3.1.1 The error
It is a well known fact that the amount of precipitation measured is an under-estimate of the ”ground true” precipitation. Experiments have been made in order to develop models to correct the underestimate. However such models de-pend on many factors, mainly the weather condition and the type of rain gauge used.
The main precipitation measurement error in Iceland is caused by aerodynam-ical effects near the rim of the gauges. No scientific experiments have been performed in Iceland in order to achieve a model to correct the underestimate.
In 1987 a complete experimental field in Jokioinen in Finland was put up in order to develop models for operational correction of nordic precipitation data, see (Førland et al. 1996). Several models were developed. All of them included wind speed as a factor in the correction model. The Swedish, Danish and Norwegian countries included their national gauges in the experimental field.
Unfortunately the accuracy of the models can be questioned since the average wind speed at Jokioinen is about 4 m/s whereas in the other Nordic countries the average wind speed is much higher. Hence, the models need to be extrap-olated extensively. Furthermore, for practical purposes, the wind speed data must be available which often is not the case, at least not in Iceland.
The meteorologist Flosi Hrafn Sigurdsson states that measurements, not dis-turbed by wind, can be achieved by using a precipitation gauge, located in a hole in the ground with the gauges opening located at ground level. This type of gauge can only be used for measuring rain. During a summer period, May -September the ground level gauge in Reykjavik measured 21.7% more rain than the nipher gauge at 1.5 m height. Based on the ground level measurements and some other data, Flosi assumes that an average correction caused by wind for rain is 28% in Reykjavik and 32% in Hveravellir1The difference is mainly caused by stronger wind in Hveravellir. Furthermore, Flosi assumes that average wind correction for snow is 80% in Reykjavik and 100% in Hveravellir. More about Sigurdsson experiment and results can be seen in (Sigbjarnarson 1990).
3.2 Discharge
The discharge is a flow of water, having the unit [m3/s]. Considering a cross sectional area across a river the discharge is the velocity, integrated over the
1Hveravellir is located between Hofsj¨okull and Langj¨okull in middle of Iceland at a 646 m height.
cross sectional area. In general, the discharge is not measured on-line but the water level is measured.
The most commonly used methods for measuring water level are the floating principle and pressure measurements. Figure 3.3 shows a sketch of the floating
Pipe Floating
Bottom
Surface matter
indicates that water is flowing from the viewpoint
Cross section profile
Figure 3.3: The floating principle
principle. An L shaped pipe (open in both ends) is installed in the river. One part of the pipe is in the river, parallel to the bottom, so that the stream is at the same level as the open area. The other part stands perpendicular to the river’s surface. The water level inside the pipe is the same as outside the pipe.
The water remains undisturbed in the pipe (no wind disturbance etc.) and the water level can be measured. This is done by using a floating device in the pipe.
By using the one to one relationship of pressure and depth, pressure measure-ments are also used to construct water level data. Figure 3.4 shows an outline
measured pressure
Bottom
Figure 3.4: Sketch of a pressure transducer.
of a pressure transducer instrument. The transducer has a membrane and the pressure on the membrane is measured. (The measured pressure is corrected due to air pressure.) The pressure is sometimes measured by using bubbles.
Then a tube is led into the river and small quantity of gas is put in the tube continuously. The pressure in the tube depends on the pressure at the tubes opening in the river.
The measured dept is used to calculate the discharge by using the fact that the flow equals the velocity intergrated over the cross sectional area.
Conse-3.2 Discharge 37
quently, velocity measurements are required. Several methods and instruments for velocity measurements exist. The first mentioned method, and probably the oldest one, is to use a screw, as shown in Figure 3.5. The cross section is divided
Figure 3.5: Outline of a screw velocity-measurement instrument
into sections as shown in Figure 3.6. The screw is used to measure the velocity
velocity mesured
Bottom
Surface Cross section profile
Figure 3.6: Principles of the velocity-area method.
in each section, and then an approximative velocity map can be drawn. This method is commonly used in Iceland
Another commonly used method is the use of magnetic flow meter. The oper-ation of a magnetic flow meter is based upon Faraday’s Law, which states that the voltage induced across any conductor as it moves at right angle through a magnetic field is proportional to the velocity of that conductor. Figure 3.7 shows a magnetic flow meter. This method is also quite commonly used in Iceland.
However it is not convenient when the velocity is very large as the rocks in the bottom then move along the river.
The last mentioned method is the laser Doppler velocity meter, as shown in Figure 3.8. It sends a monochromatic laser beam toward the target and collects the reflected radiation. According to the Doppler effect the waves emitted from a source moving toward an observer are squeezed. Hence, the velocity of the object can be obtained by measuring the change in wavelength of the reflected laser light.
Figure 3.7: Magnetic flow meter
(Figure is from http://www.omega.com/prodinfo/magmeter.html).
3.2.1 The rating curve
Using velocity/flow measurements the relation between water level and discharge is found. This relation is known as the rating curve, or the Q−hrelationship (Qfor discharge andhfor depth/stage). The most commonly used formula is
Q=k(h−h0)N (3.1)
where h0 is the stage at which discharge is zero. Figure 3.9 shows water level and flow data.
3.2.2 The error
It is clear that the discharge data are far from being without a noise. The water level has to be measured and this process incorporates measurement errors as no instruments are perfect. Furthermore, the velocity has to be measured for corresponding measurement errors. Last but not the least, the Q−hrelation has to be found and this relationship is not perfectly described. Additionally the Q−h relationship is dynamic since the cross section can change in time.
Furthermore, in most real cases theQ−hrelationship is not unique. WhenQ varies with time it makes a loop, similar to the variable storage flow relationship Q−S, as shown in Figure 2.6. The hysteresis (i.e. loop-rating) in the Q−h graph is created as for a fixed depth (h) the velocity is larger when the flow is increasing and smaller when flow is decreasing. Thus two points on each side of the top of a hydrograph will have different flow velocities and discharge (Q) even though the depth is the same. Usually the time variation of the flow is slow