Probability Matching Method Research Articles

A New Post-Processing Method for Improving Track and Rainfall Ensemble Forecasts for Typhoons over Eastern China

This paper proposes a new post-processing method for model data in order to improve typhoon track and rainfall forecasts. The model data used in the article include low-resolution ensemble forecasts and high-resolution forecasts. The entire improvement method contains the following three steps. The first step is to correct the typhoon track forecast: three ensemble member optimization methods are applied to the low-resolution ensemble forecasts, and then the best optimization method is selected with the principle of the smallest average distance error. The results of rainfall forecasts show that the corrected rainfall forecast performs better than the original forecasts. The second step is to derive the high-resolution probability rainfall forecast: the neighborhood method is applied to the deterministic high-resolution rainfall forecast. The last step is to correct the typhoon rainfall forecast: the low- and high-resolution forecasts are blended using the probability-matching method with two different schemes. The results show that the forecasts of the two schemes perform better than the original forecast under all rainfall thresholds and all forecast lead times. In terms of bias score, a rain forecast from one scheme corrects the rainfall deviation from observation better for light and moderate rainfall, whereas a rain forecast from another scheme corrects the rainfall deviation better for heavy and torrential rainfall. The better performance of corrected rain forecasts in the case of Typhoon Lekima and Rumbia over eastern China is demonstrated.

Implementation of a probability matching method in developing intensity–duration–frequency relationships for sub-daily durations using IMERG satellite-based data

ABSTRACT Reliable estimation of design rainfall in time and space can play a significant role in reducing flood-related losses. However, many parts of the world suffer from a lack of dense raingauge networks. Under this condition, the use of satellite-based data can be an alternative solution. In this research, using data from a dense ground-based raingauge network and Integrated Multi-satellitE Retrievals for GPM (IMERG) satellite-based precipitation product, the performance of a probability matching method for satellite-based extreme values has been investigated. The results indicate that the correction model, especially at shorter durations, is able to reduce the error of extreme values of raw satellite-based estimates, and its performance is not affected significantly by the density of the available raingauge network. In conclusion, implementation of the proposed method in poorly gauged regions can play an effective role in providing a reliable estimate of the design rainfall and eventually reducing the financial losses caused by floods.

Quantitative Precipitation Forecasting Using an Improved Probability-Matching Method and Its Application to a Typhoon Event

This present study aims to explore how forecasters can quickly make accurate predictions by using various high-resolution model forecasts. Based on three high temporal-spatial resolution (3 km, hourly) numerical weather prediction models (CMA-MESO, CMA-GD, CMA-SH3) from the China Meteorological Administration (CMA), the hourly precipitation characteristics of three model within 24 h from March to September 2020 are discussed and integrated into a single, hourly, deterministic quantitative precipitation forecast (QPF) by making use of an improved weighted moving average probability-matching method (WPM). The results are as follows: (1) In non-rainstorm forecasts, CMA-MESO and CMA-GD have similar forecast abilities. However, in rainstorm forecasts, CMA-MESO has a notable advantage over the other two models. Thus, CMA-MESO is selected as a critical factor when participating in sensitivity experiments. (2) Compared with the traditional equal-weight probability-matching method (PM), the WPM improves the different grade QPF because it can effectively reduce rainfall pattern bias by making use of the weighted moving average (WMA). Additionally, the WPM threat score in rainstorm forecast similarly improved from 0.051 to 0.056, with a 9.8% increase relative to the PM. (3) The sensitivity experiments show that an optimal rainfall intensity score (WPM-best) can further improve the QPF and overcome all single models in both rainstorm and non-rainstorm forecasts, and the WPM-best has a rainstorm threat score skill of 0.062, with an increase of 21.6% compared with the PM. The performance of the WPM-best will be better if the precipitation intensity is stronger and the valid forecast periods is longer. It should be noted that there is no need to select models before using the WPM-best method, because WPM-best can give a very low weight to the less-skillful model in a more objective way. (4) The improved WPM method is also applied to investigate the heavy-rainfall case induced by typhoon Mekkhala (2020), where the improved WPM technique significantly improves rainstorm forecasting ability compared with a single model.

집중호우 시기 기계학습 및 PM기법을 이용한 수문학적 강우보정에 관한 연구

In meteorological data, various studies are being conducted to improve the prediction performance of rainfall with irregular patterns, unlike temperature and solar radiation with certain patterns. Especially in the case of the short-term forecast model for Dong-Nae Forecasts provided by the Korea Meteorological Administration (KMA), forecast data are provided at 6-hour intervals, and there is a limit to analyzing the impact of disasters. In this study, Hydrological Quantitative Precipitation Forecast (HQPF) information was generated by applying the machine learning method to Local ENsemble prediction system (LENS), Radar-AWS Rainrates (RAR), AWS and ASOS observation data and Dong-Nae Forecast provided by the KMA. Through the preprocessing process, the temporal and spatial resolutions of all the data were converted to the same resolution, and the predictor of machine learning was derived through the factor analysis of the predictor. Considering the processing speed and expandability, the XGBoost method of machine learning was applied, and the Probability Matching (PM) method was applied to improve the prediction accuracy of heavy rainfall. As a result of evaluating the HQPF performance produced for 14 heavy rainfall events that occurred in 2020, it was found that the predicted performance of HQPF was improved quantitatively and qualitatively.

Parameter estimation of a dual-pol radar rain rate estimator with truncated paired data

Abstract This study proposes a new method for estimating the parameters of a radar rain rate estimator, particularly of the dual-pol radar. The proposed method is similar to the probability matching method (PMM), except for being based on truncated data pairs. A truncation value is introduced to the log-transformed data in order to remove those in the low rain rate zone as well as to introduce Gaussian distribution. The parameters are then estimated by comparing the first- and second-order moments. The proposed method is applied to a total of six rainfall events observed by the Beaslesan Radar in Korea from 2014 to 2017. Summarizing the results, first, the truncation value should be applied to the horizontal reflectivity (dBZh) data. In this case only, the other two data, the rain rate (dBR) and the differential reflectivity (dBZdr), follow the Gaussian distribution well. It is also important to consider rather severe rainfall events for the parameter estimation. The parameters for only the severe rainfall events are all estimated rather reasonably. On the other hand, for the other moderate and light rainfall events, the parameters are estimated as being rather far from their normal ranges. This is mainly due to the relatively small variance of dBR compared to that of dBZh. That is, the variance of dBR is found to be greatly dependent on the peak rain rate, but the variance of dBZh remains almost unchanged, regardless of the peak rain rate. As a result, the peak rain rate plays a dominant role in the reasonable parameter estimation. These findings are also consistent with many previous studies.

Assessment of seven CMIP5 model precipitation extremes over Iran based on a satellite‐based climate data set

The ability of the seven CMIP5 models to simulate extreme precipitation events over Iran was evaluated using the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks–Climate Data Record (PERSIANN‐CDR) data set. The criterion used to select the CMIP5 models was the availability of historical daily precipitation data (PERSIANN‐CDR) for the retrospective period 1983–2005, as well as future projections for the three representative concentration pathways emission scenarios (RCP2.6, RCP4.5, and RCP8.5) and spatial resolution higher than 2 × 2°. This is the first study to focus on extreme precipitation climate model simulations over Iran that includes high topography and different climates. The results show that CCSM4 has the highest correlation coefficients (CC = 0.85) and lowest root‐mean‐square error (RMSE = 73.6 mm) compared to PERSIANN‐CDR for the mean annual precipitation. However, HadGEM2‐ES shows the best (highest CCs between 0.67–0.79 and almost the lowest root‐mean‐square errors [RMSEs] compared to PERSIANN‐CDR) performance for intensity indices; MIROC5 ranked seventh (least CCs and almost the highest RMSEs) among the selected models. The results show that BCC‐CSM1‐1‐M captures maximum consecutive dry days (CDD) better than the other models. The probability matching method (PMM) is used to bias‐correct daily precipitation events from CMIP5 models with respect to the PERSIANN‐CDR estimations. All the model performances designed to capture the mean annual precipitation, as well as extreme intensity indices, improved after correction. The ensemble, constructed from the bias‐corrected model simulations using multiple linear regression (MLR), has the best performance for simulating the mean annual precipitation and extreme indices (CCs between 0.82 for consecutive wet days [CWD] and 0.93 for the mean annual precipitation) compared to the PERSIANN‐CDR estimations. Among the seven selected models, CCSM4 has the highest ranking (CCs between 0.70 for CWD to 0.91 for mean annual precipitation) after bias correction.

Rainfall estimation from radar in different seasons over Northern Thailand

Thailand was located on the path of the tropical cyclones which were formed in the South China Sea and the Pacific ocean. The storms in Thailand are often downgraded to tropical depression. Northern Thailand has a tropical climate which can be divided into three seasons: rainy (May–October), winter (October–February) and summer (March-May). The averages rainfall is around 1,200–1,600 mm/year influenced by the two types of the monsoon winds. Northeast monsoon brings the cold and dry air mass from China to cover the major part of Thailand. Southwest monsoon brings the warm and moist air mass from the Indian Ocean toward Thailand causing abundant rain over the country. The objective of the research is to evaluate Z-R relationship (Z = ARb) for rainfall estimation in different seasons. This study uses reflectivity data from Omkoi radar station in Chiang Mai Thailand and rainfall data in the radius of 240 kilometers from the Omkoi weather radar station from the Thai Meteorological Department. The method for matching reflectivity data (Z) and rainfall rate (R) relationship is PMM (Probability Matching Method). The result show that the Z-R relationship in the rainy season is Z = 103.83R151 and the Z-R relationship in summer and winter is Z = 102.18R146. For the same rainfall intensity, reflectivity value in summer and winter season is higher than in the rainy season. This research shows that each type of monsoon wind causes different characteristics of rainfall. Thus rainfall estimation for different seasons should be based on the different Z-R relationship for more accuracy.

MORPHSIM: A new multiple-point pattern-based unconditional simulation algorithm using morphological image processing tools

Most simulation algorithms based on Multiple-Point Statistics (MPS) deploy training images that are usually constructed from conceptual 2D or 3D spatial distribution of the reservoir parameters by means of a similarity measure such as Bayesian likelihood probability or pattern-based matching methods to map complicated geological structures and heterogeneities inherent to most petroleum reservoirs. The recent pattern-based MPS algorithms employ common techniques in the course of unconditional simulation. However, there is no guarantee to ensure that the desired targets in the training patterns could have been even captured by a specified search template. That is, the number of training patterns produced by any search template size is always limited, while the data events formed during simulation could potentially show any unexpected patterns. This is where previous algorithms encounter some difficulties in finding actual patterns even if they are equipped with precise pattern recognition measures. To address this issue and avoid extra complexity in the course of simulation, we have proposed a new unconditional pattern-based simulation procedure which deploys the edge-similarity and morphological image processing concepts. In the course of our proposed algorithm, each pattern is temporarily substituted with its edge features followed by performing a k-means classification of their similarity measures using Manhattan distance function for primary infilling of optimum patterns in the simulation grid. Next, through using a combination of morphological operations with automatically determined or user-defined specifications, the algorithm named as MORPHSIM in this context would effectively improves pattern reproduction and structural continuity. Results have shown the strength and flexibility of MORPHSIM in reproducing patterns for unconditional simulations, even when the input training image is poorly constructed and includes just a simple non-stationary structure. The algorithm is not only computationally effective in terms of simulation run time and memory usage relative to FILTERSIM but also can overcome the imperfection of training image by applying morphological image processing filters.

Rainfall frequency analysis for ungauged sites using satellite precipitation products

The occurrence of extreme rainfall events and their impacts on hydrologic systems and society are critical considerations in the design and management of a large number of water resources projects. As precipitation records are often limited or unavailable at many sites, it is essential to develop better methods for regional estimation of extreme rainfall at these partially-gauged or ungauged sites. In this study, an innovative method for regional rainfall frequency analysis for ungauged sites is presented. The new method (hereafter, this is called the RRFA-S) is based on corrected annual maximum series obtained from a satellite precipitation product (e.g., PERSIANN-CDR). The probability matching method (PMM) is used here for bias correction to match the CDF of satellite-based precipitation data with the gauged data. The RRFA-S method was assessed through a comparative study with the traditional index flood method using the available annual maximum series of daily rainfall in two different regions in USA (11 sites in Colorado and 18 sites in California). The leave-one-out cross-validation technique was used to represent the ungauged site condition. Results of this numerical application have found that the quantile estimates obtained from the new approach are more accurate and more robust than those given by the traditional index flood method.

Calibration of weather radar using region probability matching method (RPMM)

This research aims to develop a novel method named region probability matching method (RPMM) for calibrating the Amir-Abad weather radar located in the north of Iran. This approach also can overcome the limitations of probability matching method (PMM), window probability matching method (WPMM), and window correlation matching method (WCMM). The employing of these methods for calibrating the radars in light precipitation is associated with many errors. Additionally, in developing countries like Iran where ground stations have low temporal resolution, these methods cannot be benefited from. In these circumstances, RPMM by utilizing 18 synoptic stations with a temporal resolution of 6 h and radar data with a temporal resolution of 15 min has indicated an accurate estimation of cumulative precipitation over the entire study area in a specific period. Through a comparison of the two methods (RPMM and traditional matching method (TMM)) on March 22, 2014, the obtained correlation coefficients for TMM and RPMM were 0.13 and 0.95, respectively. It is noted that the cumulative precipitation of the whole rain gauges and the calibrated radar precipitation at the same pixels were 38.5 and 36.9 mm, respectively. Therefore, the obtained results prove the inefficiency of TMM and the capability of RPMM in the calibration process of the Amir-Abad weather radar. Besides, in determining the uncertainty associated with the calculated values of A and B in the Z e –R relation, a sensitivity analysis method was employed during the estimation of cumulative light precipitation for the period from 2014 to 2015. The results expressed that in the worst conditions, 69% of radar data are converted to R values by a maximum error less than 30%.

Bias adjustment of infrared‐based rainfall estimation using Passive Microwave satellite rainfall data

AbstractThis study explores using Passive Microwave (PMW) rainfall estimation for spatial and temporal adjustment of Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks‐Cloud Classification System (PERSIANN‐CCS). The PERSIANN‐CCS algorithm collects information from infrared images to estimate rainfall. PERSIANN‐CCS is one of the algorithms used in the Integrated Multisatellite Retrievals for GPM (Global Precipitation Mission) estimation for the time period PMW rainfall estimations are limited or not available. Continued improvement of PERSIANN‐CCS will support Integrated Multisatellite Retrievals for GPM for current as well as retrospective estimations of global precipitation. This study takes advantage of the high spatial and temporal resolution of GEO‐based PERSIANN‐CCS estimation and the more effective, but lower sample frequency, PMW estimation. The Probability Matching Method (PMM) was used to adjust the rainfall distribution of GEO‐based PERSIANN‐CCS toward that of PMW rainfall estimation. The results show that a significant improvement of global PERSIANN‐CCS rainfall estimation is obtained.

기상청 고해상도 국지 앙상블 예측 시스템 구축 및 성능 검증

Predicting the location and intensity of precipitation still remains a main issue in numerical weather prediction (NWP). Resolution is a very important component of precipitation forecasts in NWP. Compared with a lower resolution model, a higher resolution model can predict small scale (i.e., storm scale) precipitation and depict convection structures more precisely. In addition, an ensemble technique can be used to improve the precipitation forecast because it can estimate uncertainties associated with forecasts. Therefore, NWP using both a higher resolution model and ensemble technique is expected to represent inherent uncertainties of convective scale motion better and lead to improved forecasts. In this study, the limited area ensemble prediction system for the convective-scale (i.e., high resolution) operational Unified Model (UM) in Korea Meteorological Administration (KMA) was developed and evaluated for the ensemble forecasts during August 2012. The model domain covers the limited area over the Korean Peninsula. The high resolution limited area ensemble prediction system developed showed good skill in predicting precipitation, wind, and temperature at the surface as well as meteorological variables at 500 and 850 hPa. To investigate which combination of horizontal resolution and ensemble member is most skillful, the system was run with three different horizontal resolutions (1.5, 2, and 3 km) and ensemble members (8, 12, and 16), and the forecasts from the experiments were evaluated. To assess the quantitative precipitation forecast (QPF) skill of the system, the precipitation forecasts for two heavy rainfall cases during the study period were analyzed using the Fractions Skill Score (FSS) and Probability Matching (PM) method. The PM method was effective in representing the intensity of precipitation and the FSS was effective in verifying the precipitation forecast for the high resolution limited area ensemble prediction system in KMA.

Radar Rainfall Estimation of a Severe Thunderstorm over Jeddah

The regular occurrence of flash floods over the region of Jeddah, Saudi Arabia in the past decade has highlighted the serious need for the development of early warning systems. Radar stations have been installed in Jeddah in the last decade whose active radius covers the Middle Western area of the country. Therefore, radar information and the associated the rainfall estimates are potentially useful components of an effective early warning system. Weather radar can potentially provide high-resolution spatial and temporal rainfall estimates that bring more accuracy to flood warnings as well as having applications in areas with insufficient rainfall stations coverage. Weather radar does not measure rainfall depth directly. An empirical relationship between reflectivity (Z) and rainfall rate (R), called the Z-R relationship (Z = ARb), is generally used to assess the rainfall depth. In this study, the rainfall events during August-September 2007 were analyzed to develop a Z-R relationship using the Spatial Probability Technique (SPT). This technique is based on a basic GIS function and the probability matching method. Using this technique, the Z-R pairs can be analyzed for both linear and empirical power relationships. It is found that the empirical power function is more appropriate to describe Z-R relationship than a linear function for the studied area. The method is applied with some success to the flooding event of November 25, 2009. However, the investigation of the Z-R relationship is only one step in the development of a warning system; further study of other parameters relevant to rainfall and flash flood occurrence is needed.

Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set

Abstract. In traditional hydrogeological investigations, one geological model is often used based on subjective interpretations and sparse data availability. This deterministic approach usually does not account for any uncertainties. Stochastic simulation methods address this problem and can capture the geological structure uncertainty. In this study the geostatistical software TProGS is utilized to simulate an ensemble of realizations for a binary (sand/clay) hydrofacies model in the Norsminde catchment, Denmark. TProGS can incorporate soft data, which represent the associated level of uncertainty. High-density (20 m × 20 m × 2 m) airborne geophysical data (SkyTEM) and categorized borehole data are utilized to define the model of spatial variability in horizontal and vertical direction, respectively, and both are used for soft conditioning of the TProGS simulations. The category probabilities for the SkyTEM data set are derived from a histogram probability matching method, where resistivity is paired with the corresponding lithology from the categorized borehole data. This study integrates two distinct data sources into the stochastic modeling process that represent two extremes of the conditioning density spectrum: sparse borehole data and abundant SkyTEM data. In the latter the data have a strong spatial correlation caused by its high data density, which triggers the problem of overconditioning. This problem is addressed by a work-around utilizing a sampling/decimation of the data set, with the aim to reduce the spatial correlation of the conditioning data set. In the case of abundant conditioning data, it is shown that TProGS is capable of reproducing non-stationary trends. The stochastic realizations are validated by five performance criteria: (1) sand proportion, (2) mean length, (3) geobody connectivity, (4) facies probability distribution and (5) facies probability–resistivity bias. In conclusion, a stochastically generated set of realizations soft-conditioned to 200 m moving sampling of geophysical data performs most satisfactorily when balancing the five performance criteria. The ensemble can be used in subsequent hydrogeological flow modeling to address the predictive uncertainty originating from the geological structure uncertainty.

Impacts of Satellite-Based Rainfall Products on Predicting Spatial Patterns of Rift Valley Fever Vectors*

Abstract Spatiotemporal rainfall variability is a key parameter controlling the dynamics of mosquitoes/vector-borne diseases such as malaria, Rift Valley fever (RVF), or dengue. Impacts from rainfall heterogeneity at small scales (i.e., 1–10 km) on the risk of epidemics (i.e., host bite rate or number of bites per host and per night) must be thoroughly evaluated. A model with hydrological and entomological components for risk prediction of the RVF zoonosis is proposed. The model predicts the production of two mosquito species within a 45 km × 45 km area in the Ferlo region, Senegal. The three necessary steps include 1) best rainfall estimation on a small scale, 2) adequate forcing of a simple hydrological model leading to pond dynamics (ponds are the primary larvae breeding grounds), and 3) best estimate of mosquito life cycles obtained from the coupled entomological model. The sensitivity of the model to the spatiotemporal heterogeneity of rainfall is first tested using high-resolution rain fields from a weather radar. The need for high-resolution rain data is thus demonstrated. Several high-resolution satellite rainfall products are evaluated in the region of interest using a dense rain gauge network. Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis 3B42, version 6 (TMPA-3B42V6), and 3B42 in real time (TMPA-3B42RT); Global Satellite Mapping of Precipitation (GSMaP) in near–real time (GSMaP-NRT) and Moving Vector with Kalman version (GSMaP-MVK); African Rainfall Estimation Algorithm, version 2.0 (RFE 2.0); Climate Prediction Center (CPC) morphing technique (CMORPH); and Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN) are tested and finally corrected using a probability matching method. The corrected products are then used as forcing to the coupled model over the 2003–10 period. The predicted number and size of ponds and their dynamics are greatly improved compared to the model forced only by a single gauge. A more realistic spatiotemporal distribution of the host bite rate of the RVF vectors is thus expected.

Transition probability‐based stochastic geological modeling using airborne geophysical data and borehole data

AbstractGeological heterogeneity is a very important factor to consider when developing geological models for hydrological purposes. Using statistically based stochastic geological simulations, the spatial heterogeneity in such models can be accounted for. However, various types of uncertainties are associated with both the geostatistical method and the observation data. In the present study, TProGS is used as the geostatistical modeling tool to simulate structural heterogeneity for glacial deposits in a head water catchment in Denmark. The focus is on how the observation data uncertainty can be incorporated in the stochastic simulation process. The study uses two types of observation data: borehole data and airborne geophysical data. It is commonly acknowledged that the density of the borehole data is usually too sparse to characterize the horizontal heterogeneity. The use of geophysical data gives an unprecedented opportunity to obtain high‐resolution information and thus to identify geostatistical properties more accurately especially in the horizontal direction. However, since such data are not a direct measurement of the lithology, larger uncertainty of point estimates can be expected as compared to the use of borehole data. We have proposed a histogram probability matching method in order to link the information on resistivity to hydrofacies, while considering the data uncertainty at the same time. Transition probabilities and Markov Chain models are established using the transformed geophysical data. It is shown that such transformation is in fact practical; however, the cutoff value for dividing the resistivity data into facies is difficult to determine. The simulated geological realizations indicate significant differences of spatial structure depending on the type of conditioning data selected. It is to our knowledge the first time that grid‐to‐grid airborne geophysical data including the data uncertainty are used in conditional geostatistical simulations in TProGS. Therefore, it provides valuable insights regarding the advantages and challenges of using such comprehensive data.

Applicability Evaluation of Probability Matching Method for Parameter Estimation of Radar Rain Rate Equation

본 연구에서는 Z - R 관계식의 매개변수 결정을 위한 확률대응법(Probability Matching Method, PMM)의 적용성을 평가하였다. 이를 위해 먼저, 확률대응에 적합한 반사도와 강우강도의 자료 수와 히스토그램의 구간 간격을 결정하기 위한 민감도 분석을 수행하였다. 그 결과, 확률대응법으로 매개변수를 결정할 경우 1,000개의 자료쌍이 구축되어야 한다는 것을 확인하였다. 이는 약 2시간 정도 수집된 자료 수에 해당한다. 또한, 히스토그램의 구간 수는 100 구간 정도가 되어야 한다는 것을 확인하였다. 아울러 확률대응에는 반사도와 강우강도의 누가확률 차이보다 1차 모멘트 차이를 이용하는 것이 양호한 결과를 얻을 수 있고, 30~100% 구간을 대응하는 것이 적합하다는 것을 확인하였다. 본 연구에서는 이러한 결과를 바탕으로 비슬산 레이더로 관측한 실제 호우사상에 대해 확률대응법으로 매개변수를 결정하였다. 추정된 매개변수를 이용하여 결정한 레이더 강우는 전체적으로 지상강우보다 크게 산정되었다. 하지만, 이러한 결과는 레이더 강우와 지상 강우를 쉽게 대응하기 어려운 기존의 연구 결과를 고려하면 감안할 수 있는 부분으로 본 연구에서 평가한 확률대응법이 비교적 기존의 Z - R 관계식 보다 호우사상에 적합한 레이더 강우를 산정할 수 있다고 판단하였다. This study evaluated PMM (Probability Matching Method) for parameter estimation of the Z - R relation. As a first step, the sensitivity analysis was done to decide the threshold number of data pairs and the data interval for the development of a histogram. As a result, it was found that at least 1,000 number of data pairs are required to apply the PMM for the parameter estimation. This amount of data is similar to that collected for two hours. Also, the number of intervals for the histogram was found to be at least 100. Additionally, it was found that the matching the first-order moment is better than the cumulative probability, and that the data pairs comprising 30 to 100% are better for the PMM application. Finally, above findings were applied to a real rainfall event observed by the Bislsan radar and optimal parameters were estimated. The radar rain rate derived by applying these parameters was found to be well matched to the rain gauge rain rate.

Availability of High-Quality TRMM Ground Validation Data from Kwajalein, RMI: A Practical Application of the Relative Calibration Adjustment Technique

Abstract Since the Tropical Rainfall Measuring Mission (TRMM) satellite launch in November 1997, the TRMM Satellite Validation Office (TSVO) at NASA Goddard Space Flight Center (GSFC) has been performing quality control and estimating rainfall from the KPOL S-band radar at Kwajalein, Republic of the Marshall Islands. Over this period, KPOL has incurred many episodes of calibration and antenna pointing angle uncertainty. To address these issues, the TSVO has applied the relative calibration adjustment (RCA) technique to eight years of KPOL radar data to produce Ground Validation (GV) version 7 products. This application has significantly improved stability in KPOL reflectivity distributions needed for probability matching method (PMM) rain-rate estimation and for comparisons to the TRMM precipitation radar (PR). In years with significant calibration and angle corrections, the statistical improvement in PMM distributions is dramatic. The intent of this paper is to show improved stability in corrected KPOL reflectivity distributions by using the PR as a stable reference. Intermonth fluctuations in mean reflectivity differences between the PR and corrected KPOL are on the order of ±1–2 dB, and interyear mean reflectivity differences fluctuate by approximately ±1 dB. This represents a marked improvement in stability with confidence comparable to the established calibration and uncertainty boundaries of the PR. The practical application of the RCA method has salvaged eight years of radar data that would have otherwise been unusable and has made possible a high-quality database of tropical ocean–based reflectivity measurements and precipitation estimates for the research community.

Contributions of Mixed Physics versus Perturbed Initial/Lateral Boundary Conditions to Ensemble-Based Precipitation Forecast Skill

Abstract An experiment is described that is designed to examine the contributions of model, initial condition (IC), and lateral boundary condition (LBC) errors to the spread and skill of precipitation forecasts from two regional eight-member 15-km grid-spacing Weather Research and Forecasting (WRF) ensembles covering a 1575 km × 1800 km domain. It is widely recognized that a skillful ensemble [i.e., an ensemble with a probability distribution function (PDF) that generates forecast probabilities with high resolution and reliability] should account for both error sources. Previous work suggests that model errors make a larger contribution than IC and LBC errors to forecast uncertainty in the short range before synoptic-scale error growth becomes nonlinear. However, in a regional model with unperturbed LBCs, the infiltration of the lateral boundaries will negate increasing spread. To obtain a better understanding of the contributions to the forecast errors in precipitation and to examine the window of forecast lead time before unperturbed ICs and LBCs begin to cause degradation in ensemble forecast skill, the “perfect model” assumption is made in an ensemble that uses perturbed ICs and LBCs (PILB ensemble), and the “perfect analysis” assumption is made in another ensemble that uses mixed physics–dynamic cores (MP ensemble), thus isolating the error contributions. For the domain and time period used in this study, unperturbed ICs and LBCs in the MP ensemble begin to negate increasing spread around forecast hour 24, and ensemble forecast skill as measured by relative operating characteristic curves (ROC scores) becomes lower in the MP ensemble than in the PILB ensemble, with statistical significance beginning after forecast hour 69. However, degradation in forecast skill in the MP ensemble relative to the PILB ensemble is not observed in an analysis of deterministic forecasts calculated from each ensemble using the probability matching method. Both ensembles were found to lack statistical consistency (i.e., to be underdispersive), with the PILB ensemble (MP ensemble) exhibiting more (less) statistical consistency with respect to forecast lead time. Spread ratios in the PILB ensemble are greater than those in the MP ensemble at all forecast lead times and thresholds examined; however, ensemble variance in the MP ensemble is greater than that in the PILB ensemble during the first 24 h of the forecast. This discrepancy in spread measures likely results from greater bias in the MP ensemble leading to an increase in ensemble variance and decrease in spread ratio relative to the PILB ensemble.

Reinforcement learning and evolutionary algorithms for non-stationary multi-armed bandit problems

Multi-armed bandit tasks have been extensively used to model the problem of balancing exploitation and exploration. A most challenging variant of the MABP is the non-stationary bandit problem where the agent is faced with the increased complexity of detecting changes in its environment. In this paper we examine a non-stationary, discrete-time, finite horizon bandit problem with a finite number of arms and Gaussian rewards. A family of important ad hoc methods exists that are suitable for non-stationary bandit tasks. These learning algorithms that offer intuition-based solutions to the exploitation–exploration trade-off have the advantage of not relying on strong theoretical assumptions while in the same time can be fine-tuned in order to produce near-optimal results. An entirely different approach to the non-stationary multi-armed bandit problem presents itself in the face of evolutionary algorithms. We present an evolutionary algorithm that was implemented to solve the non-stationary bandit problem along with ad hoc solution algorithms, namely action-value methods with e-greedy and softmax action selection rules, the probability matching method and finally the adaptive pursuit method. A number of simulation-based experiments was conducted and based on the numerical results that we obtained we discuss the methods’ performances.