Mean Areal Rainfall Research Articles

Comparisons of gauge and satellite rain estimates for the central United States during August 1979

Rainfall estimates, inferred from the thermal infrared channel of the Geostationary Operational Environmental Satellite‐East (GOES‐East) for August 1979, are compared with gauge rainfalls over hourly and daily time frames for area‐averaged amounts and point values. The area of interest is a 3.6×106 km2 region in the central third of the United States. Over the month the satellite rainfalls tend to be smaller by 20–40% than the corresponding gauge amounts, but mean sampling errors inherent in a gauge network of this density (1 gauge/4000 km2) are estimated to be minimally 100% of the areal mean rainfall. Root‐mean‐square errors are approximately 1 mm for daily and 0.1 mm for hourly area‐averaged rainfalls and are 14 mm for daily and 5 mm for hourly point rainfalls. Satellite‐gauge differences of daily (hourly) point values can be large, but 50% of the satellite amounts are within ±4 (±2) mm of the gauge amount, and 90% are within ±20 (±8) mm, reinforcing the fact that the satellite‐derived rainfall is an area‐averaged rather than a point estimate of rain amount. Timing of rain events is comparable for daily area‐averaged satellite and gauge data. However, hourly area‐averaged gauge data exhibit considerably more short‐term fluctuations than the hourly satellite data. For the two satellite algorithms tested, the streamlined technique requires the least computation time (10% of that needed by the life history technique) and shows a little difference in its comparisons with the gauges.

A simple and efficient conceptual catchment model allowing for spatial variation in rainfall

ABSTRACT In developing countries, the use of mathematical models in hydrological forecasting is increasing, making for optimal planning and management of water resources systems. Such application, however, faces different problems. One of these problems is that computers may not be available. Even if they are available, computer time is expensive. Hence, there is a need for simple models which can be run on pocket calculators or which are computer-time efficient, with high accuracy. This paper presents a rainfall-runoff model with a very simple structure. With simple algorithms, the model can be used with computers with small memory capacity. A method for estimating mean areal rainfall, representing the detailed distribution of rain over an area, is also put forward. The model has been applied to a small, mainly rural catchment in northern Tunisia for both single rainfall event simulation and continuous simulation for longer periods. The outcome was most encouraging. In the present paper the measured and ...

COMPARING SOME METHODS OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT: A comparison of 13 different methods of estimating mean areal rainfall was made on two areas in New Mexico, U.S.A., and one area in Great Britain. Daily, monthly and yearly rainfall data were utilized. All methods, in general, yielded comparable estimates, especially for yearly values. This suggested that a simpler method would be preferable for estimating mean areal rainfall in these areas.

Analysis of the effects of orography on surface rainfall by a parameterized numerical model

A numerical model is formulated for estimating the spatial distribution of rainfall on the meso-local scale. Widespread rainfall not influenced by convective processes is considered. The observed rainfall on the soil surface unaffected by orographically produced contributions and meteorological parameters on the large scale are used as inputs to the model. It is then used for computing the spatial distribution of rainfall incorporating the orographic effects in a parameterized form. The model is applied to four rainfall events over an area of the Upper Tiber River, central Italy, basin and the results compare reasonably well with the observations in each event. The error in computing mean areal rainfall ranges in magnitude from 1% to 15% and further for each event at least 75% of the pointestimates has an error of less than ± 30%.

An analytically derived distribution function for mean areal rainfall

Both temporal and spatial information on rainfall distributions are important in various types of hydrologic studies concerning the determination of runoff characteristics. In reality, rainfall is measured at a point. Hence, for practical purposes, it is necessary to establish some relationships for the transformation of point rainfall at a fixed location to average rainfall over a catchment area in order to provide a more reliable input for rainfall-runoff models. The least equivocal method for deriving values of areal correction factor seems to be directly from frequency curves of areal and point rainfalls. Knowledge of the probability distribution of mean areal rainfall, therefore, is of paramount importance in solving this complex practical problem in hydrology.

Variation of Rainfall Distribution in and around Japan in July

The purpose of this paper is to clarify the regionality of rainfall fluctuation in and around Japan (Fig. 1) in July. Using the data of monthly precipitation during 1951-1980, “cluster analysis” based on similarity of interannual fluctuations was applied (Fig. 2). The area was divided into five regions (A-E) which were distributed from north to south (Fig. 3). Fluctuations of areal mean rainfall of the regions were compared with each other from the the viewpoint of anomaly.A change of interrelation on rainfall fluctuation among the regions was found at the latter half of 1960's (Figs. 4 and 5), which means a turning point as to geographical pattern in rainfall fluctuation.Characteristics of year-to-year vasiation of anomaly distribution during 1951-1971, the former period, was northward or southward gradual movement of the areas with +sign and -sign anomaly (Fig. 7, Table 1).During the latter period (1967-1980), the following two patterns of anomaly distribution appeared frequently (Table 2), being connected to the appearence of fronts at the 850mb level (Fig. 6).(I) +area: Honshu, Shikoku and Kyushu.-area: Over Hokkaidou and Ryukyu Islands.(II) +area: Over the sea of Okhotsk and Ryukyu Islands.-area: From Hokkaidou to Kyushu.From these facts, it is found that the two periods are different each other on the variation mode of rainfall distribution in and around Japan in July.

An application of network design procedures for redesigning Kizilirmak River basin raingauge network, Turkey

ABSTRACT Recently developed rainfall network design techniques are discussed and compared. Present day hydrological studies require high levels of accuracy from collected data. Also, scientists need to know the degree of accuracy of the information they use. The existing rainfall network in the Kizilirmak basin must be redesigned in order to meet the required level of accuracy preset by rainfall data users. The three following techniques were applied: optimum interpolation procedure which is a flexible method; variance of mean areal rainfall; and the analysis of variance. The existing network of 52 gauges is redesigned so that the network will have an average root mean square error (rmse) of ⩽ 32 mm and the percentage of the area with rmse > 36 mm is limited to 10%. It is found that the proposed criteria are satisfied by a network of 53 gauges of which eight were newly established and seven of the existing ones removed.

The Large-Scale Circulation and Heat Sources over the Tibetan Plateau and Surrounding Areas during the Early Summer of 1979. Part I: Precipitation and Kinematic Analyses

The time evolution of the large-scale precipitation, low-level (850 mb) wind, moisture and vertical motion fields over the Tibetan Plateau and surrounding areas during a 40-day period from late May to early July 1979 is studied based on the objectively analyzed FGGE Level II-b data set. During this period the general circulation over East Asia undergoes a distinct change characterizing the onset of the summer monsoon circulation. The Tibetan Plateau exerts profound orographic and thermal influences upon the low-level wind field. The inflow towards the eastern part of the Plateau with a marked diurnal change in its intensity is the most prominent feature of the low-level wind field. The areas of organized precipitation are well related to synoptic systems seen in the 850 mb flow: the quasi-stationary Burma-India trough, the disturbances forming on the trough, the “Mei-yü (Baiu)” front, and the “transverse trough” extending eastward from the Plateau. There is a sharp contrast between the western and eastern Plateau in terms of precipitation and moisture distributions. The eastern Plateau acts as a huge chimney funneling water vapor from the lower to the upper troposphere. Maxima of 40-day mean upward velocities are located above the eastern Plateau, above the Assam-Bengal region and along the Mei-yü frontal zone. The vertical motions above the Plateau are more upward in the evening than in the morning. The reverse is true in the surrounding areas. Detailed examinations of daily values of the areal mean vertical p-velocity, mixing ratio and rainfall are made for four heat source regions (the western Plateau and adjacent areas, the eastern Plateau, the Yangzi River, the Assam-Bengal region) as a preliminary to the discussion of heating mechanisms operating in these regions.

Assessment of »True« Variability of Small Rainfall Events in a Small Mountainous Watershed in the Summer

The standard error of mean areal rainfall was calculated for various densities of rain gauge network in a small mountainous watershed in the summer of 1978. It is shown that a) the optimum gauge density required to assess mean rainfall is about 3 gauges/km2; b) the »true« variability in the spatial distribution of rainfall decreases with increasing rainfall amount; and c) the relationship between »true« variability and rainfall volume is linear in that watershed.

A study of the errors in the areal mean rainfall arising out of missing observations

This is an experimental study of the mean errors in the areal rainfall in situations of missing observations. The area selected is Amravati district in Vidarbha having a very good network of raingauges and the periods considered are the months June to September and the monsoon season. Errors in the areal rainfall have been examined separately in each of the five situations when anyone, two, three, four or five stations are missing in each year, and histograms of the percentage relative error have been given, and extreme values of the percentage relative error have been brought out. Limits on the deciles of the error distribution have been obtained. Percentage Root Mean Square Error (RMSE) has also been computed for the typical monsoon month, July, and for the monsoon season for each of the situations of one, two, three, four and five stations missing randomly in space and time; the same for July is found to vary from 2.8 to 8.8 per cent as the number of missing observations varies from one to five, and for the season 2.2 to 7.0 per cent. Finally the percentage RMSE has been computed in a situation when the number of missing stations (zero to five) is random and the missing of stations is random in space and time; this error for the typical monsoon month, July, is 6.2 per cent and for the monsoon season, 5.6 per cent.

Measurement of Convective Mean Rainfall over Small Areas using High-Density Raingages and Radar

Abstract Techniques of measuring area-mean convective rainfall over small areas (<2000 km2) are investigated using data from several gage-radar rainfall measurement studies. These data suggest that for low gage densities (≲1 gage per 250–300 km2) and for some climates (e.g., Illinois) that gage-radar area-mean convective rainfall measurements may be more accurate than gage-only measurements. The same result was not supported by data from another climate, suggesting that changes in raincell size and rain evaporation rate may affect the results. Further studies are needed to verify these suggestions. The data indicate that radar adds little to gage measurement of mean areal convective rainfall for gage densities of ≳1 gage per 100–200 km2. Use of a space-variable gage adjustment of radar data is seen to be preferable to use of an averaged single adjustment factor, except in cases involving extrapolations of the space-variable adjustment factor. For such cases, e.g., over large lakes or outside of gage netwo...

A RAPID METHOD OF ESTIMATING MEAN AREAL RAINFALL1

ABSTRACT. A special case of generalized trend surface analysis is examined. This includes a linear surface. It is shown that for most hydrologic problems this case determines mean areal rainfall sufficiently accurately. Based on this conclusion, equations for rapid computation of mean areal rainfall are derived for this linear case. Results of the linear case are compared with other traditional methods of estimating mean areal rainfall.

COMPARISON OF THE METHODS OF ESTIMATING MEAN AREAL RAINFALL

A comparison of nine different methods of estimating mean areal rainfall is made. Five areas from three continents of the world are selected for application of the methods. The methods are utilized to estimate mean areal rainfall for daily, monthly and yearly values. It is shown that all methods generally yield comparable results, and that for most hydrologic problems simpler methods of estimating mean areal rainfall are sufficiently accurate-an observation contradicting the traditional belief.

The design of rainfall networks in time and space

A methodology for the design of precipitation networks is formulated. The network problem is discussed in its general conception, and then focus is made on networks to provide background information for the design of more specific gaging systems. The rainfall process is described in terms of its correlation structure in time and space. A general framework is developed to estimate the variance of the sample long‐term mean areal precipitation and mean areal rainfall of a storm event. The variance is expressed as a function of correlation in time, correlation in space, length of operation of the network, and geometry of the gaging array. The trade of time versus space is quantitatively developed, and realistic examples are worked out showing the influence of the network design scheme on the variance of the estimated values.

The application of the analysis of variance to mean areal rainfall estimation

The estimation of mean areal rainfall for a region and a measure of its precision is shown to be closely related to a statistical model expressing point rainfall as a linear function of certain parameters to be estimated. Different assumptions about the nature of the rainfall surface require the estimation of different sets of parameters and lead to different measures of the precision of mean areal rainfall. If this measure of precision is to be used to examine the adequacy of a network of raingauges, then it is shown that conclusions may be very different according to which set of initial assumptions are adopted. It is suggested that two components of variance are required to express the precision of mean areal rainfall estimates: σE 2, a measure of the ‘residual’ variation in point measures of rainfall, and σP 2, a measure of the variation in point rainfall from period to period.

SPACE‐TIME VALIDATION OF A THUNDERSTORM RAINFALL MODEL1

ABSTRACTA probability model for predicting the occurrence and magnitude of thunderstorm rainfall developed in the southwestern United States was tested in the metropolitan Chicago area with reasonable success, especially for the moderate to the extreme runoff‐producing events. The model requires the estimation of two parameters, the mean number of events per year and the conditional probability of rain given that an event has occurred. To tie in the data from more than one gage in an area, an event can be defined in several ways, such as the areal mean rainfall exceeding 0.50 inch and at least one gage receiving more than 1.0 inch. This type of definition allows both of the model parameters to be obtained from daily warm‐season rainfall records. Regardless of the definition used a Poisson distribution adequately described the number of events per season. A negative binomial distribution was derived as representing the frequency density function for rainfall where several gages are employed in defining a storm. Chicago data fit both distributions very well at events with relatively high return periods. The results indicate the possibility of using the model on a regional basis where limited amount of data may be used to estimate parameters for extensive areas.

ESTIMATION OF RAINFALL IN SPARSELY GAUGED AREAS

Synopsis In areas of accentuated relief, some of the basic assumptions made in the use of standard methods of assessing areal mean rainfall are often untenable. It is shown in this paper, that, not only does topography affect the actual rainfall distribution, but that the areal variability, measured as the correlation between any two points, is also dependent on the relief. Two methods are used to show this. Once method compares the areal variability of a flat area to one of accentuated relief, while the second method relates areal variability to topographic factors using a multiple regression technique. The conclusions reached are then used for three purposed. The first is to develop a method of ascribing objectively areas or points to a particular raingauge, taking into account the nature of the terrain. The second is to establish a procedure for estimating the rainfall at ungauged points, by taking into account the rainfall at a selected nearby rainguage and the topographic situation of the points, and...

Optimum density of rainfall networks

Techniques of harmonic analysis and the concepts of distributed linear systems are used to study the sensitivity of peak catchment discharge to the characteristic spatial variability of convective and cyclonic storm rainfall. Application of the sampling theorem leads to quantitative general relations for optimum rainfall network density for flood forecasting purposes. Specification of network density for the study of long‐term, catchment‐average rainfall is accomplished by considering the long‐term point rainfall as a homogeneous random variable to be sampled spatially. Incorporation of catchment dynamics into the design of flood forecasting networks reduces the number of gages needed when compared with that obtained solely through consideration of precipitation variability. In many studies little advantage is gained by utilizing more than two properly located stations for the determination of long‐term areal mean rainfall.

Distribution of excessive rainfall amounts over an urban area

Data recorded over a 10-year period from a network of 11 recording rain gages was used in a study of the distribution characteristics of excessive rainfall amounts over the 10-square-mile urban area of Champaign-Urbana, Illinois. All storms were used in which one or more rain gages recorded an amount equalling or exceeding the 2-year return period value of point rainfall for durations of 30 minutes, 1 hour, 2 hours, 3 hours, 6 hours, 12 hours, and 24 hours. Factors investigated include: the frequency of excessive rainfall amounts within the area compared with the frequency at a given observation point within the area; the percentage of the urban area experiencing excessive rainfall amounts during individual storms and the frequency distribution of this percentage; the adequacy of a single point to define the frequency distribution of areal mean rainfall within a small area; the frequency with which excessive amounts for 30-minute to 24-hour periods occur within the same storms; and urban influences on the distribution of heavy storm rainfall. Based on the 10-year sampling period, results indicate that twice as many excessive rainfall amounts occur within a 10-square-mile area compared with the number recorded at specific points; on the average, the percentage of the 10-square-mile area experiencing excessive rainfall amounts increases with increasing storm duration; the majority of the excessive amounts for duration of 30 minutes to 24 hours occur in the same storms; a point rainfall record is a satisfactory index of the areal mean rainfall frequency distribution in a 10-square-mile area; and urban influences, if present, are not of practical significance.

RAINFALL RATES IN FLORIDA HURRICANES

Hourly rainfall amounts from 16 hurricanes are plotted relative to the center of the storm to obtain the mean areal rainfall rates around the storm. The rates ahead of the center are greater than those to the rear, but the differences in rates between the right and left sides are not large. The frequency distributions of various hourly amounts are tabulated for stations within about 100 miles of the center. Finally, the latent heat of condensation is calculated from the mean areal rainfall data. This is found to be about 6 × 1026 ergs per day.