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Republic of Yemen Ministry of Water and Environment National Water Resources Authority
The National Water Resources Authority
in association with the United Nations Development Programme
presents:
A WORKSHOP
ON RAINFALL MEASUREMENT
AND RAINFALL DATA PROCESSING
Sana'a – Aden
2005
National Programme for Integrated Water Resources Management
A WORKSHOP ON RAINFALL MEASUREMENT AND RAINFALL DATA PROCESSING
Presented by NWRA in association with UNDP
Sana’a Suites Hotel, Al Hasaba, 24th and 25th September
A Text on Rainfall and Hydrometeorology
by Dr. Gordon Stanger
comprising:
Topic page Sources of measurement Error 1
Correction by Double Mass Curves 5
Rainfall Measurement 7
Raingauge Networks 10
Physiographic Effects upon the Rainfall 12
Rainfall Variability 17
Rainfall in Relation to Changing Climate 18
Point to Areal Estimation 20
Rainfall Enhancement 23
Raingauge Network Optimization 23
Appendix A: A Note Upon the Correlation Coefficient 26
Appendix B: Rainfall Enhancement by Cloud Seeding 29
Appendix C: Raingauge Costs and Design 32
Pictures: How not to use raingauges! 34
Types of gauges 35
(Practical exercises and directions are in a separate document)
Rainfall and Hydrometeorology
The following notes are intended to provide a sound basis for understanding rainfall, its measurement, and analysis of rainfall data. It is commonly assumed that it is a simple matter to collect good rainfall data. It is not! There are numerous sources of systematic and non-systematic error which require a sound knowledge and dedicated professionalism to overcome.
Likely Errors Most people, even many professionals, have little or no idea of how inaccurate rainfall data is. They are quite happy to quote ‘mean annual rainfall’ (MAR), for example, as ‘2044.61 mm’. In fact, all raingauges collect and register less than the true rainfall, with the average undercatch for a 5-inch gauge being about 7% under normal conditions Larger diameter gauges are more accurate. An 8-inch gauge catches about 5% more than a 5-inch gauge. However, errors in the order of 20% are common, whilst very turbulent winds, such as occur under tropical storm conditions, can cause an undercatch in the order of about 50%. No matter how careful we are numerous sources of error result in a scatter of measured data around a mean that under-represents the true rainfall. Determination of the true rainfall really requires either a large scale weighing lysimeter, a laboratory calibrated infra-red sensor, or a ground level gauge in an anti-splash grid. The latter is still not completely accurate, but provides a close approximation for all practical purposes.
Sources of Measurement Error • Poor Instrumentation.
Raindrops are impeded by cracked and peeling paint, where they collect and evaporate. Blockage of the funnel by dust, dead insects, lizards, etc. is a very common cause of serious undercatch. Failure to keep the rim horizontal also affects the catch – it is designed to catch vertically falling raindrops! A few dents in the gauge are unimportant, but the sharp rim must not be dented or bent. Encrustation of the tipping bucket with in-washed dust can be a major source of error over time. Obviously, the tipping bucket needs to be carefully cleaned, without harming its bearings, i.e clean it gently! (The observer should carry a tooth-brush for this routine task). When replacing the funnel remember to precisely level its rim.
• Calibration Error. In the case of tipping bucket raingauges the instrument should be recalibrated at least annually. A very approximate field calibration may be achieved by slowly pouring a precisely measured volume of water into the funnel, and comparing the theoretical response with the actual instrumental response. For more accurate calibrations CAMA, (Yemen’s Civil Aviation and Meteorological Authority), has recently opened an instrument calibration laboratory. Unfortunately, most software
1
has a pre-set calibration which is difficult to change, but for highly accurate work try to ensure (at the time of purchase) that the calibration can be user re-specified. Superficially one might expect a raingauge to have a linear calibration, but this is not so, particularly with the tipping bucket type. Initial wetting losses are relatively large at low intensities, whilst response-time errors become increasingly important at high rainfall intensities. In practice a second-order calibration curve is adequate, i.e. taking the form: ( ) cIbIaIe rrr ++= .. 2
Where a, b and c are empirical constants, Ir is the ‘reference intensity’ supplied to the instrument, and e is the percentage error associated with that intensity. The above second order polynomial is estimated by measuring the errors over a range of laboratory controlled intensities. Each error measurement is determined as:
%100.r
rm
III
e−
= where Im is the intensity measured by the instrument. After
obtaining the curve for a range of intensities, the experiments are repeated 5 times. The maximum and minimum curves are discarded, and the remaining three curves averaged. This is taken as the definitive calibration curve for that instrument. Note that is only the ( )rIe instrumental error, and is independent of physiographic and microclimatic errors (mainly wind). All three types of error are additive.
• Reading error. Poor manual record keeping, that mixes up ‘no rainfall’ with ‘no data’ has caused more confusion and error than any other problem in the entire history of hydrology. The next most confusing issue is when the decimal point is in the wrong place. The third most common error is caused by the reporter relying on memory before he/she gets the result on paper, and the fourth most common error is caused by faulty manual transcription or computer data entry. Most of these problems should be overcome by the use of dataloggers, but check that the data from the dataloggers is realistic, and set to the correct tipping bucket volume, and instrumental calibration. When reading from the measuring cylinder of a manual raingauge, the precipitation value is taken as the nearest 0.1 mm to the lowest point of the meniscus. If less than 0.05 mm are measured then the day’s record is defined as ‘trace’ even if rain is seen to fall in the vicinity of the gauge. A ‘rain-day’ is defined as ≥ 0.25 mm. Conventionally, the gauge is read at 9.00 am local time, unless it is part of a synoptic station, in which case it is measured six-hourly.
• Evaporation. Evaporative loss from manual gauges can occur either through wetting loss or through storage loss. The former is normally insignificant provided the gauge is read promptly. The latter can be significant in a high temperature-low humidity environment but, again, should not be great if the gauge is in good condition and properly read. Evaporation loss is insignificant in tipping bucket gauges.
2
• Micro-aerodynamic turbulence. This is a function of wind speed and gauge design, and is the main reason for gauge undercatch since raindrops are blown around the gauge rather than into it. Much research has gone into the velocity distribution around a raingauge, and has proved the consistent systematic error involved. Small raindrops are more easily blown off course by turbulence. A ground level gauge with anti-splash protection typically collects 6.6% more rain than a free standing gauge.
• Site-aerodynamic turbulence. Trees, buildings, cliffs and walls create turbulence on a greater scale, which contributes to additional under-catch. In one example, of a lighthouse in Taiwan affected by local up-draughts from the surrounding cliffs, the gauge collected only about a third of the true rainfall! Apply the 30º rule:
Satisfactory Unsatisfactory
30° 30°
• In-splash.
A ground-level gauge reduces aerodynamic losses at the expense of potential surface inflow and in-splash. Experiments have shown that beyond a radius of 90 cm, the in-splash error is < 0.1%. Also, the error is insignificant above a rim height of 7.5 cm. Obviously, to avoid surface runoff the gauge location must be drained. In the case of natural surrounds it is found that splash errors are least from rough grass, higher for a well-maintained lawn, and highest for bare earth or tarmac. Hence the need for a multi-slatted anti-splash grid. Gauges have been known to read anomalously high from sprinkler irrigation!
• Interception. Use double mass curve analysis to see if there is any long term influence from trees growing in the vicinity of the gauge. It isn’t just trees that intercept rainfall. Long grass and shrubs can also seriously reduce the catch, as has been observed in many gauges in many countries.
3
• Crest turbulence. Crest turbulence is a train of vortices that typically distorts the rainfall distribution near the top of a scarp or cliff. Place the gauge at least 30 metres away, or twice the height of the scarp/cliff, whichever is the greater. Do not place the gauge on an isolated summit. Data from such a site will certainly be unrepresentative.
envelope of air turbulence, typically at least 30 metres long. wind
appropriate gauge locations
Medium to high hill with scarp face to windward
• Security. Theft or vandalism is a problem in many areas, especially in remote locations (which often provide the most useful data). If so, deploy the gauge in a secure compound, with a razor wire or electrified wire fence, and a large notice, in Arabic and English, explaining what the instrumentation is for and why it is in everybody’s interests to keep the instrumentation functional. Hold meetings with nearby communities and schools to make sure that everyone has a sense of ownership of ‘their gauge’. Raingauges seem to hold an unfortunate fascination for people with guns. Try providing an alternative target! In the case of brightly coloured or reflective metal raingauges, try painting the exterior of the gauge with camouflage paint, and/or coat the surface with local earth or dust so that it is inconspicuous.
• The Human Factor Laziness is always a potential sources of error. In arid and semi arid areas it is difficult to find reliable observers when there may be something to observe only two or three times per year. Blatant dishonesty can also be a problem. For example, some of the older records for Ibb are faked. There is no way to know how much is reliable and how much is false, so many years of rainfall data are effectively rendered useless. In order to detect false data it is very important to compare independently collected data from adjacent stations.
Use of a ground-level gauge can be used to estimate the error of free-standing gauges. The two adjacent gauges need to be read concurrently for 2 to 3 years. If there is a good relationship a correction curve can be used for several gauges in comparable physiographic contexts within the same or adjacent catchment. Note, the amount of work in reading two gauges is only marginally more than that required for a single gauge. The advantage of accurate data is well worth the effort.
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Free-standing gauge catch
1:1 correction
Ground level gauge catch
CORRECTING BY DOUBLE MASS CURVES In any network of raingauges inspection of the site will indicate that some records are likely to be better than others. Double mass curves are a means of detecting systematic error, and even of correcting it. It is easily done with an excel spreadsheet. The steps are. 1. Categorize the stations into dependable and doubtful data. 2. List a time-series of (A) questionable record, and (B) relatively reliable record. 3. On separate columns, construct a cumulative data listing. 4. Plot cumulative suspect vs cumulative reliable. If it is a uniformly straight line, no
problem. If there is a linear deviation, then apply a correction, as shown in Figure 1:
correcti
Example of a Double Mass Curve
0
500
1000
1500
2000
2500
3000
3500
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300
Cumulative A
Cum
ulat
ive
A+B
+C
Correction
5
Table 1 The double mass curve data used in Figure 1
10-daily cumulative 10-daily cumulative
rain (A) rain (A) rain (B+C+D)
rain (B+C+D)
31 31 107 1073 34 10 117
41 75 141 25811 86 38 29619 105 65 36114 119 48 409
5 124 17 42682 206 283 70923 229 79 78724 253 84 87138 291 129 100040 331 137 113774 405 230 136776 480 218 158564 544 167 175278 622 194 1946
113 735 258 2204267 1002 577 2781136 1138 275 3056
45 1183 87 3143 In an Excel spreadsheet the cumulative data can be easily calculated. First highlight the second numerical cell in the column, say B4, then insert an equation of the form ‘=B3+A4’. ‘Enter’ Then highlight the rest of the column, say B4 to B22. Under ‘Edit’ click ‘Fill’, ‘Down’. Repeat for the second cumulative column (column D). To construct the graph, highlight both of the cumulative columns, including titles. Do this by holding down the ‘Control’ whilst dragging the mouse over the data with the button held down. Click on the ‘Chart Wizard’ icon. Select ‘XY Scatter’. Click ‘Next’. Click ‘Next’ again. Insert Chart Title and Chart Axis Parameters (your choice of text). Select ‘Gridlines’ (if you want gridlines on your chart), and format to your choice. Click on ‘Next’, ‘Finish’. To reformat the chart to your satisfaction click on ‘Chart’, Chart Options’, or click on either chart axis or chart area, and reformat according to your preferences.
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RAINFALL MEASUREMENT Raingauges There are dozens of different designs of raingauges. A larger diameter raingauge is generally more accurate than a smaller diameter raingauge, whilst aerodynamic gauges are generally preferable to cylindrical designs. However, modern raingauges all record very similar results. From the perspective of collecting good data, deploying the raingauge at a secure and physically suitable site is much more important that the raingauge design! Raingauges are made from many materials including fiberglass, copper, galvanized iron, and plastic. Plastic gauges are the cheapest but are not recommended for Yemen. The summer heat at low elevations, or the intense ultraviolet light at high elevations, both tend to denature the plastic so that it becomes brittle and cracks – thereby yielding no information at all! For manually read raingauges, have spare measuring cylinders as backup equipment. They break easily, but are cheap. The limiting factor is not cost; it is availability! It is very frustrating to have needless gaps in the record because of the instrumental replacement time, which may be many months. Most recording raingauges, also called pluviometers, are of ‘tipping bucket’ design, with each tip of the bucket usually being equivalent to 0.2 mm. By measuring the time of each tip the rainfall intensity can also be estimated. Modern pluviometers usually record the data on battery or solar driven loggers which may be downloaded at pre-set intervals, such as every three months. Modern loggers usually have two options: ‘Event mode’ records the time of each bucket tip, whilst ‘time mode’ records the number of bucket tips per pre-set time interval. The latter is more convenient for most purposes, but event mode is more useful for recording detailed frequency-intensity-duration data (as used in flood risk analysis), which is typically represented by a family of curves of the form: 20 yr 10 yr 5 yr
Duration, minutes or hours, also plotted logarithmically
Increasing ARI upwards, i.e. decreasing frequency.
Rainfall Intensity
on a logarithmic
scale
The older style ‘autographic’ recorders have a clockwork or battery driven scroll chart, giving ‘hard copy’ results. Although this style is relatively old fashioned, autographic recorders have high reliability, are easy to use and interpret, do not require a lap-top to download data, and may therefore still be useful in some circumstances.
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Weather Radar (Radio Detection And Ranging)
How can we interpolate the rainfall between point measurements? Apart from guessing isohyets and interpolating either graphically or by computer, weather radar also provides a useful means of interpolation. Weather radar is at least an order of magnitude less precise than a rainguage network. On the other hand, it has the advantage of yielding a spatial impression of a storm’s distribution. This is particularly useful in arid, semi-arid and tropical areas where localized convective storms may yield heavy rain over a storm-track width of only a few kilometers. Hence, where it is used, the radar may record a rainstorm which was completely missed by a widely spaced raingauge network. The principle is that a pulsed radar beam is reflected back to a scanner by raindrops within a particular range of diameters. The reflected power, Pr, is expressed as:
24
6
...
RDnk
Pr λ∑=
where k is a characteristic system constant, λ is the radiant wavelength, R is the distance between transmitter and receiver, and n is the number of reflecting drops of diameter D. As in any radiation equation, the object distance conforms to an inverse square law.
is the ‘reflectivity factor’, which may be equated to a rainfall intensity function of the form A.I
6∑nDB , where A and B are empirical constants, and I is the rainfall intensity in
mm.hour-1. A varies from about 20 to 600, but is typically about 200, (except for snow where A may be about 2000). This variation in A gives the impression of very low precision but, if the synoptic conditions giving rise to the rainfall are carefully monitored and correlated with raingauge results, the overall accuracy may be acceptable. Claimed errors in the estimation of aerial rainfall by radar ranges from about ±10% to ±60%. The maximum range of weather radar is about 300 km, but this is greatly reduced in mountainous areas, where ‘shadow zones’ behind mountain peaks may conceal important rainstorms. In such areas the correlation between radar and raingauge totals is not very good, typically between about 0.66 and 0.78 (cf. the notes on correlation, Appendix A). The chosen wavelength is important because it responds differently to different kinds of rain. The three available wavelengths are the X band (3 cm), the C band (5.0 or 5.7 cm), and the S band (10cm). The shorter wavelength is the most sensitive, being capable of detecting very light rainfall and snow. It accurately reflects the near side of a rainstorm, but cannot ‘see’ to the far side of a storm cell. On the other hand, the S band, which is often used in aircraft, is well suited to detecting storms with heavy rain. It yields less spatial sensitivity, but can see into the storm, not just to its edge. Rainfall Estimation from Satellites Very remote sensing, from an array of 6 geostationary satellites1, is a science which is still under development, but which has already produced important results. The first generation of weather satellites used the Infra-Red and Visible spectrum. High visible reflectance (the ‘albedo’) is caused by more ice crystals in the cloud tops, which
1 The geostationary radius is 36000 km above the Earth’s surface.
8
correspondence to high rainfall. Low infra-red brightness corresponds with higher (colder) cloud tops, and hence also with more rainfall. Any given region must carefully correlate the raingauge data with the combined IR/Vis signal in order to quantify the overall rainfall. This method tends to overestimate rainfall from slow-moving thunder-storms with broad anvils, because of overestimating the storm-cloud’s footprint area. On the other hand rainfall from warm-top stratus tends to be underestimated in coastal and mountainous areas, like Yemen. In 1997 the ‘Tropical Rainfall Measuring Mission’ (TRMM) satellite was launched, carrying a combination of passive microwave, IR, Visible and radar sensors. This provides the best available remote sensing between latitudes 35°N and 35°S (which includes Yemen). Theoretically it could provide good rainfall data for the coastal and desert interior areas but, unfortunately it is of low accuracy in areas of topographically forced updrafts, which are typical of the Yemen mountains. In view of the great geostationary distance the best spatial-resolution is about 4 x 4 km, whilst the time-resolution is about 30 minutes. However, despite the difficulties of interpretation, a combination of raingauge network, radar and satellite imagery is the best available way to estimate the regional or basin-wide rainfall for water resources analysis. Infra-red Attenuation A relatively new method of measuring precipitation, introduced in 1988, is the infra-red attenuation method, in which a horizontal beam of infra-red light is continuously measured. Raindrops falling between the emitter and receiver absorb, refract or reflect the infra-red light; an effect which can be calibrated in terms of the rainfall intensity. The equipment, shown on page 35, has the great advantage that nothing disturbs the raindrop trajectory. There are, however, three disadvantages. Firstly, the instrument is expensive, secondly, it requires a continuous power supply of 20 to 50 watts, and thirdly, like radar, its calibration is heavily dependent upon raindrop size, which can vary from less than 0.1mm to about 5 mm.2
In Yemen it is commonly observed that rainstorms produce raindrops of at least two contrasting diameters, very small and very large. This could be due to either the break-up of large raindrops, or to a difference in the number of cycles of convection within cumulus clouds. Whatever the reason, mixed raindrop sizes makes calibration of radar or infra-red sensors more difficult, and therefore it becomes even more important to have a good network of accurate pluviometers.
2 Water droplets in clouds are typically about 0.01 mm diameter, which is sufficiently small that gravity has little or no effect on them. Raindrops of larger than 5 mm diameter are dynamically unstable and usually break up rapidly. The largest raindrops ever recorded, of 8 mm diameter, nucleated around smoke particles in a Brazilian forest fire.
9
RAINGAUGE NETWORKS It is usually assumed, both in text-books and in practice, that a single national raingauge network will suit all purposes. It is rare to find any discussion of why we want this rainfall data, what kind of network will best suit these needs, and how the network could be optimized to provide the required data. The purposes of raingauge networks are as follows:
1) General overviews of synoptic conditions across the country 2) Water resources assessment and management 3) Crop water requirements, particularly for dryland farming 4) Urban stormwater design 5) Small research networks for specific projects.
The network requirements are different for each case. For a synoptic overview we need typical regional data, without local anomalous details. For crop water requirements we need rainfall data within our farmed area, not in some far away headwater. Similarly for stormwater design we need the rainfall distribution within a specific local (usually urban) area, whilst for specific projects we need a small intensive network to highlight the local physiographic variation in rainfall. Arguably the most important reason for a network is to evaluate the national water resources, for which we need truly representative rainfall over the whole country. This is almost never achieved because raingauges are deployed on a logistic basis, such as ease of access and availability of observing staff, instead of a sound scientific basis. Consequently raingauges are concentrated where people live – in highly populous lowland areas and along main roads. Most of the rainfall occurs in highland areas. Therefore, the apparent regional rainfall is less than the true regional rainfall, which leads to potentially large errors in resource estimation, and to bizarre conclusions – such as a catchment runoff exceeding the apparent catchment rainfall (which is, of course, impossible). Poor network design can easily lead to errors in water resources estimates of between 20 and 50%! This is particularly true in mountainous terrains like Yemen, so it is very important for us to ensure that the network is optimized. For a National Survey it may be sufficient to site gauges within a representative area of about 500 to 1500 km2. For estimating the yield of a water supply catchment a gauge area of about 5 to 50 km2 would be more appropriate, whilst for research purposes a very dense network in the order of 1 gauge per km2 may be needed. In most parts of the world, and particularly in some developing countries, national network densities of >2500km2 per raingauge are common, and even many of the existing gauges are either unreliable or inappropriately sited. Such a density may suffice for low- to mid-relief regions with consistent rainfall, but in most temperate, Mediterranean and tropical mountainous areas the World Meteorological Organization, (WMO, 1994) recommends 100 to 250 Km2 per raingauge, supplemented by higher density networks to evaluate complex physiographic conditions. This guideline is based more upon logistic convenience than upon scientific necessity, and should not be taken too literally! Networks should be optimized on the basis of local data, not global approximation! Some examples of national raingauge network densities are given in Table 2, whilst two assessments of network errors are given in Tables 3 and 4.
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Table 2 Examples of National Raingauge Network Densities Country Average Density Area (km2.gauge-1) (million km2) UK 40 0.24 Slovakia (mountains) 70 0.05 Austria 340 0.08 Irian Jaya (East Indonesia) 520 0.41 Oman 550 0.21 USA 600 9.63 Nepal 620 0.14 Philippines (Luzon &Visayas) 975 0.20 Australia 1025 7.69 Cambodia (Monsoonal SE Asia) 1140 0.19 Thailand 1890 0.51 Yemen 1950* 0.53 Eritrea 2581 0.12 Uzbekistan 6046 0.45 * This is based upon 190 of the registered 325 stations being operational in 2005 (a decrease of 12% compared to the 1995 network). A further assumption is that the network is representative of only 70% of the total land area of Yemen, there being no gauges in the uninhabited desert areas, where effective rainfall is assumed to be zero. A raingauge network density of about 2000 km2 per gauge is inadequate to realistically evaluate complex rainfall patterns in low-rainfall sub-tropical mountainous areas like Yemen. Put another way, the Yemen network needs to be increased four-fold to be comparable with networks in most other countries, and increased ten-fold to provide accurate and realistic rainfall quantities and distributions. Table 3 Rainfall Measurement Errors Associated with Varying Gauge Densities: An Example from Japan (After Kawabata, 1960).
Area per gauge (km2) 280 140 90 70 50 3 Percentage error in the foothills 25 18 13 10 6 3 Percentage error in flat terrain 17 12 9 7 Table 4 Raingauge Performance in Western India (Modified after Gole et al, 1972) The Table gives optimum raingauge density in km2 per gauge. Catchment Type Tolerable error Confidence Coefficient (%) 90% 95% 99% 332 km2, with an altitude 5 6.4 4.1 1.9 range of 342 m, based upon 10 26 16 7.5 3 years of rainfall data 15 55 37 17
900 km2, with an altitude 5 9.2 5.7 2.5 range of 792 m, based upon 10 36 23 10 7 years of rainfall data. 15 82 53 22
Note: Consider the implications of the above table for the raingauge network inYemen!
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PHYSIOGRAPHIC INFLUENCES UPON THE RAINFALL Physiographic parameters, such as altitude, aspect, exposure and continentality, play a very important, but complex role in influencing the distribution of precipitation. Non-specialists often have a naive perception of rainfall as increasing linearly and predictably with altitude. Unfortunately the picture is more complex, but as professional water resources specialists we have an obligation to analyze and quantify these complexities! In temperate maritime environments rainfall tends to be fairly consistent, whereas rainfall in desert environments is so sporadic that neither temporal trends nor physiographic influences may be discernible. An example of the latter environment is the Eastern Oman Mountains, where there is no discernible rainfall-altitude relationship between sea level and an elevation of 750 meters. In another example, from the Negev desert, long-term experiments show that the ‘spottiness’ of desert rainfall does not average out to any consistent value (at least on any time scale that is of interest to us!). Throughout most of Yemen the rainfall is intermediate, i.e. neither fully temperate nor fully desert, so it will be interesting to examine the determinacy of rainfall-physiographic relationships in this mountain environment. In mountainous terrains sub-tropospheric air flow, together with its precipitable moisture, tends to concentrate in preferred pathways of minimum resistance, and hence any rainfall - physiographic relationships that we may quantify must be regarded as provisional and local until and unless its’ more general application can be demonstrated. Particular attention must be paid to valleys and mountain passes where the rainfall distribution may differ significantly from other parts of the highlands. Nevertheless, in practice, numerous empirical relations have been developed around the world. Some examples are given in Table 5, below: Location Linear relationship of R (mm) vs. elevation, h (m)
South Australia R = 500+0.98h Western Scotland R = 700+2.5h Western Canada R = - 416+0.636h* Central Sweden R = 90+0.18h Taiz basin R = ? Sanaá basin R = ? *This is an intermediate relief relationship, obviously not applicable near sea level! Such empirical relationships may be adequate for relatively low altitude intervals of a few hundred metres, but do not use them with greater relief, or over large regions. Also, check to see whether different relationships exist between summer and winter conditions. Note: It is not valid to convert the contours of a topographic map to isohyets using such a linear relationship – although some naïve people have attempted to do just that! Consider the vapour pressure – temperature relationship shown in Figure 2. At an elevation of 3000 metres the temperature is often below 0°C, whereas at elevations around 10,000 metres the temperatures are typically between -30 and -50°C. Clearly at such low temperatures the vapour pressure, and hence the precipitable moisture, is negligible. Consequently, the increasing rainfall with elevation observed near sea level
12
cannot be maintained at higher elevations. Instead, there is always a dramatic reversal of the curve, some examples of which are shown in Figure 3 Figure 2
Water Saturation Pressure vs. Air Temperature
0
10
20
30
40
50
60
70
80
90
100
-5 0 5 10 15 20 25 30 35 40 45Temperature, deg C
Vapo
ur p
ress
ure
(mb)
Figure 3
Rainfall - Altitude Relationships in Mountainous Areas
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 200 400 600 800 1000 1200 1400 1600 1800
Rainfall (mm)
Alti
tude
(m)
European Alps KilimanjaroColumbian Andes Hawaii (eastern)Hawaii (western)
Figure 3 also shows that there is no consistency of the altitude of maximum rainfall, although one may draw a few general conclusions from the published data (other factors being equal!).
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• The elevation of maximum rainfall tends to increase with increasing latitude. • The elevation of maximum rainfall in summer is higher than in winter.
Some examples of the altitude of maximum precipitation are given in table 6, below: Location Latitude (° N3) Altitude (m) of maximum precipitation
Alberta, Canada 51 2360 European Alps 47 2250 Tajikistan, FSU 39 3800 NW Pakistan 35 1500 Jebel Akhdaar, Oman 23 1400 to 2200 Hawaii 20 900 Yemen 13 ? Columbia, Venezuala 8 2200 Kilimanjaro, Tanzania 0 1500 There is some equivocal evidence that the rainfall altitude relationships follow the latitudinal scheme shown in Figure 4. Figure 4 Schematic Altitude-Precipitation Relationships for Differing Climatic Zones
Sub-tropical
Elevation
Increasing precipitation
warm temperate
cold temperate
polar
Most of these relationships are best described by a second order, or even a third order equation, of the form: , which is easy to calculate with off-the-shelf statistical software, provided we have sufficient good quality rainfall data from high
32 dhchbhaR +++=
3 That is, north of the geographic equator. The climatic equator is about 5° south, due to the asymmetry of continental-oceanic distribution.
14
altitude locations. In reality, this is seldom available, and usually requires a purpose designed experimental sub-network of recording gauges capable of operating reliably at low temperatures. This involves substantial effort, but is unavoidable if we are serious about estimating the rainfall yield of mountainous catchments. A study of physiographic influences in Colorado (southeastern USA) showed that altitude alone accounted for only 30% of the total variance, whereas the influence of altitude combined with other physiographic parameters accounted for 88% of the total variance. At various times and in various places, the following physiographic parameters have been analysed:
Tropicality, a latitudinal index – probably quite important in Yemen. Continentality, i.e. distance from the coast along the prevailing wind direction.
This parameter will probably become dominant further eastwards, as the mountains give way to desert.
Trend, the distance parallel to the coast. In Yemen’s case, trend and tropicality may be regarded as effectively synonymous.
Aspect, The orientation of a hillside relative to the prevailing wind. Exposure, the distance from the nearest upwind ‘mountain barrier’ of comparable
altitude to the site in question, and: Rain-shadow, or ‘carry-over’ effect.
Barrier, rain-shadow and carry-over are all illustrated in Figure 5, below
precipitation curve
rain shadow
advective carry over
Barrier distance
Air flow Elevation
15
However many variables are considered they may be assessed by the statistical method of ‘multiple regression’, in which the rainfall is approximated by a ‘best fit’ of the form:
............321 ++++= dxcxbxaR etc.,
Where a, b, c, d, etc are empirically derived coefficients, and x1, x2, x3, etc., are the chosen physiographic variables. Naturally, the exact rainfall also includes an un-quantifiable random element which may be regarded as a residual error. A simple example from an experimental catchment in Alberta (Canada) is:
22 0051.0000265.0155 DBhR ++= Where h is the elevation in metres and DB is the distance (in kilometers) to the nearest upwind mountain barrier. Two other analyses illustrate the typical relative importance of various physiographic parameters in terms of their percentage contribution to the determinate variance.
Region altitude continentality trend aspect South Africa 58 22 5 to 14 8 to 15 South Australia 52 15 31 not calculated The climates of these studies are similar, and it is probable that, in other climates, the importance of altitude is more varied than these data suggest. On the basis of the limited data available, the altitude component of the variance seems to vary between about 30% and 60% in moderate to wet high relief environments. No such analysis has yet been made for Yemen, but it is suggested that, when adequate raingauge data become available, an appropriate multivariate analysis would take the form: )()(2 longelatdchbhaR ++++=
Where a to e are empirically derived constants, h is the altitude, lat is the latitude (more or less corresponding to the trend), and long is the longitude (approximating the continentality). Such a physiographic analysis should work reasonably successfully for the western mountainous areas, where most of Yemens’ population is concentrated. For the Hadhramaut region, and particularly for the eastern Hadhramaut, where the monsoonal influence is strongest, a separate relationship would be appropriate, in which longitude approximates the trend, whilst latitude approximates the continentality. Prior to determining the above coefficients, it would be helpful to conduct an eigenvector or principle component analysis of the rainfall data to establish which physiographic parameters would be most helpful to quantify. Although this is a somewhat sophisticated statistical procedure, it should not be too difficult to achieve using modern statistical software applications.
16
RAINFALL VARIABILITY In addition to the mean daily, monthly and annual rainfalls, a description of the rainfall régime requires some indication of its variability. The indicators in common usage are:
The Standard Deviation, ( )
nxi∑ −
=2µ
σ
The Relative Variability, defined as %100.µµn
xi∑ −
The Coefficient of Variation, %100.µσ
The Inter-Annual Variability, or ‘IAV’, ( ) %100.1
1
−
−∑ −
nxx ii
µ
and the Variability Index, %100.50
1090percentile
percentilepercentile −
Where µ is the mean, is the rainfall total for year i, and n is the number of data points in the distribution (i.e. the number of years for which annual totals are available).
ix
The above expressions are easy to obtain from a spreadsheet, using cell formulae. Some examples are given in the following table:
To calculate…… ….type in the following cell formula
Number of values in a range of cells, n =COUNT(“range”)
Mean value of a range of cells, µ =AVERAGE(“range”)
The standard deviation, σ =STDEVA(“range”)
Absolute value, ii xx −−1 =ABS(“cell i-1”-“cell i”)
Sum, or total, Σ(range of cells) =SUM(“range”)
90 percentile value of a range of cells =PERCENTILE(“range”,0.9)
The quickest way to ‘type in’ a range of cells is to click and drag the cells in question. The coefficient of variation of the first six values of a spreadsheet might therefore be specified as: =100*STDEVA(A1:A6)/AVERAGE(A1:A6)
There is no objective basis for saying that one index is better than another. All have their uses. The ‘standard deviation’, ‘relative variability’ and ‘coefficient of variation’ are all indicators of the scatter of data. As the name implies, the ‘inter-annual variability’ is a good measure of rainfall variation from one year to another, whilst the ‘variability index’ is often used in arid to semi arid areas as an indicator of drought prevalence. For general statistical use the ‘standard deviation’ is most commonly used but, for rainfall, many hydrologists prefer to use the IAV.
17
RAINFALL IN RELATION TO CHANGING CLIMATE An important question that we face this century is how much variation is ‘normal’ and how much may be due to changing climate. Most global climatic models indicate that changes in climate will be least in the tropics, but become progressively more intense in mid to high latitude areas. However there will be local exceptions, particularly in the intensity and distribution of tropical storms and monsoonal systems, caused by increasing sea surface temperatures. On the other hand, increasing mean air temperatures will cause increased drying of soils. In Yemen we may ask ‘what effect, if any, changing climate will have upon the annual advance and retreat of the ‘inter-tropical convergence zone’ (ITCZ). At the local level, detailed effects of global warming are exceedingly difficult to predict with any confidence. Instead, it will be necessary for most areas to make their own assessment by analyzing accurate rainfall records. It is therefore important that (a) continuity of records be maintained, (b) that quality control of the rainfall records be maintained, including correction of systematic errors, and (c) that the data are analyzed rigorously. It is easy to jump to wrong or misleading conclusions! We can only be confident of our conclusions if a medium to long-term well-defined rainfall trend is consistently reported from numerous stations. An anomaly at one station just means that we should be suspicious of the data! In this respect, comparison of graphs of long-term annual or seasonal rainfall, are invaluable. An example is shown below: Figure 6
Annual Rainfall Variation at Aparri, Northern Luzon, Philippines
Aparri Annual Rainfall
1000
1500
2000
2500
3000
3500
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
Year
mm
In this graph a linear regression appears to indicate a declining annual rainfall for this station, but if we remove the two minima of 1997 and 2002, the apparent decline disappears. Other stations in the river basin have a ‘flat’ trend (no change) suggesting that these two anomalies are just part of the natural variation. On the other hand, an effect of
18
global warming is likely to be more variable weather, so we should be guarded about the effects and significance of short-term anomalies.
Even if there is no long term change in the overall rainfall, changing climate can have important effects upon other parameters such as air temperature, pan evaporation, wind speed, etc, so that it is possible to have normal or even slightly increased rainfall, whilst experiencing increasing dry farming conditions. In one example, from south-western USA, the long term trend was towards more intense but more infrequent storms. This resulted in an increasingly serious flooding problem, even though the total annual rainfall remained unchanged.
19
POINT TO AREAL RAINFALL ESTIMATES Estimation of catchment rainfall involves extrapolation from the open area of a raingauge to the total area of a catchment. Such extreme extrapolation, of some 8 to 10 orders of magnitude, has the potential to incur enormous errors, especially if the catchment is large compared to the ‘rainstorm footprint’, or if there is substantial physiographic variation. Both of these factors apply in Yemen. Therefore, areal rainfall estimates should be regarded as, at best, semi-quantitative estimates until (a) the raingauge network density is improved, and (b) the catchment’s physiographic influences have been evaluated.
How should catchment rainfall be estimated? There are about six methods, ranging from the simplest and least accurate, to highly sophisticated computer estimates.
1) The Mean Rainfall The volumetric rainfall = r.A x 103 m3, where r is the averaged raingauge catch in mm, and A is the catchment area in km2. This can work well in catchments of low relief, and with a reasonable raingauge distribution. Note that not all the gauges need to be in the catchment in question, and that raingauges in adjacent catchments can also be used if they are not too distant.
This method is not valid where there are ungauged highlands with only raingauge records from lowland parts of the catchment. In such circumstances, which are quite common, we can end up with huge errors leading to such absurdities as apparent runoff in excess of apparent rainfall (which is clearly impossible!).
2) Theissen Polygons The catchment area corresponding to each gauge is apportioned by constructing lines between each gauge (broken lines), and bisecting these (bold lines). The total rainfall is then This method is well suited to non-mountainous areas. ∑= ii ArTR .
Figure 7
The 5 raingauges, shown as circles, are not necessarily within the catchment, but each has a representative area within the catchment.
20
3) Height Weighted Theissen Polygons Here it is the vertical distance between gauges which determines the areal boundaries, thereby giving a better representation of the rainfall-altitude relationship. The method is well suited to hilly environments, but is tedious to construct. Also, there are untidy ‘triangles of ambiguity’ at polygon triple boundaries. The bold line indicates the division of representative sub-catchment areas Figure 8
Catchment plan
h/2
Catchment elevation
4) Akin Triangles This is another modification of the Thiessen polygon method, in which the area is divided up into triangles. If there is doubt over the validity of data from a particular rainguage, then the triangles can be arranged to give a lesser weighting (i.e. a reduced representative area) to the gauge in question, as in Figure 9, below.
dubious gauge
21
5) Isohyetal Methods Although this is a more subjective approach, hand-drawn isohyets drawn by a skilled hydrologist are prpbably the best means of estimating the rainfall distribution. Problems may arise regarding the average rainfall between isohyets. For example the average of isohyets r1 and r2, shown below, is clearly not a realistic value for the intermediate catchment area because the lengths of isohyets within the catchment are greatly different. In such cases a useful expression for the representative rainfall is
( ) ( )( )ba
barrrR++
−+=32.121 where R is the representative rainfall, a and b are isohyet
lengths within the catchment of interest, r1 and r2 are the isohyet values, and r2 > r1.
r1
r2
Figure 10
catchment area
a
b
6) Computer Methods
These require a uniform grid of point precipitation values to which a ‘trend surface’ can be fitted mathematically, or to which a contouring application, such as ‘Surfer’, can be applied. Raingauge networks are not distributed according to a regular grid, so point rainfalls on the regular grid have to be estimated from the nearest gauges. One
way to do this is by using the expression ∑∑ ÷= 22
1
ii
i
rrP
R where Pi is the rainfall
amount in gauge i, at a distance of ri between the actual gauge and the grid point being estimated.
The gridding technique does not have to be a function of r2. Several other more sophisticated expressions are available, including some with a cutoff beyond a set radius of r. Although this method gives the impression of high sophistication, the human eye is better at pattern recognition than any computer, and hence isohyetal methods are often better, particularly in mountainous terrains like Yemen.
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RAINFALL ENHANCEMENT For over half a century artificial rainfall enhancement, also known as ‘rainmaking’ or ‘cloud seeding’, has been the subject of intermittent research in many countries. America, Australia and Israel have led this research, and useful research, relevant to Yemen, has also been undertaken in the UAE. Despite all this work there is still vigorous argument about whether rainfall enhancement really works. Of the hundreds of experiments that have been done around the world, only about 2% have produced statistically sound positive results. A much larger percentage of experiments may have produced enhanced rainfall, but without scientific proof. The main problems are:
1) It is difficult to demonstrate a small artificial increase in rainfall in a cloud system in which there is a large natural variation in rainfall,
2) The errors involved in instrumental rainfall measurement may be similar in magnitude to the overall gain in artificial rainfall,
3) Highly intensive and expensive research is needed to demonstrate any statistically accurate estimates of the gain in rainfall,
4) The increased rainfall does not always fall where it is needed, 5) In some cases, inappropriate cloud seeding may actually reduce the rain yield, 6) An increase in rainfall in one place may be at the expense of decreased rain
further downwind, 7) The long time-frame required for adequate cloud seeding research is inconsistent
with the short time-frame for results required by politicians who authorize the funding.
In the 1950s to 1970s there was great optimism that weather modification in semi-arid areas could be achieved simply by inserting condensation nuclei into clouds. We now know that the physics of rainfall production in clouds is much more complex than was originally thought. It is not always possible to enhance rainfall from clouds, but under the right circumstances, and with appropriate technology and commitment to fairly intensive research it is probable that some increase in rainfall can be produced. This leaves open the question ‘is such a research effort cost-effective’? An introduction to the technology of rainfall enhancement is discussed in Appendix B RAINGAUGE NETWORK OPTIMIZATION
It is not advisable to keep changing one’s mind about where a raingauge should be sited. Continuity of data collection at a given site is very important, even though the site may not be ideal, whilst analytically impossible problems of interpretation are caused by changing a raingauge position by just a kilometer or two. (Are changes between the old and new data caused by changing weather patterns, differing physiography, or by a differing observer?). In decades past, when most raingauges were of the daily totalizer type, the primary consideration of gauge location was availability of observers. Now that most new raingauges are automatic there is no excuse for locating raingauges anywhere other than in their optimum location.
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Considerations of continuity apart, there are no existing raingauge networks that cannot be greatly improved by deploying new raingauges in appropriate places. New networks need to be designed, not just deployed randomly! In designing a network the objective is to optimize the data to yield maximum information about rainfall distribution. Considerations should include:
Distribution of gauges over the maximum possible range of elevations (subject to avoiding summit turbulence). Include some intermediate elevations to determine linearity or non-linearity of the rainfall-elevation relationship.
For water resources purposes, concentrate on placing gauges in the highland / watershed / headwater areas, where rainfall variation is likely to be highest.
In major catchments try to have gauges at the upstream, mid and downstream reaches.
Have some gauges upwind and downwind of mountains, at similar altitudes to evaluate carry-over, aspect and rain-shadow effects.
Try to have variation in the network density. Have a few gauges relatively close together to evaluate local as well as regional variations.
If you have a scatter of raingauges in lowland areas, with even a short record of rainfall, their relative importance can be assessed by means of a correlation matrix. The idea is to calculate non-zero rainfall correlations (10-daily or monthly data is best). Those stations with the highest mean correlation should be relocated to areas where they will yield lowest correlations. This is because, in any two stations with a high correlation coefficient, the data from one gauge can be used to predict the rainfall in the second gauge, so one or other gauge is essentially redundant. For a small network we can calculate the correlation coefficients on a spreadsheet, and inspect the matrix manually. For large networks this process becomes arduous, but there are specialist computer programs which use more sophisticated methods. There are two commonly used, but similar, computer-based methods known as Inverse Distance Weighting (IDW), and ‘kriging’, or ‘geostatistics’. The basic idea is to draw a ‘semi-variogram’. This is a mathematical description of the relationship between the semi-variance of pairs of observation points such as two raingauges (i.e the dissimilarity between their data), vs. their inter-station distance. (Note, the variance is the square of the standard deviation)
Mathematically, ( ) ( ) ( ) ( )[( ) 2
121 ∑
=+−=
hN
ihii xzxz
hNhγ ] where γ(h) is the semi-variance, N(h)
is the total number of pairs of observations, separated by the inter-station distance, h, and z(xi) are the actual data points. This is a mathematically lengthy procedure, but is made easy by the appropriate commercial software, such as Practical Geostatistics 2000, or Arc GIS Geostatistical Analyst. In practice, one needs a minimum of about 8 stations in the network to obtain a reasonable semi-variogram, whilst many more stations are preferable. The most important part of the semi-variogram is its shape near the origin, which gives a good impression of well-related two sets of data are in relation to their inter-station distance. Where the graph flattens out there is essentially no correlation between the stations, and
24
therefore the raingauge network is too sparse to yield a reliable rainfall distribution. The semi-variogram indicates the optimum inter-station distance (other factors being equal), and also which stations are so close together that one of them needs to be relocated. The ‘h value’ at 95% of the sill may be taken as the distance beyond which there is no meaningful relationship between raingauge records. Figure 11, A Typical Semi-Variogram (of ‘spherical type’) sill range h
γ
Some caution is needed in interpreting the semi-variogram. If there is a significant rainfall gradient across the network, then there will be a higher spatial autocorrelation in one direction than in another; a condition called anisotropy, resulting in a wide scatter of data, and consequent difficulty of fitting a semi-variogram The software can correct for such anisotropy by the use of a linear transformation
25
APPENDIX A: A NOTE UPON THE CORRELATION COEFFICIENT We often need to know how closely related one set of data is to another. The most commonly used measure is the ‘correlation coefficient’, or ‘Pearson Correlation Coefficient’, denoted as ‘r’. This is defined as:
( ))( covariance).( covariance
, covarianceyx
yx or
( )( )
( ) ( ) 5.022
1.
1
1.
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−
−
−
−
−
−−
∑∑
∑
nyy
nxx
nyyxx
In practice we can visualize the correlation coefficients associated with various x-y scattergrams:
y y
x
y
y
y
x
y
x
y
●● ●
● ●● ●●
●
●
0
The correlation coefficient can only lie an r value of 1.0, perfect randomness yvalue of -1.0. Most data sets of related vvalues, and these can be very helpful inall r values at ‘face value’, we must
●
0
●●●● ●●
●
betweields ariab inter be a
26
●
en ± 1.0. T0.0 and a ples in the rpreting theware of w
●
x x
● ●●
●
y
x
y
x
hat is, a perfeerfect anti-co
eal world yiel data. Howevays in which
●
ct crreld soer, b th
●
orreatiome efo
ey
●
●
lationn yielintermre acccan b
●
●
●
●●
x
●●
●
●
●
●
●
●●
●
●
●
●
●●●
●
● ●●
● ●●
●
●x
●●
●●
ydseee
●
●r = 1.
r = 0.
r = -0.96
r is indeterminate
r = 0.90r = 0.03
r = -0.14
r = 0.81r = -0.59
ields an r diate pting mis-
interpreted. In particular, there are three ways in which spuriously high correlation coefficients can be generated:
1. Outliers, or extreme value data points. These have an inordinately high weighting in the calculation of correlation coefficients. For example, compare the 7th and 8th scattergrams, shown above, (third row, left and middle graphs). The effect of adding just one extreme data point is to dramatically increase the correlation from -0.14 to +0.81! This is because there is a reasonably well-defined straight line between any outlier and a tight cluster of points. In view of this we need to have some measure of significance in order to rigorously interpret our correlations, (see below).
2. Closed Number Systems, or the ‘closure problem’. For correlation purposes we need to work with independent unbounded variables, such as the absolute concentrations of dilute salts, A and B, in water. However, the same variables can be forced into a dependent relationship by calculating the relative proportions of A and B. Thus, we could calculate Na and Ca as mg.l-1 in solution, i.e. independent variables, or we could calculate Na and Ca as percentage cations, in which case Ca is forced to lie within the limits of 0 and (100-%Na). As the %Na increases, the % Ca is forced to decrease, and vice versa. Hence the relationship appears to have a strong negative correlation when there may be no significant correlation in absolute terms. Indeed, to take the example further, evaporation along a water course may create a strong positive correlation using concentration data, but a strong negative correlation in proportional terms.
3. Chance. If the number of x-y data points is small then even a very high correlation coefficient may occur just by chance. To reduce the problem to the absurd limit, any two totally random data points, x1,y1 and x2,y2, must yield a correlation of 1.0 or -1.0 since a line can be drawn through all the data without any scatter! Obviously, as the number of random data points increases, the probability of their all falling on or close to a straight line, purely by chance, decreases, and we have more confidence in the significance of a high correlation coefficient.
The way significance is presented in statistics texts, calculator handbooks and statistical software packages, varies, but essentially consists of tables in which the number of ‘degrees of freedom’(in this case, ‘data points = 2’), and the associated correlation coefficient, can be related to the probability of achieving the same correlation by chance alone. Correlations are widely used in hydrology, especially in comparing the hydraulic conditions between catchments, and in optimizing point data collection networks such as raingauges. For example, given a time-series of data from a network of gauges, we can compile a correlation matrix with an entry for each pair of gauges. For many purposes we seek a high correlation between two variables but, in the case of a raingauge network, two gauges with a high correlation coefficient means that one of them is essentially redundant. In other words, a low correlation coefficient gives us more information about the spatial variability of rainfall. Therefore, an optimized raingauge network is one in which the correlation coefficients are minimized. An analytical technique known as kriging (also known as ‘geostatistical optimization’),
27
expands upon this principle by evaluating the relative significance of an array of x-y sample values. Except in the most elementary cases, the calculations are lengthy, and therefore the method is effectively limited to specialized statistical packages for computer. Given a trial set of geographically located data, it is therefore possible to optimize any sampling network (rainfall, transmissivity, water chemistry, etc.), although in reality, sampling or monitoring sites are heavily skewed to certain sites by logistic considerations. Exercise for the reader: A small network of raingauges, A to G, yields the following correlation matrix of annual rainfall data. Which gauge is the least useful, and would improve the network by being relocated?
B C D E F G 0.81 0.68 0.59 0.87 0.55 0.39 A
0.71 0.74 0.88 0.58 0.53 B 0.66 0.72 0.77 0.41 C 0.67 0.51 0.64 D 0.98 0.88 E 0.83 F
Answer :
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APPENDIX B: RAINFALL ENHANCEMENT BY CLOUD SEEDING Raindrops form by water vapour freezing onto nuclei. These nuclei are microscopic, typically between 0.1 and 10.0 microns (µm) in diameter, and are most effective at initiating raindrop formation when they are similar in size and molecular structure, to ice crystals. Nuclei may be:
• natural, such as pre-existing ice crystals, atmospheric sea-salt or particles of clay dust,
• artificial-accidental, such as pollution aerosols like soot and SO2 or its oxidized derivatives, or
• artificial-deliberate, such as silver iodide (AgI), salt (NaCl), and dry-ice (CO2). Silver Iodide in the form of smoke is particularly favoured as cloud seeding material due to its ease of fine dispersion, and to its molecular size and structure which is similar to that of ice. The processes by which raindrops form are still the subject of continuing research. The natural mechanism involves cumulus cloud dynamics, in which the internal structure of the cloud contains convective cells with both updraft and downdraft limbs. In the updraft cells warm low density air is buoyant and rises. As it does so it expands and cools. There are two possible processes, dependent upon temperature. Above 0°C the cloud droplets coalesce until they reach sufficient size for them to fall as raindrops against the updraft. Below freezing temperature, the supercooled cloud droplets continue to rise until they are amongst naturally nucleated ice crystals. Here the air is saturated with respect to water but supersaturated with respect to ice, so the water droplets evaporate and condense onto the ice crystals in the form of a porous low-density granular solid, called grauple (shown in the photomicrographs).
Graupel formation on ice platelets Graupel formation on snow-ice
Photomicrographs courtesy of the USDA, ARS, EMU. As the ice-grauple particles grow, they also begin to fall, eventually melting into large raindrops. For a long time it was assumed that all one had to do was to introduce more condensation nuclei into the cloud, and correspondingly more ice crystalls would grow, thereby creating more rain. We now know that this is oversimplified, and that three approaches to cloud seeding are feasible: static, dynamic and hygroscopic seeding.
29
Static Seeding This is a ground-based technique in which condensation nuclei are introduced into the base of an updraft cell by means of rockets, flares, artillery etc. As the nuclii and water droplets rise, the efficiency of ice crystal formation, and hence of graupel growth, increases. However, there are conditions for this to work:
1) The cumulus clouds have to be relatively cold based and continental (not maritime).
2) The cloud-top temperatures have to be in the range -10°C to -25°C, which can be determined from real-time infra-red satellite imagery.
3) Seeding must be at just the right time, when the availability of super-cooled water droplets is at or near its maximum. Such droplets are eventually depleted, either by entrainment, or by natural precipitation.
Recognition of these conditions requires an advanced monitoring system combined with cloud forecasting skills. Failure to meet these seeding conditions in the past has resulted in some disappointment, and even abandonment of cloud-seeding altogether. Dynamic Seeding Here, the objective is to enhance the vertical air currents, thereby drawing huge quantities of supercooled water droplets into the upper cloud where they glaciate by graupel accretion (as in static seeding). The main difference from static seeding is that so much seed is injected into the cold upper cloud that it induces rapid and intense ice crystallization, which glaciates the rising air. The ensuing latent heat of freezing and vapour deposition warms the air mass, giving it additional buoyancy, and causing accelerated updraft deeper into the troposphere, where cloud-top-temperatures are exceedingly cold. As a result of this faster uplift, more moist air is drawn into the cloud base. Indeed, an abundant supply of cloud droplets (supercooled at higher levels) is an essential factor, which requires a warm cloud base. For dynamic seeding to work also requires an initially strong updraft to carry the droplets into the supercooled region against the downward flow of raindrops. In this method, seed is introduced either from the cloud top, or laterally into the upper part of the cloud where glaciation will occur rapidly. Dynamic seeding utilizes much larger quantities of seed, to achieve up to a million ice crystals per cubic meter. This is about a hundred times the concentration used in static seeding. In theory, the strengthened updraft also results in adjacent downdrafts which stimulate adjacent cumulus towers into more vigorous convection, and hence more rain, although this hypothesis is not well proven. A requirement for successful dynamic seeding is for warm-based maritime clouds with a broad cloud droplet distribution. Where successful, dynamic seeding produces more rain than static seeding.
30
Hygroscopic Seeding Hygroscopic seeding uses finely ground salt particles to attract water by vapour deposition until they reach a size of about 25 to 30 microns, whence they are large enough to grow by drop coalescence. This process I most effective in warm-based maritime clouds. There is no doubt that such seeding can accelerate precipitation, but there is some doubt as to whether the same rain would have fallen eventually without intervention, but as yet the method has not been intensively researched. Rainfall Intensity, as opposed to rainfall amount, shows a reasonably strong correlation with cloud-top temperatures. This relationship is shown in Figure 12. Figure 12 Empirical Relationship between Cloud Top Temperatures (CTTs) and Rainfall Intensity
0
5
10
15
20
25
30
-85 -80 -75 -70 -65 -60 -55 -50 -45 -40 -3Temperature, degrees C
Rai
nfal
l Int
ensi
ty, m
m/h
5
r
31
APPENDIX C. RAINGAUGE COSTS AND DESIGN. Some examples of typical tipping bucket pluviometers (raingauges) and logger costs are shown in the table below. These costs are current for the third quarter of 2005. Bear in mind that accessories, such as mounting plates, software, cables, batteries or solar-panels, technical documentation and casing, could all incur an additional cost of up to about 25%. The cost of agent’s fees, freight, customs and taxes is not included. Currency US $ € UK £ ¥R x 1000 gauge logger gauge logger gauge logger gauge loggerSeba 781 1953 584 1459 425 1063 150 375 Wescor 614 431 459 322 334 235 118 82.8 651 1048 486 782 354 570 125 201 Novalynx 545 95 409 71 297 52 105 18.2 Campbell Scientific A 554 1150 412 860 300 626 106 221 Campbell Scientific B 1850 1150 1381 860 1006 626 355 221 Fairmont 732 275 549 206 400 ~150 141 53 Cassella 1408 1055 768 271 Lambrecht 2083 1559 1136 401 Considerations when Ordering: Numerous raingauges are marketed with a funnel diameter of 6 inches (152mm) or less. These are too small to give accurate results, and are not recommended. An 8 inch (mm) funnel is normally satisfactory except for highly exposed windy conditions. In general, the larger the funnel diameter, the greater the accuracy. Tipping buckets are designed for 0.1, 0.2, and 0.5 mm per tip (occasionally even larger). The bucket size is a trade-off between instrumental error and instrumental sensitivity. 0.2 mm per tip is a reasonable compromise for most purposes. For areas with high rainfall intensities 0.1 mm, and perhaps even 0.2 mm per tip, is not suitable. Plastic gauges should be avoided. If a dust/insect screen is deployed within the funnel, its negative effects should be quantified by insisting upon an independent instrumental calibration. Treat manufacturers’ specifications on accuracy and precision with some scepticism, but as far as instrumentation is concerned, the old saying “You get what you pay for”, applies. The more expensive instruments are made of precision machined metal with high quality bearings in the tipping mechanism. These are more accurate, and last longer. The cheapest gauges are manufactured with mainly plastic components, and may cease to yield good results after a few years, although this may not be obvious from the data. There seems little point in buying the most expensive loggers unless you wish to measure short-term rainfall intensities with ultra-high precision. Higher capacity loggers may allow the continuous collection of data for over a year, but since the instrument will need maintenance at least every three months, such a high capacity logger seems unnecessary. For remote but secure locations, or where access is difficult, either batteries (usually 12V) connected in parallel, or solar panels may be used. For ‘stand-alone’ raingauges, where the logger’s time increment is over a minute, the dataloggers’ average current drain is close to the system’s ‘quiescent drain’, typically around 1.3 mA. On the other
32
hand, if the datalogger is measuring frequently as, for example, in a micrometeorology station, then the average current drain will be very much higher, which must be taken into account in the provision of battery or solar panel capacity. One example, given by Campbell Scientific, depicts the current drain as in the graph, Figure 13, below:
Sensitivity of Current Drain to Scan Rate
0
1
2
3
4
5
6
7
8
9
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Current Drain (mA)
Scan
Rat
e (s
econ
ds)
Warnings: The old style of logger output ports (‘serial’ = RS232) is still regarded as the industry standard by most manufacturers despite the fact that it is incompatible with modern laptops. Serial to USB connecting cables do not necessarily solve this problem as the logger’s software may not support downloading to a USB port, i.e. the standard port on laptops since about 2002. That is, most loggers download to hand-held data transfer devices and to old laptop computers, but not to modern laptops. A further problem is that data logger design is frequently updated, which also requires that the accompanying software is also updated. Some manufacturers are careless in this respect, so make sure that the software you use is the version compatible with the loggers that you purchase.
33
HOW NOT TO USE RAINGAUGES!
▼Keep the rim horizontal!
▲ Protect from vandalism
▲ Open area of insect screen: only 52%! Use environmentally suitable materials ►
34
TYPES OF GAUGES High precision weighing pluviometer Infra-red attenuation gauge
Manual gauge with alter shield
Old style manual gauge
35
