scholarly journals Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data

2011 ◽  
Vol 8 (4) ◽  
pp. 7261-7291
Author(s):  
D. E. Rupp ◽  
P. Licznar ◽  
W. Adamowski ◽  
M. Leśniewski
Keyword(s):  
Rain Rate ◽  
Covariance Structure ◽  
Rain Gauge ◽  
Model Parameters ◽  
Spatial Covariance ◽  
Simple Method ◽  
Frequency Distributions ◽  
Rain Gauges ◽  
Cascade Generator ◽  
Radar Imagery

Abstract. Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges are available, rather than from the full rainfall field. The number of gauges need only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km2. MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density of the random cascade generator to vary with spatial scale.

scholarly journals Multiplicative cascade models for fine spatial downscaling of rainfall: parameterization with rain gauge data

2012 ◽  
Vol 16 (3) ◽  
pp. 671-684 ◽  
Author(s):  
D. E. Rupp ◽  
P. Licznar ◽  
W. Adamowski ◽  
M. Leśniewski
Keyword(s):  
Rain Rate ◽  
Covariance Structure ◽  
Rain Gauge ◽  
Model Parameters ◽  
Spatial Covariance ◽  
Simple Method ◽  
Frequency Distributions ◽  
Rain Gauges ◽  
Cascade Generator ◽  
Radar Imagery

Abstract. Capturing the spatial distribution of high-intensity rainfall over short-time intervals is critical for accurately assessing the efficacy of urban stormwater drainage systems. In a stochastic simulation framework, one method of generating realistic rainfall fields is by multiplicative random cascade (MRC) models. Estimation of MRC model parameters has typically relied on radar imagery or, less frequently, rainfall fields interpolated from dense rain gauge networks. However, such data are not always available. Furthermore, the literature is lacking estimation procedures for spatially incomplete datasets. Therefore, we proposed a simple method of calibrating an MRC model when only data from a moderately dense network of rain gauges is available, rather than from the full rainfall field. The number of gauges needs only be sufficient to adequately estimate the variance in the ratio of the rain rate at the rain gauges to the areal average rain rate across the entire spatial domain. In our example for Warsaw, Poland, we used 25 gauges over an area of approximately 1600 km2. MRC models calibrated using the proposed method were used to downscale 15-min rainfall rates from a 20 by 20 km area to the scale of the rain gauge capture area. Frequency distributions of observed and simulated 15-min rainfall at the gauge scale were very similar. Moreover, the spatial covariance structure of rainfall rates, as characterized by the semivariogram, was reproduced after allowing the probability density function of the random cascade generator to vary with spatial scale.

scholarly journals Improving Satellite-Based Subhourly Surface Rain Estimates Using Vertical Rain Profile Information

2019 ◽  
Vol 20 (5) ◽  
pp. 1015-1026 ◽  
Author(s):  
Nobuyuki Utsumi ◽  
Hyungjun Kim ◽  
F. Joseph Turk ◽  
Ziad. S. Haddad
Keyword(s):  
Rain Rate ◽  
Tropical Rainfall Measuring Mission ◽  
Rain Gauge ◽  
Rain Gauge Data ◽  
Rain Gauges ◽  
Gauge Data ◽  
Surface Rain Rate ◽  
Trmm Precipitation ◽  
Time Lagged ◽  
Rain Rates

Abstract Quantifying time-averaged rain rate, or rain accumulation, on subhourly time scales is essential for various application studies requiring rain estimates. This study proposes a novel idea to estimate subhourly time-averaged surface rain rate based on the instantaneous vertical rain profile observed from low-Earth-orbiting satellites. Instantaneous rain estimates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) are compared with 1-min surface rain gauges in North America and Kwajalein atoll for the warm seasons of 2005–14. Time-lagged correlation analysis between PR rain rates at various height levels and surface rain gauge data shows that the peak of the correlations tends to be delayed for PR rain at higher levels up to around 6-km altitude. PR estimates for low to middle height levels have better correlations with time-delayed surface gauge data than the PR’s estimated surface rain rate product. This implies that rain estimates for lower to middle heights may have skill to estimate the eventual surface rain rate that occurs 1–30 min later. Therefore, in this study, the vertical profiles of TRMM PR instantaneous rain estimates are averaged between the surface and various heights above the surface to represent time-averaged surface rain rate. It was shown that vertically averaged PR estimates up to middle heights (~4.5 km) exhibit better skill, compared to the PR estimated instantaneous surface rain product, to represent subhourly (~30 min) time-averaged surface rain rate. These findings highlight the merit of additional consideration of vertical rain profiles, not only instantaneous surface rain rate, to improve subhourly surface estimates of satellite-based rain products.

scholarly journals A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems

2010 ◽  
Vol 23 (10) ◽  
pp. 2759-2781 ◽  
Author(s):  
Martin P. Tingley ◽  
Peter Huybers
Keyword(s):  
Time Series ◽  
Covariance Matrix ◽  
Expectation Maximization Algorithm ◽  
Covariance Structure ◽  
Model Parameters ◽  
Data Types ◽  
Spatial Covariance ◽  
Bayesian Algorithm ◽  
Climate Anomalies ◽  
Instrumental Values

Abstract Reconstructing the spatial pattern of a climate field through time from a dataset of overlapping instrumental and climate proxy time series is a nontrivial statistical problem. The need to transform the proxy observations into estimates of the climate field, and the fact that the observed time series are not uniformly distributed in space, further complicate the analysis. Current leading approaches to this problem are based on estimating the full covariance matrix between the proxy time series and instrumental time series over a “calibration” interval and then using this covariance matrix in the context of a linear regression to predict the missing instrumental values from the proxy observations for years prior to instrumental coverage. A fundamentally different approach to this problem is formulated by specifying parametric forms for the spatial covariance and temporal evolution of the climate field, as well as “observation equations” describing the relationship between the data types and the corresponding true values of the climate field. A hierarchical Bayesian model is used to assimilate both proxy and instrumental datasets and to estimate the probability distribution of all model parameters and the climate field through time on a regular spatial grid. The output from this approach includes an estimate of the full covariance structure of the climate field and model parameters as well as diagnostics that estimate the utility of the different proxy time series. This methodology is demonstrated using an instrumental surface temperature dataset after corrupting a number of the time series to mimic proxy observations. The results are compared to those achieved using the regularized expectation–maximization algorithm, and in these experiments the Bayesian algorithm produces reconstructions with greater skill. The assumptions underlying these two methodologies and the results of applying each to simple surrogate datasets are explored in greater detail in Part II.

scholarly journals Estimation of convective precipitation: the meteorological radar versus an automatic rain gauge network

2005 ◽  
Vol 2 ◽  
pp. 103-109 ◽  
Author(s):  
M. C. Llasat ◽  
T. Rigo ◽  
M. Ceperuelo ◽  
A. Barrera
Keyword(s):  
Rain Rate ◽  
Rain Gauge ◽  
Space Distribution ◽  
Convective Precipitation ◽  
Precipitation Event ◽  
Convective Rainfall ◽  
Rainfall Events ◽  
Rain Gauges ◽  
Meteorological Radar ◽  
Rain Gauge Network

Abstract. The estimation of convective precipitation and its contribution to total precipitation is an important issue both in hydrometeorology and radio links. The greatest part of this kind of precipitation is related with high intensity values that can produce floods and/or damage and disturb radio propagation. This contribution proposes two approaches for the estimation of convective precipitation, using the β parameter that is related with the greater or lesser convective character of the precipitation event, and its time and space distribution throughout the entire series of the samples. The first approach was applied to 126 rain gauges of the Automatic System of Hydrologic Information of the Internal Basins of Catalonia (NE Spain). Data are series of 5-min rain rate, for the period 1996-2002, and a long series of 1-min rain rate starting in 1927. Rainfall events were classified according to this parameter. The second approach involved using information obtained by the meteorological radar located near Barcelona. A modified version of the SCIT method for the 3-D analysis and a combination of different methods for the 2-D analysis were applied. Convective rainfall charts and β charts were reported. Results obtained by the rain gauge network and by the radar were compared. The application of the β parameter to improve the rainfall regionalisation was demonstrated.

scholarly journals Statistical and neural classifiers in estimating rain rate from weather radar measurements

2007 ◽  
Vol 10 ◽  
pp. 111-115
Author(s):  
C. I. Christodoulou ◽  
S. C. Michaelides
Keyword(s):  
Electromagnetic Radiation ◽  
Rain Rate ◽  
Weather Radar ◽  
Radar Data ◽  
Rain Gauge ◽  
Meteorological Conditions ◽  
Swiss Alps ◽  
Rain Gauges ◽  
Weather Radars ◽  
Radar Measurements

Abstract. Weather radars are used to measure the electromagnetic radiation backscattered by cloud raindrops. Clouds that backscatter more electromagnetic radiation consist of larger droplets of rain and therefore they produce more rain. The idea is to estimate rain rate by using weather radar as an alternative to rain-gauges measuring rainfall on the ground. In an experiment during two days in June and August 1997 over the Italian-Swiss Alps, data from weather radar and surrounding rain-gauges were collected at the same time. The statistical KNN and the neural SOM classifiers were implemented for the classification task using the radar data as input and the rain-gauge measurements as output. The proposed system managed to identify matching pattern waveforms and the rainfall rate on the ground was estimated based on the radar reflectivities with a satisfactory error rate, outperforming the traditional Z/R relationship. It is anticipated that more data, representing a variety of possible meteorological conditions, will lead to improved results. The results in this work show that an estimation of rain rate based on weather radar measurements treated with statistical and neural classifiers is possible.

Satellite Data Application to Cover Lack of In-situ Observations for Mapping Precipitation and Direct Runoff in Semi-arid Basin

2020 ◽  
Author(s):  
Mahdi Akbari ◽  
Ali Torabi Haghighi
Keyword(s):  
Hydrological Modeling ◽  
Rain Gauge ◽  
Model Parameters ◽  
Lake Basin ◽  
Lake Urmia ◽  
Direct Runoff ◽  
Rain Gauges ◽  
High Elevations ◽  
Semi Arid

<div> <p>Hydrological modeling in arid basins located in developing countries often lacks sufficient hydrological data because, e.g., rain gauges are typically absent at high elevations and inflow to ungauged areas around large closed lakes such as Lake Urmia is difficult to estimate. We tried to improve precipitation and runoff estimation in Lake Urmia, Iran as an arid basin using satellite-based data. We estimated precipitation using interpolation of rain gauge data by kriging, downscaling Tropical Rainfall Measuring Mission (TRMM), and cokriging interpolation of in-situ records with Remote Sensing (RS)-based data. Using RS-based data in estimations gave more precise results, by compensating for lack of data at high elevations. Cokriging interpolation of rain gauges by TRMM and Digitized Elevation Model (DEM) gave 4–9 mm lower Root Mean Square Error (RMSE) in different years compared with kriging. Downscaling TRMM improved its accuracy by 14 mm. Using the most accurate precipitation model, we modeled annual direct runoff with Kennessey and Soil Conservation Service Curve Number (SCS-CN) models. These models use land use, permeability, slope maps and climatic parameter (Ia) to represent the annual climatic condition of modeled basin in sense of wetness or dryness. In runoff modeling, Kennessey gave higher accuracy in annual scale. It was found that classification of years to wet, dry and normal states in Kennessey by default assumptions on Ia is not accurate enough for semi-arid basins so by solving this issue and calibration Kennessey model parameters, we made this model applicable for Urmia Lake basin. Calibrating Kennessey reduced the Normalized RMSE (NRMSE) from 1 in the standard model to 0.44. Direct runoff coefficient map by 1 km spatial resolution was generated by calibrated Kennessey. Validation by the closest gauges to the lake gave a NRMSE of 0.41 which approved the accuracy of modeling.</p> </div>

scholarly journals Combination of Radar and Rain Gauge Information to Map the Snowy Region in Jeju Island, Korea: A Case Study

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Jung Mo Ku ◽  
Chulsang Yoo
Keyword(s):  
Rain Rate ◽  
Rain Gauge ◽  
Coastal Areas ◽  
Radar Reflectivity ◽  
Jeju Island ◽  
Rain Gauges ◽  
Rate Information ◽  
Fixed Threshold ◽  
Reflectivity Data

Hallasan Mountain is located at the center of Jeju Island, Korea. Even though Hallasan Mountain has a height of just 1,950 m, the temperature during the winter decreases below −20 degrees Celsius. On the contrary, the temperature on the coastal areas remains just above freezing. Therefore, large snowfalls in the mountain and rainfall in the coastal areas are very common in Jeju Island. Most of the rain gauges are available around highly populated coastal areas, and snow measurements are available at just four locations on the coastal areas. Therefore, it is practically impossible to distinguish the rainfall and snowfall in Jeju Island. Fortunately, two radars (Seongsan and Gosan radars) operate on Jeju Island, which fully covers Hallasan Mountain. This study proposes a method of using both the radar and rain gauge information to map the snowy region in Jeju Island, including Hallasan Mountain. As a first step, this study analyzed the Z-R and Z-S relationships to derive a fixed threshold of radar reflectivity to separate snowfall from rainfall, and, in the second step, this study additionally considered the observed rain rate information to implement the problem of using the fixed threshold. This proposed method was applied to radar reflectivity data collected during November 1, 2014, to April 30, 2015, and the results indicate that the method considering both the radar and rain gauge information was satisfactory. This method also showed good performance, especially when the rain rate was very low.

scholarly journals A Variational Approach to Retrieve Rain Rate by Combining Information from Rain Gauges, Radars, and Microwave Links

2013 ◽  
Vol 14 (6) ◽  
pp. 1897-1909 ◽  
Author(s):  
Blandine Bianchi ◽  
Peter Jan van Leeuwen ◽  
Robin J. Hogan ◽  
Alexis Berne
Keyword(s):  
Variational Approach ◽  
Rain Rate ◽  
Rain Gauge ◽  
Sources Of Information ◽  
Rain Gauges ◽  
Strongly Nonlinear ◽  
Using Data ◽  
The Cost ◽  
Microwave Link ◽  
Link Information

Abstract Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimate with greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Zürich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge and microwave link information.

scholarly journals Using High-Speed Photography to Study Undercatch in Tipping-Bucket Rain Gauges*

2014 ◽  
Vol 31 (6) ◽  
pp. 1330-1336 ◽  
Author(s):  
Claude Duchon ◽  
Christopher Fiebrich ◽  
David Grimsley
Keyword(s):  
High Speed ◽  
Rain Rate ◽  
Slow Motion ◽  
Rain Gauge ◽  
The Other ◽  
High Speed Photography ◽  
High Speed Camera ◽  
Rain Gauges ◽  
Linear Correction ◽  
Rain Rates

Abstract To better understand the undercatch process associated with tipping-bucket rain gauges, a high-speed camera normally used in determining the structure of lightning was employed. The photo rate was set at 500 frames per second to observe the tipping of the bucket in a commonly used tipping-bucket rain gauge. The photos showed detail never seen before as the bucket tipped from one side to the other. Two fixed rain rates of 19.9 mm h−1 (0.78 in. h−1) and 175.2 mm h−1 (6.90 in. h−1), the minimum and maximum available, respectively, were used. The data from four tips at each rain rate were examined. The results show that the time from the beginning of a tip to the time the bucket assembly is horizontal—defined as the period during which undercatch occurs—was an average of 0.450 s for the eight cases. The average time for a complete tip was 0.524 s; thus, the vast majority of the time of a tip, 86%, is spent in undercatch mode. Because there was no apparent dependence of these times on rain rate, it should be possible to apply an accurate linear correction for undercatch as a function of rain rate given the time that undercatch occurs during a tip. Over all eight tips, the undercatch was found to be 0.98% for the 19.9 mm h−1 rate and 8.78% for the 175.2 mm h−1 rate. The procedure used to estimate the undercatch is described. Slow motion videos of the tipping of a bucket are available online.

scholarly journals Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results

2012 ◽  
Vol 9 (12) ◽  
pp. 14205-14230
Author(s):  
A. Chebbi ◽  
Z. K. Bargaoui ◽  
M. da Conceição Cunha
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Rain Gauge ◽  
Model Parameters ◽  
Optimization Approach ◽  
Rain Gauges ◽  
Hydrological Variability ◽  
Idf Curves ◽  
Intensity Duration Frequency ◽  
Rain Gauge Network

Abstract. Based on rainfall intensity-duration-frequency (IDF) curves, a robust optimization approach is proposed to identify the best locations to install new rain gauges. The advantage of robust optimization is that the resulting design solutions yield networks which behave acceptably under hydrological variability. Robust optimisation can overcome the problem of selecting representative rainfall events when building the optimization process. This paper reports an original approach based on Montana IDF model parameters. The latter are assumed to be geostatistical variables and their spatial interdependence is taken into account through the adoption of cross-variograms in the kriging process. The problem of optimally locating a fixed number of new monitoring stations based on an existing rain gauge network is addressed. The objective function is based on the mean spatial kriging variance and rainfall variogram structure using a variance-reduction method. Hydrological variability was taken into account by considering and implementing several return periods to define the robust objective function. Variance minimization is performed using a simulated annealing algorithm. In addition, knowledge of the time horizon is needed for the computation of the robust objective function. A short and a long term horizon were studied, and optimal networks are identified for each. The method developed is applied to north Tunisia (area = 21 000 km2). Data inputs for the variogram analysis were IDF curves provided by the hydrological bureau and available for 14 tipping bucket type rain gauges. The recording period was from 1962 to 2001, depending on the station. The study concerns an imaginary network augmentation based on the network configuration in 1973, which is a very significant year in Tunisia because there was an exceptional regional flood event in March 1973. This network consisted of 13 stations and did not meet World Meteorological Organization (WMO) recommendations for the minimum spatial density. So, it is proposed to virtually augment it by 25, 50, 100 and 160% which is the rate that would meet WMO requirements. Results suggest that for a given augmentation robust networks remain stable overall for the two time horizons.

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