Modeling distribution of temporal sampling errors in area-time-averaged rainfall estimates

In this paper, the authors examine models of probability distributions for sampling error in rainfall estimates obtained from discrete satellite sampling in time based on 5 years of 15-min radar rainfall data in the central United States. The sampling errors considered include all combinations of 3, 6, 12, or 24 h sampling of rainfall over 32, 64, 128, 256, or 512 km square domains, and 1, 5, or 30 day rainfall accumulations. Results of this study reveal that the sampling error distribution depends strongly on the rain rate; hence the conditional distribution of sampling error is more informative than its marginal distribution. The distribution of sampling error conditional on rain rate is strongly affected by the sampling interval. At sampling intervals of 3 or 6 h, the logistic distribution appears to fit the conditional sampling error quite well, while the shifted-gamma, shifted-weibull, shifted-lognormal, and normal distributions fit poorly. At sampling intervals of 12 or 24 h, the shifted-gamma, shifted-weibull, or shifted-lognormal distribution fit the conditional sampling error better than the logistics or normal distribution. These results are vital to understanding the accuracy of satellite rainfall products, for performing validation assessment of these products, and for analyzing the effects of rainfall-related errors in hydrological models.     

Evaluation of TMPA satellite-based research and real-time rainfall estimates during six tropical-related heavy rainfall events over Louisiana, USA

This study focuses on the evaluation of 3-hourly 0.25° × 0.25° satellite-based rainfall estimates produced by the Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA). The evaluation is performed during six heavy rainfall events that were generated by tropical storms passing over Louisiana, United States. Two surface-based rainfall datasets from gauge and radar observations are used as a ground reference for evaluating the real-time (RT) version of the TMPA product and the post-real-time bias adjusted research version. The evaluation analysis is performed at the native temporal and spatial scales of the TMPA products, 3-hourly and 0.25° × 0.25°. Several graphical and statistical techniques are applied to characterize the deviation of the TMPA estimates from the reference datasets. Both versions of the TMPA products track reasonably well the temporal evolution and fluctuations of surface rainfall during the analyzed storms with moderate to high correlation values of 0.5–0.8. The TMPA estimates reported reasonable levels of rainfall detection especially when light rainfall rates are excluded. On a storm scale, the TMPA products are characterized by varying degrees of bias which was mostly within ± 25% and ± 50% for the research and RT products, respectively. Analysis of the error distribution indicated that, on average, the TMPA products tend to overestimate small rain rates and underestimate large rain rates. Compared to the real-time estimates, the research product shows significant improvement in the overall and conditional bias, and in the correlation coefficients, with slight deterioration in the probability of detecting rainfall occurrences. A fair agreement in terms of reproducing the tail of the distribution of rain rates (i.e., probability of surface rainfall exceeding certain thresholds) was observed especially for the RT estimates. Despite the apparent differences with surface rainfall estimates, the results reported in this study highlight the TMPA potential as a valuable resource of high-resolution rainfall information over many areas in the world that lack capabilities for monitoring landfalling tropical storms.     

Sub-daily scale validation of satellite-based high-resolution rainfall products

Recent research efforts have been geared towards developing high-resolution rainfall products from satellites for hydrological applications. A necessary step in assessing the potential and utility of these products is to quantify the uncertainty associated with them at validation scales appropriate for hydrological applications. The main objective of this paper is to evaluate the accuracy of the widely-known PERSIANN-CCS high-resolution (hourly, 0.04° × 0.04°) satellite rainfall products against high-quality NEXRAD radar rainfall observations in the Little Washita watershed. Our results reveal that (1) PERSIANN-CCS shows high skills in reproducing the patterns of inter-annual rainfall variability on a monthly basis; (2) both at the hourly and storm scales, the performance statistics of PERSIANN-CCS exhibit large spread, suggesting that the quality of PERSIANN-CCS product is almost unique for each hour and storm; and (3) significant improvement in performance statistics is obtained as PERSIANN-CCS products are averaged to longer sub-daily time scales. The implications of our results are: (1) PERSIANN-CCS could be used with high confidence for inter-annual rainfall variability studies; (2) PERSIANN-CCS products need to be accompanied by corresponding hourly error estimates in order to provide meaningful error estimates for hydrological applications; and (3) research is needed to characterize the tradeoff between the quality of rainfall input and the space-time resolution of hydrological modeling, as a function of watershed size and hydrologic model complexity level.     

A new method to compare hourly rainfall between station observations and satellite products over central-eastern China

This study employs a newly defined regional-rainfall-event (RRE) concept to compare the hourly characteristics of warm-season (May-September) rainfall among rain gauge observations, China merged hourly precipitation analysis (CMPA-Hourly), and two commonly used satellite products (TRMM 3B42 and CMORPH). By considering the rainfall characteristics in a given limited area rather than a single point or grid, this method largely eliminates the differences in rainfall characteristics among different observations or measurements over central-eastern China. The results show that the spatial distribution and diurnal variation of RRE frequency and intensity are quite consistent among different datasets, and the performance of CMPA-Hourly is better than the satellite products when compared with station observations. A regional rainfall coefficient (RRC), which can be used to classify local rain and regional rain, is employed to represent the spatial spread of rainfall in the limited region defining the RRE. It is found that rainfall spread in the selected grid box is more uniform during the nocturnal to morning hours over central-eastern China. The RRC tends to reach its diurnal maximum several hours after the RRE intensity peaks, implying an intermediate transition stage from convective to stratiform rainfall. In the afternoon, the RRC reaches its minimum, implying the dominance of local convections on small spatial scale in those hours, which could cause large differences in rain gauge and satellite observations. Since the RRE method reflects the overall features of rainfall in a limited region rather than at a fixed point or in a single grid, the widely recognized overestimation of afternoon rainfall in satellite products is not obvious, and thus the satellite estimates are more reliable in representing sub-daily variation of rainfall from the RRE perspective. This study proposes a reasonable method to compare satellite products with rain gauge observations on the sub-daily scale, which also has great potential to be used in evaluating the spatiotemporal variation of cloud and rainfall in numerical models.     

A new methodology of rainfall retrievals from indirect measurements

Summary  A new methodology for rainfall retrievals from indirect measurements is proposed and illustrated using IR brightness temperature and radar rainfall observations collected during TOGA-COARE. Since (1) rain rate has a mixed distribution with a delta-function for a zero rain and lognormal distribution for nonzero and (2) the least squares method which is used to calculate regression coefficients gives a priori consistent estimates only for normally distributed data, it is proposed to convert the rain rate to a normally distributed set and only after that to develop a retrieval method and estimate the skill of this method. Consideration of the physics of clouds and cloud ensembles, the goal to minimize errors in the radar data, and the desire to remove the influence of cirrus clouds lead us to use: a) minimum of IR brightness temperatures over a 1° × 1° area and a 3 hour interval as a predictor, and b) radar rainfall, averaged over 3 hours over a 1° × 1° area, with the radar in its center, as the truth. Results using the TOGA-COARE data show that the correlation of the rain rate transformed to normal distribution is significantly higher with minimum temperature than with the fraction of area covered by high clouds. The sizes of heavy rainfall areas obtained using the new methodology are reasonable. The regression coefficients should change with latitude, season and location. Taken together, the results indicate that it is possible, in principle, to retrieve rainfall from IR satellite observations and obtain reliable rainfall data. To realize this goal it is necessary to process radar and IR data using the new methodology for different latitudes, seasons, over land and ocean. Received December 27, 1999 Revised May 17, 2000     

Squall lines and rainfall over Western Africa during summer 1986 and 87

Summary Using digitized IR images from the European satellite Meteosat, 153 squall lines (SLs) were observed over Western Africa during July, August and September 1986 and 87. The SL mean rainfall volume was computed using the daily rainfall amounts of more than 800 raingauges: 15 km³ in 1986 and 22.5 km³ in 1987. A mean amount of 15 mm was collected per rainy episode at a given station, however, as only about half of the stations situated under a SL experienced a rainy episode, the rainfall amount averaged along the total SL’s swath was 6.8 mm. With the help of the 8 daily Meteosat slots the SL’s area daily variation could be estimated: namely a minimum around noon and a maximum around midnight. Using the SLs displacements (east–west) one had access to the daily variation of the rainfall volume, a minimum in the morning and a maximum toward the end of the afternoon, as already found by several authors who used Meteosat images.     

The role of raindrop coalescence and breakup in rainfall modeling

In a one dimensional model, the microphysical properties of rainwater content (M), rainfall rate (R) and radar reflectivity factor (Z) are examined in five numerical experiments. In general, neglecting both coalescence and breakup produces less than 10% of the errors in M and R within the top 2 km of a rainshaft (below cloud base). This is true regardless of the rain intensity and downdraft strength for Mashall-Palmer distributions at the top boundary. However, as the distance from the top boundary increases, the errors of M, R and Z calculated without including the collisional processes become larger. These errors tend to increase as the rain intensity increases or the downdraft decreases. The errors due to neglecting breakup are generally larger than those resulting from the exclusion of both coalescence and breakup. At lower levels, the errors for Z are usually very large unless the rainfall is very light (less than 10 mm h⁻¹ ). For heavy rainfall with strong downdraft, coalescence and breakup can be neglected for fall distances greater than 2 km without appreciable errors. On the other hand, for heavy rainfall in a weak downdraft, coalescence and breakup must be included to ensure accuracy.     

Intense rainfall events over the west coast of India

Summary The west coast of the Indian peninsula receives very heavy rainfall during the summer Monsoon (June–September) season with average rainfall over some parts exceeding 250 cm. Heavy rainfall events with rainfall more than 15 cm day⁻¹ at one or more stations along the west coast of India occur frequently and cause considerable damage. A special observational programme, Arabian Sea Monsoon Experiment, was carried out during the monsoon season of 2002 to study these events. The spatial and temporal distributions of intense rainfall events, presented here, were used for the planning of this observational campaign. The present study using daily rainfall data for summer monsoon season of 37 years (1951–1987) shows that the probability of getting intense rainfall is the maximum between 14° N–16° N and near 19° N. The probability of occurrence of these intense rainfall events is high from mid June to mid August, with a dip in early July. It has been believed for a long time that offshore troughs and vortices are responsible for these intense rainfall events. However, analysis of the characteristics of cloud systems associated with the intense rainfall events during 1985–1988 using very high resolution brightness temperature data from INSAT-IB satellite shows that the cloud systems during these events are characterized by large spatial scales and high cloud tops. Further study using daily satellite derived outgoing longwave radiation (OLR) data over a longer period (1975–1998) shows that, most of these events (about 62%) are associated with systems organized on synoptic and larger scales. We find that most of the offshore convective systems responsible for intense rainfall along the west coast of India are linked to the atmospheric conditions over equatorial Indian Ocean.     

On the relations of the rainfall variability and distribution with the mean rainfall over India

Summary Along with averages, rainfall variability and distribution are important climatological information. In this study, using 114 years (1871–1984) data of 306 stations, it is demonstrated that the variability and spatial distribution of annual, summer monsoon and monthly rainfall are highly dependent upon the respective period mean rainfall variation over India. The magnitude of three selected absolute measures of variability, e.g. standard deviation, absolute mean deviation and mean absolute interannual variability is found to increase linearly with mean rainfall.In order to describe the relation between the rainfall frequency distribution and the mean rainfall, a linear regression between the rainfall amount expected with a specified exceedance/non-exceedance probability and the mean rainfall amount is presented. Highly significant linear curves for a large number of probabilities specified in an average probability diagram clearly demonstrate the dependence of the rainfall frequency distribution on mean rainfall over India.With 8 Figures     

强降雨监测预警产品原理和应用

通过对强降雨监测预警产品原理和方法的阐述,介绍了根据强降雨规律性特征和概念模型原理,利用卫星与自动站资料生成的强降雨监测预警产品制作流程,指出了产品特点、应用方式和注意事项,为强降雨监测预警产品的合理使用提供参考.     

The effect of rainfall on measurements of mean wind speed with cup anemometers in the surface layer at sea

A mathematical model is developed to estimate rain-induced errors in cup anemometer readings. Based upon a two-cup hemispheric model, the indicated wind speed is calculated for a given true wind speed, fall velocities of the drops, and a general drop-size distribution.The results of these computations show that the effect of rainfall is small as expected. The influence on derived profiles of mean wind speed is rather a displacement of the profile to lower velocities than a change in the slope of the profile.The magnitude of these errors is a few percent or less even for heavy rainfall.Now Deutscher Wetterdienst, Offenbach, F.R.G.     

Homogeneous clusters over India using probability density function of daily rainfall

The Indian landmass has been divided into homogeneous clusters by applying the cluster analysis to the probability density function of a century-long time series of daily summer monsoon (June through September) rainfall at 357 grids over India, each of approximately 100 km × 100 km. The analysis gives five clusters over Indian landmass; only cluster 5 happened to be the contiguous region and all other clusters are dispersed away which confirms the erratic behavior of daily rainfall over India. The area averaged seasonal rainfall over cluster 5 has a very strong relationship with Indian summer monsoon rainfall; also, the rainfall variability over this region is modulated by the most important mode of climate system, i.e., El Nino Southern Oscillation (ENSO). This cluster could be considered as the representative of the entire Indian landmass to examine monsoon variability. The two-sample Kolmogorov-Smirnov test supports that the cumulative distribution functions of daily rainfall over cluster 5 and India as a whole do not differ significantly. The clustering algorithm is also applied to two time epochs 1901–1975 and 1976–2010 to examine the possible changes in clusters in a recent warming period. The clusters are drastically different in two time periods. They are more dispersed in recent period implying the more erroneous distribution of daily rainfall in recent period.

     

Validation of satellite rainfall products for operational flood forecasting: the case of the Evros catchment

An extensive validation of two of the most popular and recently upgraded satellite rainfall products, 3B42 and 3B42RT, was performed over the Evros catchment in southeastern Europe using data recorded from January 2000 to April 2009. For conducting this validation study, the Climate Prediction Center's (CPC) ground data were used. The satellite data products were aggregated to daily time series, remapped to spatial resolution of 0.5°, validated against CPC, and intercompared using a variety of statistical indices and coefficients. After the validation process, all three data sets (CPC, 3B42, and 3B42RT) were separately fed in a statistical rainfall?Crunoff model, in order to predict the five major recorded flood events which occurred in the Evros catchment during the last decade. It has been found that post-calibration with ground data, which is present only in 3B42 product, is a necessity for operational flood forecasting and similar studies conducted in areas at mid-latitudes. Knowledge of rainfall events with small intensities is crucial for estimating the total rainfall height and drastically improves the skill of the satellite product.     

Investigating the implications of meteorological indicators of seasonal rainfall performance on maize yield in a rain-fed agricultural system: case study of Mt. Darwin District in Zimbabwe

The study focuses on the impacts of climate variability and change on maize yield in Mt. Darwin District. The rainfall and temperature data for the period under study that is from 1992 to 2012 were obtained from Meteorological Services Department of Zimbabwe at daily resolution while crop yield data were obtained from Department of Agricultural, Technical and Extension Services (AGRITEX) and Zimbabwe Statistics Agency (ZIMSTAT) at seasonal/yearly resolution. In order to capture full rainfall seasons, a year was set to begin on 1 June and end on 31 July the next year. Yearly yield, temperature and rainfall data were used to compute time series analysis of rainfall, temperature and yield. The relationship between temperature, rainfall, quality of season (start, cessation, dry days, wet days and length) and yield was also investigated. The study also investigated the link between meteorological normal and maize yield. The study revealed that temperature is rising while rainfall is decreasing with time hence increasing risk of low maize yield in Mt. Darwin. Correlation between maize yield was higher using a non-linear (R ² = 0.630) than a linear regression model (R ² = 0.173). There was a very high correlation between maize yield and number of dry days (R = −0.905) as well as between maize yield and length of season (R = 0.777). We also observed a strong correlation between percentage normal rainfall and percentage normal maize yield (R ² = 0.753). This was also agreed between rainfall tessiles and maize yield tessiles as 50 % of the seasons had normal and above normal rainfall coinciding with normal and above normal maize yield. Of the 21 seasons considered, only one season had above normal rainfall while maize yield was below normal. The study concluded that there is a strong association between meteorological normal and maize yield in a rain-fed agricultural system. Climate information remains crucial to agricultural productivity hence the need to train farmers to access the information and use it for the benefit of their activities.

     

How effective is the new generation of GPM satellite precipitation in characterizing the rainfall variability over Malaysia?

We investigated the potential of the new generation of satellite precipitation product from the Global Precipitation Mission (GPM) to characterize the rainfall in Malaysia. Most satellite precipitation products have limited ability to precisely characterize the high dynamic rainfall variation that occurred at both time and scale in this humid tropical region due to the coarse grid size to meet the physical condition of the smaller land size, sub-continent and islands. Prior to the status quo, an improved satellite precipitation was required to accurately measure the rainfall and its distribution. Subsequently, the newly released of GPM precipitation product at half-hourly and 0.1° resolution served an opportunity to anticipate the aforementioned conflict. Nevertheless, related evidence was not found and therefore, this study made an initiative to fill the gap. A total of 843 rain gauges over east (Borneo) and west Malaysia (Peninsular) were used to evaluate the rainfall the GPM rainfall data. The assessment covered all critical rainy seasons which associated with Asian Monsoon including northeast (Nov. - Feb.), southwest (May - Aug.) and their subsequent inter-monsoon period (Mar. - Apr. & Sep. - Oct.). The ability of GPM to provide quantitative rainfall estimates and qualitative spatial rainfall patterns were analysed. Our results showed that the GPM had good capacity to depict the spatial rainfall patterns in less heterogeneous rainfall patterns (Spearman’s correlation, 0.591 to 0.891) compared to the clustered one (r = 0.368 to 0.721). Rainfall intensity and spatial heterogeneity that is largely driven by seasonal monsoon has significant influence on GPM ability to resolve local rainfall patterns. In quantitative rainfall estimation, large errors can be primarily associated with the rainfall intensity increment. 77% of the error variation can be explained through rainfall intensity particularly the high intensity (> 35 mm d^-1). A strong relationship between GPM rainfall and error was found from heavy (~35 mm d^-1) to violent rain (160 mm d^-1). The output of this study provides reference regarding the performance of GPM data for respective hydrology studies in this region.     

Daily rainfall trend in the Valencia Region of Spain

Summary ?We have analyzed daily rainfall trends throughout the second half of the 20^th century in the western Mediterranean basin (Valencia Region, E of Spain). The area is characterized by high torrentiality, and during the second half of the 20^th century some of the highest daily rainfall values in the Mediterranean basin have been recorded. In this area, mean annual rainfall varies between 500 and 300 mm and is overwhelmingly dependent on just a few days of rain. Daily maximum rainfall varies on average from 120 mm day⁻¹ to 50 mm day⁻¹, and represents a mean of 17% (coastland) to 9% (inland) of annual rainfall. The 10 days in each year with the heaviest rainfall (called “higher events”) provide over 50% of the annual rainfall and can reach more than 400 mm on average. We compared the annual rainfall trend and the trend of higher and minor events defined by percentiles, both in volume and variability. We, therefore, tested whether annual rainfall changes depend on the trend of the higher (rainfall) events. To overlap spatial distribution of trends (i.e.: positive, no significant and negative trends) we have used cross-tab analysis. The results confirm the hypothesis that annual rainfall changes depend on changes found in just a few rainy events. Furthermore, in spite of their negative trend, higher events have increased their contribution to annual rainfall. As a consequence, although torrential events may have diminished in magnitude, future scenarios seem to be controlled by a limited number of rainy events which will become more and more variable year on year. The high spatial density of data used in this work, (97 observatories per 24.000 km², overall mean 1 observatory per 200 km²), suggests to us that extreme caution should be applied when analyzing regional and sub-regional changes in rainfall using GCM output, especially in areas of high torrentiality. Received August 1, 2002; revised November 11, 2002; accepted December 1, 2002 Published online May 19, 2003     

Impact of different regression frameworks on the estimation of the scaling properties of radar rainfall

Rainfall is characterized by high variability both in space and time. Despite continuous technological progress, the available instruments that are used to measure rainfall across several spatio-temporal scales remain inaccurate. To remedy this situation, scaling relationships of spatial rainfall offer the potential to link the observed or predicted precipitation quantities at one scale to those of interest at other scales. This paper focuses on the estimation of the spatial rainfall scaling functions. Standard scaling analysis constructed by means of the ordinary least squares method often violates such basic assumptions implicit in its use and interpretation as homoschedasticity, independence, and normality of the errors. Consequently, the authors consider alternative regression frameworks i.e. bootstrapping regression, semi parametric linear model, and multilevel normal linear model to show how these different approaches exert a significant impact on the multifractal analysis of radar rainfall. In addition, the uncertainties associated with the construction of the scaling function due solely to the regression procedure are quantified. The radar data come from the polarimetric C-band weather radar located in Rome, Italy, and the scaling properties are computed for a square domain centred on the radar site with a side length of 128 km and a finest resolution of 1 km².     

Association between cloudiness and rainfall over Fars province in Iran

Relationship between precipitation sum and cloud properties over Fars province in Iran was analyzed for the cases of light (4 mm), moderate (17 mm), and heavy (62 mm) precipitation. The cloud properties (temperature and pressure at the top, cloud optical thickness and cloud water path) were obtained from satellite data of spectoradiometer MODIS (MODO6). The spatial distribution of rainfall was obtained from the 3-hourly data of TRMM (3B42). The multivariate regression model was developed to predict the spatial distribution of rainfall. A strong significant positive association between the spatial distribution of cloud characteristics and heavy precipitation was found, while no clear correlation was revealed between light precipitation and cloud properties. The developed regression model comprised 64, 47, and 24% of spatial variance of heavy, moderate, and light rainfall, respectively. The influence of cloud water path on the spatial distribution of rainfall dominates.     

Satellite estimates and subpixel variability of rainfall in a semi-arid grassland

卫星估雨精度的不确定性受到当地降雨类型和像元内降雨非均匀性影响,而结合这两个关键因素开展半干旱草原卫星估雨的研究有限.2009年夏,我们在中国锡林郭勒半干旱草原用多部微雨雷达和雨量计构建了9 km卫星像元降雨观测网,观测了像元内降雨非均匀性(空间变异系数CV),并评估了卫星估雨精度.结果表明:(1)CV值受像元内平均降雨量,降雨类型,降雨云面积及移向等影响,如高Cv值的降雨过程大多为平均降雨量小,对流性降雨过程,降雨云边缘像元CV值较高;(2)TRMM 3B42V7卫星估雨产品适用性较好,CMORPH和PERSIANN次之,但TRMM 3B42V7易在半干旱草原湖泊处高估降雨.     

The coherence of satellite infrared temperatures with monsoon rainfall at preferred frequencies and the triplex behavior of the Indian summer monsoon

Summary The behavior of the Indian summer monsoon during the period 1979–1985 is examined with surface rainfall and infrared satellite data in order to determine how well the satellite measurements mimic the episodic rainfall processes. It is shown that equivalent-black-body-temperatures derived from satellite measured outgoing longwave radiation (OLR) estimates are reliable indicators for reproducing the timevariant zonal structure of monsoon rainfall over the Indian sub-continent—but only at preferred frequencies. The Indian summer monsoon is found to exhibit a distinct three episode cycle of active-break periods along two north-south aligned cross-sections; the first along the west Indian coast, the second through central India up to the plains of west Uttar Pradesh.We use the triplex behavior of the monsoon as a framework to describe individual monsoons from 1979 to 1985. This is done in terms of the initiation or phase, amplitude, duration, and propagation of the individual episodes. Cospectrum calculations between the rainfall and satellite temperature show that significant coherence is only associate with the frequencies corresponding to specific sub-seasonal fluctuating modes of the monsoon, i.e. 30–50 day and 10–20 day modes. The 30–50 day mode exhibits particularly strong coherence. It is shown how the behavior of the rainfall normals can be used to aid the calculation of a synthetic satellite temperature normal. Coherance at the 30–50 day mode in the co-spectrum of the departure time series is also strong; coherence at the 10–20 day mode is weaker but significant. This suggests that although satellite derived temperature is not a universal for rainfall, it could be used as a variable for monitoring the inra-annual behavior of the fluctuating rainfall modes of the monsoon.With 12 Figures