Radar Measurement of Rain Storage in a Deciduous Tree

Transcription

1 39 Chapter 3 Radar Measurement of Rain Storage in a Deciduous Tree Joost de Jong, Henk de Groot, Wim Klaassen, and Piet Kuiper Abstract. The potential of radar to estimate the amount of rain, stored in a deciduous tree canopy, is experimentally investigated. A ground-based X-band radar was pointed at the canopy of a mature ash (Fraxinus excelsior). Radar backscatter increased during a shower until 2 mm rain had fallen. With further rain, radar backscatter maintained a constant level. Radar backscatter decreased exponentially after rain stopped. Given the correlation between radar backscatter variation and the variation in water storage due to rainfall and evaporation, it is argued that X-band radar can be used to monitor the amount of rain, stored in the canopy of a forest. This new direct measurement technique therefore promises great improvements to forest hydrological research. 3.1 Introduction Interception is defined as precipitation that is temporarily stored on vegetation and evaporates without reaching the ground. Interception accounts for approximately 25 to 40% of the net evaporation of temperate forests (Linacre and Geerts, 1997, p. 98). A key parameter in interception is the amount of precipitation temporarily stored on vegetation, which is called storage (Horton, 1919). The interception process is still subject of investigations (e.g. Calder and Wright, 1986; Lankreijer et al., 1993; Klaassen et al., 1998; Gash et al., 1999). Uncertainties in the interception process are the evaporation rate, the maximum storage, and to which degree the precipitation rate (Aston, 1979; Calder, 1986), and windspeed (Hutchins et al., 1986; Hörmann et al., 1996) influence maximum storage. Few non-destructive measurement techniques have been developed to monitor storage at canopy scale (Olszyczka and Crowther, 1981; Calder and Wright, 1986; Bouten et al., 1991). These techniques are based on attenuation of gamma or microwave radiation passing through a tree canopy or forest stand. A disadvantage of these methods is the complexity of the experimental set-up: to obtain a profile of storage the transmitter and receiver have to be moved vertically along two towers at opposite sides of the forest stand.

2 40 Remote Sensing of Wet Forests A large part of storage in the canopy of a deciduous tree is located at the surface of leaves (Horton, 1919; Helvey and Patric, 1965; Aston, 1979). Theoretically, radar is sensitive to storage at the surface of leaves (De Jong et al., 2000a). Radar has the advantage of an integrated transmitter and receiver. If radar could quantify storage, a flexible, simple and relatively cheap measurement technique would become available to monitor storage directly. The aim of this study is to investigate the potential of ground-based radar to monitor storage in a deciduous tree. The study was executed using an existing portable radar, of which wavelength, range and Doppler-velocity resolution were optimised for the experiment. The costs were kept low by keeping the radar, radar use, and radar signal processing as simple as possible. Weather parameters were monitored simultaneously to estimate the amount of rain storage in the canopy. The data from the first week of October 1999 were analysed to relate the radar signal to weather parameters. 3.2 Radar General Radar transmits an electromagnetic wave that might be reflected by a target, and subsequently received by the radar. The amount of reflected power or backscatter depends on the target parameters and the wavelength of the radar. An important target parameter is the dielectric constant. In case of vegetation, the dielectric constant is mainly determined by the water content of the plant tissues (e.g. Tan, 1981; El-Rayes and Ulaby, 1987). Intercepted rain is stored at the surface of leaves and branches as a film of water or as droplets. As the thickness of the water film or droplets is small compared to common radar wavelengths (~3-60 cm), the dielectric constant of a leaf or branch with stored water at its surface theoretically equals the volumetric average of the dielectric constants of the leaf or branch and the stored water (De Jong et al., 2000a). Therefore, radar backscatter is proportional to storage. Signal processing Radar essentially receives a reflected radiowave with a certain power, N. Reflection or backscatter takes place at a certain distance or range, r. The range is retrieved from the delay between transmission and reception of the signal. A measure of radar backscatter is the radar cross section, σ 0. The radar cross section in decibel (db) is related to N and r by the radar equation: σ 0 4 r = 10log N C (3.1) where C denotes the radar constant, which accounts for the system parameters of the radar. A precise measurement of the radar constant C is complicated. Under the

3 Radar Measurements of a Wet Tree 41 assumption of a constant range, C is easily eliminated by redefining σ 0 as the backscatter difference relative to a reference measurement, N ref : σ 0 = 10log N N ref (3.2) By using the averaged received power as N ref, the resulting backscatter change, σ 0, becomes the relative deviation from the mean backscatter. Moreover, N may now be recorded in any arbitrary unit. Some additional signal processing is executed to correct for crosstalk, a system effect. Despite the isolation between the transmitter and receiver, part of the transmitted power leaks to the receiver. This leaked power is denoted as the background spectrum. The background spectrum is quantified by pointing the radar beam into the air. The backscatter change from the target is calculated by subtracting the background spectrum, N b, from the received power. This results in: σ 0 N N b = 10log N ref N b (3.3) Equation (3.3) is based on the assumption that the radar constant C does not change with time. This has to be verified by regular calibration. A sufficient calibration method of radar is feeding a part of the transmitted power through the receiver and the electronics (Ulaby et al., 1981, H10). The background spectrum satisfies this criterion, and the radar is therefore calibrated on the background spectrum at ranges where no target is present. The signal is also sensitive to fading. Fading is caused by the interference of waves with a different phase, arising from reflection of the radar wave from different parts of the canopy. The consequence of fading is a stochastic variation in the radar signal. To estimate σ 0 accurately, a sufficient number of independent samples have to be averaged. Two approaches to averaging are (i) spatial and (ii) temporal (Ulaby et al., 1981, H7). Temporal averaging is only effective when the target changes in time. When the tree moves in the wind, each sample is expected to be independent, and temporal averaging is feasible (McDonald et al., 1991). Advantages of temporal averaging are: (i) it suppresses noise in the electronics, as noise also has a stochastic nature, and (ii) it keeps the system simple and cheap compared to the spatial averaging approach, as a directional scanning utility is not needed. We therefore opt for temporal averaging to suppress fading. The reliability of the measurements will be secured by using the Doppler shift of the received signal, as this additional characteristic of the received signal is a direct measure of the motion of the tree in the direction of the radar beam. The standard deviation of the Doppler velocity, σ v, is calculated as a measure of the Doppler shift.

4 42 Remote Sensing of Wet Forests Figure 3.1. The 20-m-tall ash photographed from the location of the radar. The centre of the radar beam was a few meters below the top of the tree. At that range, the diameter of the radar beam was 3 m. The weather station is visible in front of the ash.

5 Radar Measurements of a Wet Tree Site and Instrumentation Site The experiment was conducted on an experimental field of the University of Groningen, the Netherlands (6 40 E, N). The field is a tree bordered square with sides of 60 m. The radar was pointed at an ash tree (Fraxinus excelsior) in the centre of a tree line, clearly separated from the other trees (Figure 3.1). The height of the ash was 20 m, the crown projection 250 m 2. Radar The Micro Tree-Radar (MTR, Metek GmbH) is an FM-CW Doppler radar, adapted from the Micro Rain-Radar MRR-1 (Peters, 1995; Klugman et al., 1996). The radar has an integrated transmitter and receiver based on the homodyne principle. This technique results in a strong coupling between the transmitter and the receiver. The radar processed the reflected power from raindrops with fast-fourier transformations on-line into arbitrary digital units for 16 range cells and 32 Doppler-velocity cells. The tree radar on-line processing was optimised compared to the rain radar processing by: (i) decreasing the resolution of the Doppler-velocity classes because branches and leaves move slower than raindrops, and (ii) decreasing the range-cell resolution because the radar is used at a relative short distance from the tree. Additionally, the operation frequency was set at X-band (10.4 GHz). X-band backscatter theoretically arises mainly from leaves (McDonald et al., 1991; Karam et al., 1992). The radar was put on a robust aluminium stand, which was equipped with a small roof to avoid the radar and the parabolic reflector from getting wet. The transmitter and receiver were kept at a constant temperature of 60 C to prevent temperature induced sensitivity shifts in the electronics. The reflector was heated to prevent dew formation on its surface. The radar characteristics are presented in Table 3.1. TABLE 3.1 Characteristics of the Micro-Tree Radar. Type frequency modulated, continuous wave (FM-CW) Transmit power 10 mw Beamwidth 3 degrees Polarisation vertical Frequency 10.4 GHz (X-band) Averaging time 5 min No. range cells 16 Range cell resolution 5 m No. Doppler cells 32 Doppler cells resolution m.s -1 Weight (incl. Frame) 6 kg (25 kg)

6 44 Remote Sensing of Wet Forests Figure 3.2. Mean background spectrum in every range cell and Doppler-velocity cell in digital numbers on a logarithmic scale. The background spectrum is the transmitted power that leaks to the receiver. The first range cell did not contain data. The background spectrum was highest in the second range cell with zero Doppler velocity. The radar was installed at 60 m distance from the centre of the tree. The radar was pointed at the upper canopy because even small showers wet the upper canopy. Moreover, the largest tree motions occur in the wind-exposed upper canopy, reducing the influence of fading. The shape of the radar beam passing through the canopy resembled a cylinder with a length of 16 m and a diameter of 3 m. The on-line processed radar data were logged on a HP palmtop computer. Weather station Weather parameters were monitored by a weather station at 2.5 m height located in the centre of the field (Figure 3.1). Essential instruments were: a cup anemometer for windspeed measurement (Vector Instruments AR100), wet and dry bulb thermometers for water vapour pressure measurements (Vector Instruments H301 Psychrometer), a wetness sensor (Campbell 237) and tipping bucket rain gauge for rain measurements (Campbell ARG100). When the windspeed was 0.2 m.s -1, the cup anemometer recorded a windspeed of 0.2 m.s -1 to compensate for errors due to stalling. The resolution of the rain gauge was 0.2 mm. The 5-min-averaged weather parameters were logged on a Campbell XR10 datalogger.

7 Radar Measurements of a Wet Tree 45 Figure 3.3. The variation of the background spectrum relative to the mean background spectrum in range cell 9, recorded during 9 days and plotted versus time of the day. The background spectrum had a systematic and a noise component. 3.4 Results Signal processing The background spectrum was obtained by pointing the radar beam into the air from 29 November till 6 December The temporal averaged background spectrum was highest at shorter ranges and low velocities due to the homodyne principle of the radar (Figure 3.2). A number of unexpected isolated peaks were visible in higher Dopplervelocity cells. The total background spectrum varied less than 0.4 db with time. The maximum deviation from the mean was found in range cell 9, on top of the peak visible in Figure 3.2. The background spectrum in range cell 9 was correlated with the variation in the other isolated peaks, visible in Figure 3.2. The variation in background spectrum in range cell 9 had a systematic component with a period of 24 hours, and a random component of smaller amplitude (Figure 3.3). The latter component is attributed to noise. Weather conditions were variable during this observation period (frost, rain and storm). It was checked that the variations in background spectrum were not correlated with variations in weather variables. Even falling raindrops did not influence radar backscatter.

8 46 Remote Sensing of Wet Forests Figure 3.4. The received power of the tree and the background spectrum. According to field measurements, the tree was present in range cell 11, 12, 13 and 14. The reflection from the tree was measured from 1 till 7 October This resulted in a strong backscatter increase in range cells 11, 12, 13 and 14 (Figure 3.4). These range cells coincide with the location of the tree. The signal in the adjoining range cells 9, 10, 15 and 16 was slightly increased. This increase was attributed to leakage due to the method of on-line processing of the received signal. The difference in the received power between the October and the background spectrum was insignificant for the other 8 range cells, which indicates that these range cells are useful for radar calibration, and that the radar constant did not change in time. The influence of background spectrum variations on the accuracy of the tree measurements was assessed. The derived σ 0 from the tree is strongest influenced by variations in background spectrum (N b ), when the recorded signal from the tree (N) is relatively low compared to the background spectrum, see Equation (3.3). The accuracy is therefore determined by selecting the lowest received power from the tree, and calculating σ 0 from the tree with the highest and the lowest recorded background spectrum. The resulting difference in σ 0 for range cell 11, 12, 13 and 14 was 0.50, 0.23, 0.13, and 4.66 db, respectively. The poor accuracy of range cell 14 results from the low tree reflection in that particular range cell. Range cell 14 was therefore excluded from further processing. As the reflected powers in range cell 11, 12 and 13 were strongly correlated with each other (correlation coefficient > 0.9), the received powers of range cell 11, 12 and 13 were summed to determine the total tree backscatter change, σ 0. The influence of background spectrum variations on σ 0 was < 0.25 db, even for the lowest recorded tree backscatter.

9 Radar Measurements of a Wet Tree 47 Figure 3.5. Hour-averaged backscatter change, Doppler velocity standard deviation, temperature, windspeed, and cumulative rainfall during the first week of October The marks on the x-axis are set at midnight. Some weather data were missing on 4 October. Weather was stormy in the first half of the week, and calm at the end of the week. It rained regularly.

10 48 Remote Sensing of Wet Forests Tree radar reflection in relation to weather The tree backscatter change, σ 0, Doppler-velocity standard deviation, σ v, temperature, windspeed and precipitation are shown in Figure 3.5. Weather data from 4 October between 11 a.m. and midnight are missing. Due to the location of the weather station in a clearing, the measured windspeed was lower than the windspeed near the upper canopy of the tree. The reliability of our windspeed measurements was therefore assessed by comparing it with windspeed measured at Groningen Airport by Royal Dutch Meteorological Organisation (KNMI). The windspeed was measured at 10 m height above grass at Groningen Airport, which is located at 8 km from our experimental site. It was found that the hour-averaged windspeed in the clearing was strongly correlated, a correlation coefficient of 0.9, with windspeed at Groningen airport. The windspeed at the airport was 5.6 times higher than the windspeed in the clearing. We prefer to use the windspeed in the clearing as a measure of the windspeed near the top of the ash, as gusts of wind occur locally. The windspeed at the top of the ash is assumed to be a constant multiple of the windspeed in the clearing. The correlation coefficients between radar and weather parameters are presented in Table 3.2. Fading Fading is only averaged out when successive samples are independent due to tree motion. Therefore, we focus on the relation between σ v and windspeed, the driving force of tree motion. Figure 3.6 is based on hour-averaged data, as 5-min-averaged data would result in larger scatter in the relation between windspeed and σ v. For windspeed above 0.5 m.s -1, windspeed and σ v were related. At low windspeed, σ v was not sensitive to measured windspeed. This is attributed to coupling between adjacent Doppler cells, which results in an offset in σ v, and motions smaller than the resolution of the Doppler velocity cells. One might think that measurements influenced by fading should therefore be best excluded on the basis of windspeed and not on σ v. On the other hand, low windspeed occurred at night (Figure 3.5), when the atmosphere was stable. In a stable atmosphere, the windspeed at low heights in the clearing will be coupled badly with windspeed near the top of the canopy. For example, very low windspeeds ( 0.2 m.s -1 ) occurred in the clearing at night, while the windspeed measured at the airport never dropped below 1 m.s -1. Consequently, we could not objectively identify measurements influenced by fading. We therefore preferred an arbitrary threshold, based on the most direct measure of tree motion: the Doppler velocity. TABLE 3.2 Pearson correlation coefficients between the radar signal and weather parameters. temperature wind direction windspeed rain intensity humidity Backscatter change Doppler-velocity standard deviation

11 Radar Measurements of a Wet Tree 49 Figure 3.6. Hour-averaged Doppler standard deviation measured in the upper canopy of the tree versus the windspeed measured at 2.5 m height. It is noted that 0.2 m.s -1 is the lower detection limit of the cup anemometer used for the windspeed measurement. With the threshold σ v < 0.05 m.s -1, 11 hours with data were excluded. Excluded were e.g. the lowest measured σ 0, which occurred simultaneously with the lowest measured σ v and windspeed. From the resulting data, the σ 0 of just one observation was below -1.1 db. As this observation borders an excluded observation, fading might occur during a significant fraction of the time span of this observation. Sensitivity of radar backscatter to storage Rain intensity and σ 0 of the tree were found to be correlated (Table 3.2). Radar backscatter theoretically depends on storage. As storage might be related with rain intensity, the sensitivity of σ 0 to storage is investigated with data of 5-6 October, when two small showers with respectively 0.8 and 0.6 mm of rain occurred (Figure 3.7). The 5-min-averaged σ 0 was used to reveal the temporal behaviour most clearly. It should be noted that the small integration time results in a larger measurement uncertainty. The radar reflection increased immediately after the beginning of the shower, and was almost proportional with cumulative precipitation. When rainfall stopped, the backscatter decreased in a few hours to the same level as before the shower, -0.5 db. The negative value of a dry canopy results from the averaged backscatter being defined as 0 db, while the wet canopy backscatter values were generally above 0 db.

12 50 Remote Sensing of Wet Forests Figure 3.7. The 5-min-averaged and hour-averaged backscatter between 5 and 6 October 12h00. The x- axis hours are equal to the hours in Figure 3.5. After the beginning of the shower backscatter increased strongly and decreased exponentially. During the first shower the rain gauge measured 0.8 mm rainwater and during the second 0.6 mm rainwater. Evaporation of storage is relatively small during a shower, as the atmospheric humidity is high. Consequently, storage can be assumed to be a single function of the amount of precipitation. The increase in σ 0 after the beginning of all showers was therefore studied to assess the relation between storage and σ 0. First, a data selection was applied. Each shower was assumed to start as soon as the rain gauge detected rain, after at least one hour of no rain. The no rain test was used as most storage caused by a previous shower was assumed to have been evaporated within one hour. The shower was defined to end when the rain gauge did not record rain for the following half-hour. Consequently, it could stop raining for almost half an hour during the shower, causing the canopy to dry. Showers with a total precipitation of 0.2 mm, the detection limit of the rain gauge, were finally excluded due to the limited accuracy of the rain gauge measurement. 14 showers fit the selection criteria. The 5-min-averaged σ 0 was plotted versus the cumulative rainfall since the start of the shower (Figure 3.8). The backscatter level at the start of each shower was scattered. This scatter was attributed to two processes: (i) the canopy might be partly wet due to a previous shower, dew, or rain with an amount less than the resolution of the rain gauge, 0.2 mm, and (ii) fading and noise resulting from the high temporal resolution of 5 minutes. The backscatter increased with precipitation until the precipitation amount reached 2 mm. After 2 mm of rain, the backscatter remained relatively stable around σ 0 = 1.75 db, indicating that storage reached its maximum. Only 2 showers exceeded 3 mm rain. The decrease of σ 0 after 5.6 mm rain had fallen is caused by drying of the canopy. The other scatter visible during the two largest showers could be noise and fading. It is however striking that during two sharp decreases (at 4 mm and 6.2 mm),

13 Radar Measurements of a Wet Tree 51 Figure 3.8. Backscatter as a function of cumulative precipitation for 14 showers. Each shower has its own symbol. During each shower the canopy could dry for maximal 30 minutes. the windspeed had a temporary maximum, above 1.2 m.s -1, and on the third sharp decrease, at 5 mm, the precipitation rate strongly increased till 10 mm.h -1. Part of the stored rain may thus have been shaken off by gusts of wind or driving rain, causing the backscatter to decrease. The backscatter averaged over the whole week with a dry wetness sensor was db. With a water saturated canopy σ 0 of db, the sensitivity of X-band radar to storage appears to be 2 db. 3.5 Discussion The radar measured the wetness of a tree in a reproducible manner. This result will be discussed in relation to a possible future application of radar in forest hydrological research. Attention will be paid to the measurement precision and the correlation with other direct measurements of storage. The measurement precision was influenced by radar system effects and by fading. A system effect, which influenced the measurement precision, was the variation of some peaks in the background spectrum with the 24-hour period (Figure 3.3). The source of these variations was unknown, but it was demonstrated that variances in background spectrum, which included noise, in the range cells where the tree was present could account for maximal 0.25 db. The measurement precision on a time scale of hours will be less influenced by the 24-hour period in background spectrum. Under stable environmental conditions, the hour-averaged backscatter change indeed deviated only a few tenths of db, at least, as long as the tree moved, while the 5-min-averaged σ 0 deviated ~0.5 db from the hour-averaged σ 0 (e.g. Figure 3.7).

14 52 Remote Sensing of Wet Forests The deviations of the 5-min-averaged σ 0 were explained by the short interval of temporal averaging, causing fading and noise to influence the measurement precision. The precision of the 5-min-averaged σ 0 is therefore assessed to be 0.5 db, and the hour-averaged backscatter precision is assessed to be 0.25 db. Fading might seriously influence backscatter. Our approach to reduce fading was temporal averaging of backscatter from the moving tree. As our measurements were performed in a windy season and on a wind-exposed tree, only a few measurements were excluded. To our experience, it was very difficult to measure small motions on this wind-exposed single tree. Tree motion will be reduced within a forest, and the temporal averaging approach to reduce fading will be less suitable for application in forests. We recommend therefore to suppress fading by spatial averaging over independent samples in future radar measurements of single trees or forest stands. The experimental results indicate that this radar is useful to quantify rain storage. The similarity in backscatter change during and after the showers in the night of 5 to 6 October was in agreement with similar shaped exponential decrease observed by Larsson (1981), Calder and Wright (1986), Bouten et al. (1991), Theklehaimanot and Jarvis (1991), and simulated by Rutter et al. (1971). A second result that points to the usefulness of radar to quantify water storage was the wetting of vegetation by 14 showers. During the wetting, the 5-min-averaged σ 0 falls within a bandwidth of 1 db around the mean σ 0, which agrees with the estimated precision of 0.5 db. Differences between the showers could therefore be attributed to fading or noise. Other causes of differences between the showers are the initial wetness of the canopy, and the difference in evaporation rate during the shower. The general trend, however, was a saturated canopy above 2 mm precipitation, in agreement with other rainfall interception observations (Rutter et al., 1971; Hancock and Crowther, 1979; Aston, 1979; Theklehaimanot and Jarvis, 1991). 3.6 Conclusion The X-band radar backscatter of the deciduous canopy increased proportionally with cumulative rain. The backscatter stopped increasing after 2 mm of rain, indicating that the canopy was saturated. The difference in backscatter between a dry and a rain-saturated canopy was 2 db. The radar cross-section decreased exponentially within hours after rain stopped, in agreement with other published measurements on evaporation of stored water after rainfall. It is concluded that radar can monitor storage in forest canopies. As additionally the radar apparatus used in this experiment had a low weight, and an integrated receiver and transmitter, the general conclusion is that radar is a new, flexible and simple tool for forest hydrological research. It is recommended to suppress fading by spatial averaging over independent samples, instead of temporal averaging over moving tree samples.