1.Introduction
Moisture-laden air is forced to rise through mountain ranges, which cools it down. The mechanism described above results in precipitation that is tied to the windward slope of the mountain range and usually lasts for a longer period of time. The intensity and amount of precipitation usually increase with the altitude above sea level. On the leeward side of the mountain range, the air is often dry, and on average, low precipitation is recorded there, which in extreme cases can lead to arid areas with the development of dry steppes in some regions of the world. Examples: American Cordillera in the states of Oregon and Washington in the western USA, with high precipitation on the Pacific side with the development of rainforests and dry steppes to the east in the Basin and Range provinces. The desert-like Sinkian region in western China is also due to the isolation of the rain fronts moving in from India by the Himalayas, which previously made the Assam region in northern India on the windward side one of the wettest regions on earth.
2.0 Precipitation parameters
The following parameters of precipitation (with specified units) are important:
2.1. Precipitation depth H
Height of the water column [mm] if the rain were collected in a shallow container with the same surface area (as the collection area). Rain gauges without recording measure the precipitation depth between two readings.
2.2. Rain intensity R
Temporal change in precipitation depth [mm/min] or [l/(s • ha)]. The intensity of rain gauges is determined by the slope of the precipitation total curve.
2.3 Rain duration T
Duration [min, h] from the start of precipitation to the end of precipitation. The precise definition of the start or end of rainfall is sometimes difficult in cases of very light pre- or post-rainfall.
2.4 Drying time Tt
When simulating pollutant loads in sewer networks due to rainfall, the previous dry period [min, h, d] is important, as it determines the accumulation of pollutants on the surface and in the sewer system, which will be washed away during the next rainfall. The dry period is also important for storage management in storage systems.
3.0 Distribution of precipitation throughout the year
This aspect is important for agriculture and reservoir management. In urban water engineering, the entire precipitation pattern, including dry periods, can serve as an input for long-term runoff simulations. Rainfall events characterized only by a precipitation amount and duration are referred to as block rainfall events. Synthetic rainfall events, whose intensity is determined, for example, based on typical measured rainfall patterns or using statistical methods, are incorporated into hydrological procedures (e.g., in rainfall-runoff models) as so-called "model rainfall."
4.0 Point measurement methods of precipitation
4.1 General considerations
Precipitation is usually initially measured directly at a single point (except for direct integral or areal methods, such as optoelectronic laser measurement or weather radar; see Chapter 4.5). Since hydrologists are ultimately only interested in the areal precipitation in a region or catchment area, the point measurement of precipitation must then be extrapolated to an area using statistical methods (see the following chapter).
4.2.0 Rain gauges
Rain gauges or Hellmann rain recorders are used to measure rainfall. Recently, rain gauges with electronic storage of precipitation and/or remote data transmission are increasingly being used. The main specifications of the Hellmann rain gauge are a 200 cm² collection area and a mounting that can be either 1 m above ground (better for measuring snowfall) or at ground level (better for rain).
4.2.1 Rain gauge
The rain gauge measures the amount of precipitation between two readings. The temporal resolution is directly linked to the frequency of readings. Daily readings at the same time are common. Of course, this can only provide the 24-hour precipitation total. A rain gauge that collects precipitation over long periods of time is called a totalizer.
4.2.2.Rain gauge
Rain gauges record the water level in a measuring container over time by transferring the water level to a paper strip via a float and a recorder. After the measuring device is filled, the contents are siphoned off, the display resets to 0, and the filling process begins again.
The rain gauge consists of:
- collecting funnel
- Registration spring arm
- Float vessel float
- Gbag lift tube —housing
- collecting can
4.2.2.1 Rain gauges with electronic recording and/or remote transmission
More modern rain recording devices determine precipitation intensity, for example, by counting the number of drops and store these values in semiconductor memories that can be read by computers. It is also possible to transmit the signals to a central recording system.
4.2.2.2.2 Automatic rain gauge with rocker
This rain gauge measures rainfall using a low-friction rocker. The rocker is designed to automatically compensate for errors caused by incomplete dripping due to surface tension. The rocker holds 2 cm3 of water. Based on a collection area of 200 cm2 (WMO standard), one rocker fill corresponds to a rainfall depth of 0.1 mm. (see http://www.griesmavr.de/ombro.htm) When the rocker is tilted, a non-contact reed contact built into the rain gauge closes without bounce for at least 50 ms. A reed contact consists of a pair of soft magnetic contacts housed in a glass cylinder filled with inert gas. The switching is achieved via an externally applied magnetic field, which is why reed contacts have a long service life, high reliability, and short switching times. This pulse output can be electrically sensed, remotely transmitted, and recorded. These rain gauges comply with the guidelines of the WORLD METEOROLOGICAL ORGANISATION (WMO).
5.0 Problems and measurement errors in rain measurements
Although rain measurement appears technically trivial, it is subject to numerous systematic and observational errors. The more precise quantification of the latter has recently attracted particular scientific interest in connection with the more accurate estimation of the global water balance and its long-term changes due to climate variations caused by increased CO2 in the atmosphere and anthropogenic local changes in soil and vegetation (see the following chapter). Measurement errors arise primarily
- • by changing the wind field (especially when installed above ground).
- • due to wetting losses on the funnel walls.
- * by evaporation from the collection vessel.
- * at very low precipitation intensities below the
- * Response threshold of the measuring device.
The above measurement errors generally result in measured values that are too low. Depending on the type and magnitude of the wind, these can be up to 15% lower than the actual precipitation (see Fig. 4.8). However, if a rain gauge is installed at ground level, where wind problems can be partially eliminated, splash water from the surrounding soil can still penetrate into the funnel if no special measures are taken. To prevent freezing, the instruments are also equipped with electric heaters. Additional technical requirements are placed on snowfall measurements, where even greater systematic capture losses can occur.
6.0.Area measurements of precipitation
6.1 Measurement methods
6.1.1 Optoelectronic laser measurement
The most modern method of rain measurement, but still rarely used due to the technical complexity, involves the direct optical measurement of precipitation in the air using an optical laser beam between a transmitter and a receiver. The presence of rain changes the optical transmittance of the air, which, after calibration, can be used to calculate the intensity of the precipitation.
6.1.2 The weather radar
Weather radar (radio detecting and ranging) is now the most widely used method in meteorology for detecting areal precipitation within a circular area of up to 200 km around the radar station with high spatial and temporal resolution (down to 1 km2 or 5 min). Radar measurements are now carried out in the USA, Europe and Japan. Radar has the advantage over rain gauges of being able to provide comprehensive data over a large area. Although it has so far been used primarily for the qualitative visualization of rainfall, numerous scientific efforts are underway to correlate the IR intensity of the radar signals reflected by raindrops with their actual intensity. Recent comparisons of the rainfall amount determined by radar with that measured by conventional rain gauges have shown values for weather radar that are up to 200% higher. Radar works according to the following principle: A directional antenna emits pulses of electromagnetic radiation with a wavelength of approximately 3 to 10 cm (microwave range). If the radiation encounters a particle in the atmosphere larger than 0.2 mm, it is reflected by the particle. The wavelength does not change. A portion of this radiation is picked up and measured by the radar receiver before the next pulse is emitted. The time between the emitted pulse and the corresponding echo corresponds to the time it takes for the radiation to travel twice the distance to the reflecting object. The radiation travels at the speed of light, so the distance can be calculated. The reflecting particles are water droplets and ice crystals. However, correctly interpreting the strength of the echo is still problematic. It depends on the normal droplet size, the droplet size distribution, the number of droplets per unit volume, their shape, and whether the precipitation is solid or liquid. In addition, the difference between the height at which the radar is measuring and the ground level must be taken into account, as droplet size can change due to evaporation or coalescence (the coalescence of droplets). Therefore, radar readings must always be calibrated with rain gauge data. Remote sensing data is not yet accurate enough to replace ground-based instruments, but it can be used for forecasting.
6.1.3 Satellite measurements
Infrared sensor satellite measurements have so far been limited to the visualization and classification of clouds rather than being suitable for the direct quantification of precipitation. However, since 70% of the Earth consists of hydrologically inaccessible oceans, where the majority of clouds form, the analysis of such satellite images is important, if only for tracking the global atmospheric movements of large cloud fields. Satellite measurements represent the only systematic means of determining precipitation over the oceans and thus three-quarters of the Earth's surface. Satellite images are the main source for long-term observations of precipitation and global climate change. In contrast to radar, satellites are passive remote sensing systems that measure the amount and wavelength distribution of emitted and reflected solar radiation. The images are interpreted using various approaches: First, attempts are made to determine cloud morphology in order to identify potentially precipitation-producing clouds. Data from a geostationary satellite makes it possible to observe the temporal change in the vertical extent of clouds, which is particularly useful for convective cloud cover. In addition, images in the infrared and visible spectrum are evaluated together. Infrared images reflect the radiation measured by the satellite in the wavelength range from 0.7 to 14 mm. Using the Stefan-Boltzmann law (see Chapter 5), which establishes a relationship between the temperature of a body and the wavelength of the radiation it emits, the temperature, the so-called "brightness temperature," of the cloud surface can then be determined. The relationship between surface temperature and cloud height can then be used to determine the type of cloud and thus the probability of precipitation. The exact relationships, however, are still controversial. Satellites can therefore provide a rough estimate of the amount of precipitation with low spatial and temporal resolution, but precise data are not available. Another problem is that only indirect determinations can be made, since the Earth's surface is obscured by clouds.
7.0 Regionalization of point precipitation measurements
To determine the total areal precipitation in a region or catchment area, the precipitation data Pj measured at discrete locations must be extrapolated to the entire catchment area to obtain an average value P. Three main approaches are used for this. This is also referred to as regionalization.
7.1 The simple arithmetic mean precipitation
In this approach, the mean precipitation P is simply the simple arithmetic mean of all measurements Pj (i = l,n) P=l/n-£PI(4.1) This method has the disadvantage that, for spatially unevenly distributed stations, the arithmetic mean P tends toward the measurements at the more closely spaced stations, while the measured values from the more isolated stations contribute less to the mean. However, in larger catchments with limited access (mountain regions), these are often the stations of most hydrological interest.
7.2 Thießen polygon method
In this approach, the mean rainfall P is a so-called weighted arithmetic mean of all measurements P; (i = l,n) i(4.2) where A;= area of a Thießen polygon around station i AT= total area of the area = £ Aj The Thießen polygons are constructed as follows: 1) Draw the stations cartographically, preferably on transparent paper (only when measuring the areas using mm paper). 2) Connect a station i with all its immediate neighbors with a straight line. 3) Erect perpendiculars on the midpoint of each connecting line between two stations. 4) Mark the intersection points of these perpendiculars around a station i. These define the vertices of the required polygon around this station i. 5) Connecting the vertices of the polygon produces the desired representation. 6) Measure the area Aj by placing the transparent polygon map on mm paper (or measuring using a planimeter) (Fig. 4.15). Note: For stations outside a given area, partial polygons often result.
7.3. The isohyetic method
The isohyetical method is similar to the Thießen method and is an area-weighted averaging procedure. However, first, using a standard computer plotting program (e.g., SURFER™), the precipitation contour lines for the area are drawn (the so-called isohyets) (Fig. 4.9). The areas between the individual contour lines are then determined planitarily and the weighted mean is calculated using Equation (4.2). Exercise 4.1: Evaluation of precipitation data in a catchment area. The second column of Table 4.1 shows the Pj values measured at 13 stations, and Fig. 4.9 shows the cartographic location of the stations with the edges of the catchment area. Calculate the so-called effective uniform precipitation depth (EUD) for the area using (1) the arithmetic method and (2) the Thießen polygon method. Solution: (1) Arithmetic mean: P = l / n • £ P; where n =7 includes only the stations that are located within the catchment area. From the two values
Figure 20-8 Isohyets for Calculating the Precipitation EUD of a Drainage Basin (Workcd Example 20-1). Poly-EUD of a Drainage Basin. Isohyets, or lines of equal jons constmcted on the basis of the gauge-precipitation valuesprecipitation, drawn on the basis of the gauge-precipitation shown witllill the drainage basin (this is the diagram presentedvalues shown. The isohyetal method is sljghtly more accurate in the Iowar left portion of Figure 20-6).than the polygon method, but vastly more time consuming. Fig. 4.9: Locations of the measuring stations and construction of the Thießen polygons (left) and construction of the isohyetes (right) (Watson and Burnett, 1995) P; Column 2 gives: P = 3.626 cm (2) Thießen polygon method: P = l / AT • £ A; P; where the individual polygon areas A; (i = l,13) are listed in the third column and the weighted precipitation A; P; / AT in the fifth column. The sum of this column is therefore P = 3.528 cm In this case, both methods give similar values, which is due to the relatively uniform distribution of the stations.
Tab. 4.1: Evaluation of precipitation data using the simple arithmetic mean method and Thießen polygons (Watson and Burnett, 1995).
Station No.precipitationpolygon areaweighted area (AJweighted precipitation
[cm][km2][%](PJ [cm]
16,7516,111,80,797
25,7116,812,30,702
35,214,43,20,167
44,562,21,60,073
54,4519,514,30,636
62,913,82,80,081
72,7515,111,10,305
82,3614,510,60,250
92,0117,412,80,257
101,3516,312,00,162
111,465,74,20,061
121,220,50,40,005
131,084,13,00,032
Totalis3.21*13136.41003.528
7.4 Statistical interpolation methods (Kriging)
Statistical interpolation methods are based on the areal analysis of precipitation data and the subsequent interpolation of values at unmeasured grid points within the measurement region. They are also known as Kriging (Appendix 2.4) or optimal interpolation and calculate the interpolated value P(x) at point x in the area using (4.3) where yt are weighting coefficients (the Kriging coefficients) obtained by solving a system of linear equations whose constant terms are themselves calculated using an area correlation (the so-called semivariogram, see Appendix 2.3) of the measured data. Although Kriging methods are mathematically complex, there are now common PC computer programs, such as the SURFER™ program, that simplify the hydrologist's work. Many recent scientific studies show that kriging methods are the most reliable of all the methods discussed, especially when so-called trends are evident in the data. Furthermore, the kriging method also allows for an evaluation of the statistical error for the interpolated value P(x).
7.5 Statistical significance of precipitation measurements
A meaningful hydrological analysis of a region and the estimation of potential precipitation over a longer period of time is obviously better (1) the more measuring stations N there are in the area (2) the longer the period T (usually years) is over which the measurements were taken. Complex statistical calculations show that the second criterion is more important than the first, i.e. it is more advantageous to measure with a few precipitation stations over many years than to install a dense observation network for just a few years. These considerations are important for the economical operation and optimization of a station network.
7.6. Global geographical distribution of precipitation and climate zones of the Earth
The typical climate zones of the earth are both indirectly and directly determined by the decreasing effective solar radiation (E ~ cos (p) with increasing geographical latitude (latitude (p) from the equator to the pole). More important than this direct influence, however, is the indirect effect of the varying radiation on the large-scale movements of the atmosphere and ocean currents with their effects on the global geographical distribution of precipitation.
7.7 Global atmospheric circulation
Global atmospheric circulation is primarily determined by the superposition of two fundamental effects: 1) The occurrence of three zonal (north-south running) large-scale convection cells that extend over a 30° latitude interval. These are the so-called Hadlev cells (see Fig. 4.10). Due to the continuity of the flow movement, the upflow and downflow areas of two neighboring cells are always identical. Since the greatest heating and consequently the strongest upwelling of air masses occurs at the equator, the large-scale flow direction of all convection cells is defined once and for all. 2) The Coriolis force caused by the Earth's rotation (= an apparent force that occurs when a body moves in a radial direction in a rotating system), which causes northward movements in the Northern Hemisphere and southward movements in the Southern Hemisphere to be deflected eastward. The reverse applies to southward movements in the northern hemisphere, etc. (Figs. 4.11 and 4.12). Due to (1) and (2), typical wind directions with an approximate azimuth of 45° occur, particularly over the oceans (which point toward the equator near the equator due to the surface currents of the tropical Hadley cell), which was already exploited by sailors in the Middle Ages when crossing the world's oceans. Ultimately, Columbus's reaching of the American continent was only possible thanks to the southwest-flowing trade winds (Fig. 4.12).
7.8 Climate zones of the Earth
On Earth, the following climate zones can be distinguished according to the ratio of the water balance variables precipitation and potential evaporation:
Precipitation exceeds evaporation year-round (hN > hv). These conditions are found in Central Europe, Japan, and the eastern United States. Annual mean precipitation also exceeds evaporation, but there are longer periods where hN < hv (Southern Europe, South Africa). Evaporation exceeds precipitation year-round, but there are periods where hN > hv (Central and Southern India, Southwestern United States). Evaporation exceeds precipitation year-round (hN < hv) (desert regions of the subtropics, Inner Asia). Summer temperatures are insufficient to completely melt snow and ice (polar regions, glacier zones in high mountains).
The Earth's large-scale climate zones are an indirect consequence of atmospheric circulation and, in particular, the fluid and thermodynamic properties of Hadley cells. The upwelling regions of the convection cells are enriched with water vapor, resulting in higher levels of cloud formation and precipitation (Figs. 4.15, 4.16). The opposite is true for the downwelling regions of the convection cells, where there is a precipitation deficit. For the two tropical Hadley cells, the Earth's main desert regions are located in the corresponding latitude interval around 30° (Fig. 4.17).
South Latitude (degrees) North 80 60 40 20 0 20 40 60 80 -D 80
Adapted from J.P. Pelxoto and M.A. Kettani, “The Control of the Water Cycle.” Copyright© April 1973 by Sclentiflc American, Inc. Fig. 4.15: Global mean latitudinal distribution of effective precipitation. Note the correlation with the latitude of the upwelling and downwelling areas of the Hadley cells.
4.4 Temporal Variations in Precipitation 4.4.1 Seasonal Variations Seasonal variations in precipitation are of great importance to hydrologists, but even more so to farmers. They are usually presented as bar charts for total monthly precipitation and—at least when averaged over several years—are characteristic of the respective climatic region. For the USA, which, due to its size, forms a subcontinent itself, the diagrams shown below are derived for the individual regions.
N^ol mn,hly di.»ibU«on of p,.cipi«..ion in «,. Uni,.d Sa« (In.l 11 !„. - 25.4 mm). (US En.ironmen.al Do« Servke.l
Fig. 4.18: Monthly variations in precipitation in local regions of the USA (Bedient and Hubert, 1988). US NATIONAL PRECIPITATION, 1/98-12/98 PERCENT AREA AND PRECIPITATION INDEX
Fig. 4.19: Mean monthly precipitation index for the USA (http://www.ncdc.noaa.gov/ol/climat e/research/1998/ann/ann98.html)
National Climalic Dala Center, NOAA
PRECIP. INDEX [
AREA DF1Y
Tab. 4.1: Variation of monthly precipitation at the Scheyern station near Munich
Month/YearAverage 1947 - 1993 1994 1995 1996 1997 1998 1999
January52 mm61 mm66 mm12 mm2mm21 mm— mm
February48 mm35 mm47 mm48 mm48 mm23 mm— mm
March47 mm71 mm71mm16 mm61 mm54 mm— mm
April55 mm153 mm44 mm15 mm41 mm36 mm— mm
May77 mm67 mm89 mm103 mm25 mm54 mm— mm
June108mm68mm130mm47mm104mm145mm— mm
July106mm76 mm59 mm39 mm140 mm107 mm— mm
August85 mm98 mm86 mm133 mm76 mm41 mm— mm
September65 mm85 mm58 mm42 mm25 mm129 mm— mm
October51 mm31 mm13 mm47 mm68 mm194 mm— mm
November55 mm51 mm57 mm75 mm25 mm114 mm— mm
December 56 mm 65 mm 50 mm 34 mm 69 mm 17 mm— mm
Annual total 805 mm 861 mm 770 mm 711 mm 684 mm 935 mm— mm
The data from which the mean monthly precipitation totals from 1960 to 1993 were calculated were measured at a station of the German Weather Service (DWD) in Scheyern.