scholarly journals Statistical properties of spatial snowcover in mountainous catchments in Norway

2004 ◽  
Vol 35 (2) ◽  
pp. 101-117 ◽  
Author(s):  
Wolf-Dietrich Marchand ◽  
Ånund Killingtveit
Keyword(s):  
Empirical Distribution ◽  
Snow Accumulation ◽  
Distribution Functions ◽  
Statistical Properties ◽  
Distributed Model ◽  
Catchment Scale ◽  
Mountainous Catchments ◽  
Snow Distribution ◽  
Distributed Hydrological Models ◽  
Log Normal

The spatial distribution of snowcover in a catchment is determined by complex interactions between meteorological and physiographical factors, integrated over time. The snowcover shows variability over scales ranging from centimeters up to hundreds of kilometers. An important and necessary decision for modelers is to determine spatial resolution in a distributed model. Since the spatial variability in snowcover may be quite large, even within a few meters, it is difficult to use modeling units small enough so that the snow can be assumed evenly distributed within the unit. A possible method to compensate for this is to use larger units, and describe the snow distribution within each unit by a statistical model (e.g. normal, log-normal, gamma, etc). This technique requires information about spatial statistical properties of snowcover within a unit. As many of the distributed hydrological models operate on a grid basis, it would be desirable to find a statistical distribution on a sub-grid scale. However, as an initial approach, the study presented here was done on a catchment scale. The catchment scale presented the possibility of incorporating data from several historical snow surveys. These surveys were taken at the time of maximum snow accumulation in various mountainous catchments in Norway. Comparing empirical distribution functions with different theoretical distribution functions, it was shown that a mixed distribution combining two separate log-normal distributions clearly gave the best fit in most of the catchments. This seems to indicate that a mixture of at least two different populations of SWE values exists.

scholarly journals Comparison of MODIS and SWAT Evapotranspiration over a Complex Terrain at Different Spatial Scales

2017 ◽  
Author(s):  
Olanrewaju O. Abiodun ◽  
Huade Guan ◽  
Vincent E. A. Post ◽  
Okke Batelaan
Keyword(s):  
Complex Terrain ◽  
Spatial Scales ◽  
Swat Model ◽  
South Australia ◽  
Remotely Sensed ◽  
Distributed Model ◽  
Climate Data ◽  
Remotely Sensed Data ◽  
Catchment Scale ◽  
Distributed Hydrological Models

Abstract. In most hydrological systems, evapotranspiration (ET) and precipitation are the largest components of the water balance, which are difficult to estimate, particularly over complex terrain. In recent decades, the advent of remotely-sensed data based ET algorithms and distributed hydrological models has provided improved spatially-upscaled ET estimates. However, information on the performance of these methods at various spatial scales is limited. This study compares the ET from the MODIS remotely sensed ET dataset (MOD16) with the ET estimates from a SWAT hydrological model for the complex terrain of the Sixth Creek Catchment of the Western Mount Lofty Ranges, South Australia. The SWAT model analyses are performed on daily timescales with a 6-year calibration period (2000–2005) and 7-year validation period (2007–2013). Differences in ET estimation between the two methods of up to 48 %, 21 % and 16 % were observed at respectively 1 km2, 5 km2 and 10 km2 spatial resolutions. Land cover differences, mismatches between the two methods and catchment-scale averaging of input climate data in the SWAT semi-distributed model were identified as the principal sources of weaker correlations at higher spatial resolution.

scholarly journals Comparison of MODIS and SWAT evapotranspiration over a complex terrain at different spatial scales

2018 ◽  
Vol 22 (5) ◽  
pp. 2775-2794 ◽  
Author(s):  
Olanrewaju O. Abiodun ◽  
Huade Guan ◽  
Vincent E. A. Post ◽  
Okke Batelaan
Keyword(s):  
Complex Terrain ◽  
Spatial Scales ◽  
Swat Model ◽  
South Australia ◽  
Remotely Sensed ◽  
Distributed Model ◽  
Climate Data ◽  
Remotely Sensed Data ◽  
Catchment Scale ◽  
Distributed Hydrological Models

Abstract. In most hydrological systems, evapotranspiration (ET) and precipitation are the largest components of the water balance, which are difficult to estimate, particularly over complex terrain. In recent decades, the advent of remotely sensed data based ET algorithms and distributed hydrological models has provided improved spatially upscaled ET estimates. However, information on the performance of these methods at various spatial scales is limited. This study compares the ET from the MODIS remotely sensed ET dataset (MOD16) with the ET estimates from a SWAT hydrological model on graduated spatial scales for the complex terrain of the Sixth Creek Catchment of the Western Mount Lofty Ranges, South Australia. ET from both models was further compared with the coarser-resolution AWRA-L model at catchment scale. The SWAT model analyses are performed on daily timescales with a 6-year calibration period (2000–2005) and 7-year validation period (2007–2013). Differences in ET estimation between the SWAT and MOD16 methods of up to 31, 19, 15, 11 and 9 % were observed at respectively 1, 4, 9, 16 and 25 km2 spatial resolutions. Based on the results of the study, a spatial scale of confidence of 4 km2 for catchment-scale evapotranspiration is suggested in complex terrain. Land cover differences, HRU parameterisation in AWRA-L and catchment-scale averaging of input climate data in the SWAT semi-distributed model were identified as the principal sources of weaker correlations at higher spatial resolution.

Beyond the heuristic approach to Kolmogorov-Smirnov theorems

1982 ◽  
Vol 19 (A) ◽  
pp. 359-365 ◽  
Author(s):  
David Pollard
Keyword(s):  
Weak Convergence ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Heuristic Approach ◽  
Convergence Theory ◽  
Simple Method ◽  
Starting Point ◽  
Kolmogorov Smirnov ◽  
The Subject

The theory of weak convergence has developed into an extensive and useful, but technical, subject. One of its most important applications is in the study of empirical distribution functions: the explication of the asymptotic behavior of the Kolmogorov goodness-of-fit statistic is one of its greatest successes. In this article a simple method for understanding this aspect of the subject is sketched. The starting point is Doob's heuristic approach to the Kolmogorov-Smirnov theorems, and the rigorous justification of that approach offered by Donsker. The ideas can be carried over to other applications of weak convergence theory.

Mixed Generalized Linear Model for Estimating Household Trip Production

2000 ◽  
Vol 1718 (1) ◽  
pp. 61-67 ◽  
Author(s):  
Chang-Jen Lan ◽  
Patricia S. Hu
Keyword(s):  
Linear Model ◽  
Generalized Linear Model ◽  
Negative Binomial ◽  
Empirical Distribution ◽  
Distribution Functions ◽  
Model Specification ◽  
Parameter Estimates ◽  
Modeling Framework ◽  
Personal Transportation ◽  
Trip Production

An innovative modeling framework to estimate household trip rates using 1995 Nationwide Personal Transportation Survey data is presented. A generalized linear model with a mixture of negative binomial probability distribution functions was developed on the basis of characteristics observed from the empirical distribution of household daily trips. This model provides a more flexible framework and a better model specification for analyzing household-specific trip production behavior. Compared with traditional least squares-based regression models, the parameter estimates from the proposed model are more efficient. Although the mean accuracies from the two modeling approaches are comparable, the mixed generalized linear model is more robust in identifying outliers due to its unsymmetric prediction bounds derived from more correct model specification.

Discrete Distribution Functions for Log-Normal Moments

2020 ◽  
pp. 1-21
Author(s):  
Catherine M. Bonan-Hamada ◽  
William B. Jones ◽  
W. J. Thron ◽  
Arne Magnus
Keyword(s):  
Discrete Distribution ◽  
Distribution Functions ◽  
Log Normal

scholarly journals The use of personal weather station observations to improve precipitation estimation and interpolation

2021 ◽  
Vol 25 (2) ◽  
pp. 583-601
Author(s):  
András Bárdossy ◽  
Jochen Seidel ◽  
Abbas El Hachem
Keyword(s):  
Spatial Interpolation ◽  
Empirical Distribution ◽  
Precipitation Amount ◽  
Distribution Functions ◽  
Quantile Mapping ◽  
Novel Approach ◽  
Precipitation Estimation ◽  
Weather Stations ◽  
High Precipitation ◽  
Empirical Distribution Functions

Abstract. The number of personal weather stations (PWSs) with data available through the internet is increasing gradually in many parts of the world. The purpose of this study is to investigate the applicability of these data for the spatial interpolation of precipitation using a novel approach based on indicator correlations and rank statistics. Due to unknown errors and biases of the observations, rainfall amounts from the PWS network are not considered directly. Instead, it is assumed that the temporal order of the ranking of these data is correct. The crucial step is to find the stations which fulfil this condition. This is done in two steps – first, by selecting the locations using the time series of indicators of high precipitation amounts. Then, the remaining stations are then checked for whether they fit into the spatial pattern of the other stations. Thus, it is assumed that the quantiles of the empirical distribution functions are accurate. These quantiles are then transformed to precipitation amounts by a quantile mapping using the distribution functions which were interpolated from the information from the German National Weather Service (Deutscher Wetterdienst – DWD) data only. The suggested procedure was tested for the state of Baden-Württemberg in Germany. A detailed cross validation of the interpolation was carried out for aggregated precipitation amount of 1, 3, 6, 12 and 24 h. For each of these temporal aggregations, nearly 200 intense events were evaluated, and the improvement of the interpolation was quantified. The results show that the filtering of observations from PWSs is necessary as the interpolation error after the filtering and data transformation decreases significantly. The biggest improvement is achieved for the shortest temporal aggregations.

scholarly journals Limiting behavior of the perturbed empirical distribution functions evaluated at U-statistics for strongly mixing sequences of random variables

1997 ◽  
Vol 10 (1) ◽  
pp. 3-20 ◽  
Author(s):  
Shan Sun ◽  
Ching-Yuan Chiang
Keyword(s):  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Random Variables ◽  
Distribution Functions ◽  
Limiting Behavior ◽  
U Statistics ◽  
Strongly Mixing ◽  
Almost Sure Representation ◽  
Mixing Sequences ◽  
Empirical Distribution Functions

We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic Fˆn(Un) for a class of strongly mixing sequences of random variables {Xi,i≥1}. Stationarity is not assumed. Here Fˆn is the perturbed empirical distribution function and Un is a U-statistic based on X1,…,Xn.

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