une inversion des temps de propagation en distribution vitesse/profondeur par les méthodes de l'inversion x-t et du traçage de raie. Le modèle des vitesses fait apparaître des couches alternées à grandes et faibles vitesses. Les grandes vitesses sont de 6,0 à 6,6 km/sec dans la croûte supérieure et de 7,0 à 8,2 km/sec dans la croûte inférieure. Dans les zones à faible vitesse, celle-ci n'excède pas 6,25 km/sec. La profondeur du contact croûte/manteau est d'environ 28 à 30 km. Il existe une correspondance entre le modèle des vitesses de la sismique-réfraction et l'image fournie par la sismique-réflexion.

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Water supply problems in the Butana region-central Sudan with special emphasis on Jebel Qeili area

The Butana region of central Sudan is famous for its animal wealth and extensive pastures. Yet scarcity of water resources in the area especially during the dry seasons handicaps the proper utilization of these pastures. The area is occupied by non-water-bearing basement rocks and the only source of water is from direct run-off. Thus large numbers of small-size water reservoirs, haffirs, were constructed, but these are inadequate to provide enough water for the growing human and animal population. An all-year lake is here proposed to be constructed utilizing the ring-structure the Jebel Qeili igneous complex, central Butana. This lake is expected to solve the present water problem and meet the future demand of central Butana at the present rate of human and animal growth.     

A statistical method for estimating rates of soil development and ages of geologic deposits: A design for soil-chronosequence studies

A statistical method for estimating rates of soil development in a given region based on calibration from a series of dated soils is used to estimate ages of soils in the same region that are not dated directly. The method is designed specifically to account for sampling procedures and uncertainties that are inherent in soil studies. Soil variation and measurement error, uncertainties in calibration dates and their relation to the age of the soil, and the limited number of dated soils are all considered. Maximum likelihood (ML) is employed to estimate a parametric linear calibration curve, relating soil development to time or age on suitably transformed scales. Soil variation on a geomorphic surface of a certain age is characterized by replicate sampling of soils on each surface; such variation is assumed to have a Gaussian distribution. The age of a geomorphic surface is described by older and younger bounds. This technique allows age uncertainty to be characterized by either a Gaussian distribution or by a triangular distribution using minimum, best-estimate, and maximum ages. The calibration curve is taken to be linear after suitable (in certain cases logarithmic) transformations, if required, of the soil parameter and age variables. Soil variability, measurement error, and departures from linearity are described in a combined fashion using Gaussian distributions with variances particular to each sampled geomorphic surface and the number of sample replicates. Uncertainty in age of a geomorphic surface used for calibration is described using three parameters by one of two methods. In the first method, upper and lower ages are specified together with a coverage probability; this specification is converted to a Gaussian distribution with the appropriate mean and variance. In the second method, absolute older and younger ages are specified together with a most probable age; this specification is converted to an asymmetric triangular distribution with mode at the most probable age. The statistical variability of the ML-estimated calibration curve is assessed by a Monte Carlo method in which simulated data sets repeatedly are drawn from the distributional specification; calibration parameters are reestimated for each such simulation in order to assess their statistical variability. Several examples are used for illustration. The age of undated soils in a related setting may be estimated from the soil data using the fitted calibration curve. A second simulation to assess age estimate variability is described and applied to the examples.