応用水文 = Applied hydrology

Ecological data are often lognormally distributed. Nutrient concentrations, population densities and biomasses, rates of production and other flows are always positive, and generally have standard deviations that increase as the mean increases. Lognormally distributed variables have these characteristics, whereas normally distributed variables can be negative and have a standard deviation that does not change as the mean changes. Lognormal errors arise when sources of variation accumulate multiplicatively, whereas normal errors arise when sources of variation are additive. Given a normally distributed random variable Y, one can calculate a lognormally distributed random variable Z = exp(Y) where exp stands for the exponential function (exp(x) = e x). The mean Z and the standard deviation s Z of the lognormal variable are related to the mean Y and standard deviation s Y of the normal variable by) 2 / exp() exp(2 Y s Y Z = [1] 5. 0 2 ] 1) [exp(− = Y Z s Z s [2] Equation 1 can be used to correct for transformation bias in logarithmic regression. Suppose that lognormally-distributed observations Z have been log transformed as Y = log(Z) to fit a regression model such as ε + =) , (ˆ b X f Y [3] where Y is the log-transformed response variable which is predicted to be Y ˆ computed from the function f, X is a matrix of predictors, b is a vector of parameters, and the errors ε are normally distributed with mean zero and standard deviation s ε. Predictions Z ˆ in the original units are calculated using equation 1 as ] 2) ˆ exp[(ˆ 2 ε s Y Z + = [4] Note that estimates the median prediction of Z, which will be smaller than the mean for a lognormally distributed variate. Thus it makes sense to adjust the median upward, as in equation 4.) ˆ exp(Y Equation 1 is also used in drawing random numbers from a lognormal distribution. Generators for normally-distributed random variables Y are common. Suppose we draw many values of Y with mean zero and standard deviation s Y. Then from equation 1, the mean of exp(Y) will not be 1 = e 0 ; instead the mean of exp(Y) will be. Generally, however, one would prefer to have the mean of a set of lognormally distributed random numbers be 1. This can be accomplished by shifting the random numbers to Y) 2 / exp(2 Y …

対数正規分布(Lognormal Distribution)のあてはめについて

. Accurate representation of the real spatio-temporal variability of catchment rainfall inputs is currently severely limited. Moreover, spatially interpolated catchment precipitation is subject to large uncertainties, particularly in developing countries and regions which are difficult to access. Recently, satellite-based rainfall estimates (SREs) provide an unprecedented opportunity for a wide range of hydrological applications, from water resources modelling to monitoring of extreme events such as droughts and floods. This study attempts to exhaustively evaluate – for the first time – the suitability of seven state-of-the-art SRE products (TMPA 3B42v7, CHIRPSv2, CMORPH, PERSIANN-CDR, PERSIAN-CCS-Adj, MSWEPv1.1, and PGFv3) over the complex topography and diverse climatic gradients of Chile. Different temporal scales (daily, monthly, seasonal, annual) are used in a point-to-pixel comparison between precipitation time series measured at 366 stations (from sea level to 4600 m a.s.l. in the Andean Plateau) and the corresponding grid cell of each SRE (rescaled to a 0.25° grid if necessary). The modified Kling–Gupta efficiency was used to identify possible sources of systematic errors in each SRE. In addition, five categorical indices (PC, POD, FAR, ETS, fBIAS) were used to assess the ability of each SRE to correctly identify different precipitation intensities. Results revealed that most SRE products performed better for the humid South (36.4–43.7° S) and Central Chile (32.18–36.4° S), in particular at low- and mid-elevation zones (0–1000 m a.s.l.) compared to the arid northern regions and the Far South. Seasonally, all products performed best during the wet seasons (autumn and winter; MAM–JJA) compared to summer (DJF) and spring (SON). In addition, all SREs were able to correctly identify the occurrence of no-rain events, but they presented a low skill in classifying precipitation intensities during rainy days. Overall, PGFv3 exhibited the best performance everywhere and for all timescales, which can be clearly attributed to its bias-correction procedure using 217 stations from Chile. Good results were also obtained by the research products CHIRPSv2, TMPA 3B42v7 and MSWEPv1.1, while CMORPH, PERSIANN-CDR, and the real-time PERSIANN-CCS-Adj were less skillful in representing observed rainfall. While PGFv3 (currently available up to 2010) might be used in Chile for historical analyses and calibration of hydrological models, the high spatial resolution, low latency and long data records of CHIRPS and TMPA 3B42v7 (in transition to IMERG) show promising potential to be used in meteorological studies and water resource assessments. We finally conclude that despite improvements of most SRE products, a site-specific assessment is still needed before any use in catchment-scale hydrological studies.

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Temporal and spatial evaluation of satellite-based rainfall estimates across the complex topographical and climatic gradients of Chile

Influence of climate

Water governance in Chile: Availability, management and climate change

In determining the possible influence of climate change, it is important to understand the temporal and spatial variability in streamflow response for diverse climate zones. Thus, the aim of this study was to determine the presence of changes in annual maximum peak flow for two climate zones in Chile over the past few decades. A general analysis, a flood frequency analysis and a trend analysis were used to study such changes between 1975 and 2008 for a semi-arid (29°S–32°S) and a temperate (36°S–38°S) climatic zone. The historic annual maxima, minima and mean flows, as well as decadal mean peak flow, were compared over the period of record. The Gumbel distribution was selected to compare the 30-year flood values of two ±15-year intervals, which showed that streamflow decreased by an average of 19.5% in the semi-arid stations and increased by an average of 22.6% in the temperate stations. The Mann-Kendall test was used to investigate the temporal changes in streamflows, with negative trends being o...

https://www.tandfonline.com/doi/pdf/10.1080/02626667.2013.803182

Multi-decadal variations in annual maximum peak flows in semi-arid and temperate regions of Chile

Two methods that define the point of baseflow recession onset were compared using storm hydrograph data for 27 storm events that occurred between 1982-1995 in the Upeo watershed located in the Andes mountain range in central Chile (Figure 1). Three well-known baseflow recession equations were used to determine whether the method we are proposing here, that defines baseflow recession onset as the third inflection point on the logarithmic graph of the falling limb of the storm hydrograph, more accurately models observed data than the most widely used method that defines baseflow onset as the second inflection point on the same graph. Five time intervals were used to modify the recession coefficient in search of a more accurate fit. Results from the coefficient of determination, standard error, Mann-Whitney U test, and Bland-Altman test suggest that redefining baseflow recession onset via the proposed approach more accurately models baseflow recession behavior.

/pdf/on-redefining-the-onset-of-baseflow-recession-on-storm-5658xjfszc.pdf

On Redefining the Onset of Baseflow Recession on Storm Hydrographs

Vigor, vitality and seed dormancy of 14 Finnish cultivars of  Avena sativa in room temperature were studied in a 22-year laboratory experiment These parameters were studied by measuring morphological and physical characteristics of seeds and by basic germination and enzymatic tests 1, 4, 6, 11, 16, 21 and 22 years after seed harvesting in 1989 Methylene blue, Congo red and 2,3,5-triphenyltetrazolium chloride (TZ) tests were used to estimate seed quality and changes in vitality over time Seed vitality clearly decreased in all cultivars during the experiment The mean vitality declined from 963% (one year after harvest) to zero at the end Vitality according to the TZ test was higher than indicated by the basic germination test The mean vitality loss was 46% per year, but there were clear differences between cultivars The decrease in vitality correlated with loss in seed weight Clear signs of deepening dormancy were observed Seed age is an important factor infl uencing vitality and dormancy Vitality loss of seeds led to deep dormancy The appearance, water uptake and imbibition of the seeds remained normal until the end Ageing, vitality loss and dormancy are concluded to be expressions of genes It is possible that in the future electronic simulation methods will be developed that will enable accurate estimation of oat seed quality without laboratory tests

/pdf/vigor-vitality-and-seed-dormancy-of-avena-sativa-cultivars-2qaxfgnk44.pdf

Bridget Helwig

Papers

Water governance in Chile: Availability, management and climate change

Multi-decadal variations in annual maximum peak flows in semi-arid and temperate regions of Chile

On Redefining the Onset of Baseflow Recession on Storm Hydrographs

Vigor, vitality and seed dormancy of Avena sativa cultivars in a long-term experiment