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The measurement and modelling of rainfall interception by Amazonian rain forest
Agricultural and Forest Meteorology, 43 (1988) 277-294
277
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
THE M E A S U R E M E N T A N D M O D E L L I N G OF R A I N F A L L INTERCEPTION BY AMAZONIAN RAIN FOREST
C.R. LLOYD, J.H.C. GASH and W.J. SHUTTLEWORTH
Institute of Hydrology, Wallingford, OXIO 8BB (Gt. Britain) A. DE O. MARQUES F ~
Instituto Nacional de Pesquisas da Amazonia, CP 478, Manaus, Am. (Brazil) (Received December 16, 1987; revision accepted March 18, 1988)
ABSTRACT Lloyd, C.R., Gash, J.H.C., Shuttleworth, W.J. and Marques F., A. de O., 1988. The measurement and modelling of rainfall interception by Amazonian rain forest. Agric. For. Meteorol., 43: 277294. Measurements of the evaporation of rainfall intercepted by Amazonian rain forest were compared with estimates made by two models, the Rutter model and Gash's analytical model, applied to meteorological measurements made with automatic weather stations mounted above the forest. Neither of the model estimates of interception loss was significantly different from measured interception loss, which amounted to 8.9% of the measured rainfall.
INTRODUCTION
There is much concern about the environmental effects of deforestation in the humid tropics. Clearing an area of forest will almost certainly affect its local hydrology in terms of the volume and timing of run-off. If the area is sufficiently large, changes in the surface energy balance may also result in changes in climate. These changes may extend to other regions far beyond the former forest. The sensitivity of climate to changes in vegetation can be predicted using global circulation models (Eagleson, 1986 ), multi-layer models of the Earth's atmosphere which run on a timestep of typically ten minutes. These models require a representation of the surface energy balance, at the same time-scale, which can predict the surface fluxes from the meteorological variables generated by the model. In contrast, the local effects on run-off can be predicted by catchment models for which daily climatological measurements may be adequate. There is thus a requirement for a description of forest evaporation both on the ten minute and on the daily time-scale. Studies of forests in temperate regions have shown that interception loss, the evaporation which 0168-1923/88/$03.50
© 1988 Elsevier Science Publishers B.V.
278 results from rainfall intercepted by the forest canopy and evaporated before reaching the ground, is an important component of forest evaporation. Measurements and models of the interception loss from tropical forest are therefore an essential prerequisite to any quantitative prediction of the effects of deforestation. In this paper two appropriate models for estimating the evaporation of intercepted rainfall are tested against measurements made in Amazonian rain forest. The Rutter model (Rutter et al., 1971, 1975) calculates a running balance of the amount of water on the canopy, with evaporation being estimated from the meteorological variables and forest stand parameters. It is usually run with hourly meteorological data. The model has been successfully tested against data from coniferous plantation forest in Great Britain (Gash and Morton, 1978; Gash et al., 1980) and forms the basis of Calder's (1977) interception model and the interception component of the Syst~me Hydrologique Europ~en (Bathurst, 1986). Gash's analytical model (Gash, 1979) is a storm-based simplification of the Rutter model which, if calibrated using hourly meteorological data, can then be run on daily rainfall values. The model has been successfully tested against data from coniferous plantation forest in Great Britain (Gash et al., 1980), from an oak plantation in The Netherlands (Dolman, 1987) and from mixed evergreen forest in New Zealand (Pearce and Rowe, 1981). Both physically-based models have empiricism restricted as far as possible to the values of parameters whose physical significance is understood. Provided that appropriate values of these model parameters can be derived or estimated, then the models should be generally applicable and not limited to the sites for which they were originally derived. It is a major test of this modelling philosophy to determine whether these models, which were originally tested against data from temperate mono-culture plantations, can successfully estimate the evaporation from tropical rain forest. THEORY The Rutter model
Full details of the Rutter model have been given by Rutter et al. ( 1971, 1975 ). It is essentially a numerical computer model which calculates a running balance of the depth of water on the forest canopy and tree trunks. The model requires the following state parameters: S--- canopy storage capacity, the depth of water left on the canopy in conditions of zero evaporation, when rain and throughfall have ceased; p = free throughfall coefficient, the proportion of rain which falls to the ground without striking the~anopy; St = trunk water capacity; pt =proportion of rain diverted to the trunks. When the depth of water on the canopy, C, exceeds the canopy capacity the drainage rate, D, is calculated from the relationship
279
D=D~ exp[b(C-S) ]
(1)
There is thus a requirement in eq. 1 for values of D~, the drainage rate when C = S and b, which defines the rate of increase in drainage with depth of water on the canopy. The values used in the following analysis were those derived by Rutter et al. (1971) for a Corsican pine canopy modified by the ratio of the rain forest canopy capacity to the Corsican pine canopy capacity as suggested by Rutter et al. (1975). The values for D~ and b were 0.0014 mm min -~ and 5.25 respectively. In the version of the model used here no drainage is allowed when the canopy is unsaturated, ie C< S. This condition complies with the definition of the canopy capacity and avoids the weakness in the drainage equation, noted by Calder (1977), of predicting small but finite drainage from a dry canopy. Evaporation from a saturated canopy is calculated from the appropriate form of the Penman-Monteith equation, with the surface resistance set to zero. When C is less than S (indicating a partially wet canopy with no drainage ), the evaporation is reduced in proportion to the calculated value of C/S. The model is driven by hourly values of rainfall, but in addition the evaporation calculation requires hourly values of net radiation, temperature, humidity and windspeed. The aerodynamic resistance to the transport of water vapour, ra is calculated from
ra =f/U
(2)
where u is windspeed and f is a constant (Rutter et al., 1971 ). The original version of the Rutter model divided each hour into six minute periods, using analytical integrations of the model equations as smoothing functions. In the present version this has been abandoned in favour of a simpler numerical integration using the original equations. Tests using the data presented by Gash et al. (1980) showed that with a timestep of two minutes there was negligible difference between the two methods. The model has also been modified to remove the systematic increase in the duration of storms caused by the procedure of spreading each hour's rainfall equally over the whole hour. On average there will be as many storms which start (or end) less than halfway through an hour, as there will be storms which start (or end) more than halfway through an hour; so the effect of spreading the rain equally over the whole hour will, on average, be to increase the length of storms by one hour. In the tropics where storms are characteristically of short duration this may result in a significant over-estimation of interception loss by the model. The modification restricted the rainfall to the second half of any hour with rain which was preceded by a dry hour, and to the first half of any hour with rain which was followed by a dry hour.
28O
Gash's analytical model Gash's analytical model (Gash, 1979), considers rainfall to occur in a series of discrete storms each of which comprises a period of wetting up, a period of saturation and a period of drying out. The canopy is assumed to have sufficient time to dry between storms. The model is fundamentally a simplification of the Rutter model. It requires the same state variables S, p, St and Pt, and in addition E/R, the ratio of the mean evaporation rate to the mean rainfall rate for hours when rain is falling onto a saturated canopy. Interception loss is then calculated as the sum of the components given in Table 1. Where hourly meteorological data are available these can be used to derive E and/~ by applying the Penman-Monteith equation to those hours with the rainfall above a certain threshold, which are considered to represent saturated conditions. The derived values of E/R can then be applied to the rainfall data recalculated as storm totals, or be used to extrapolate the results to other sites where only rainfall data are available. In applying the model to data from Great Britain, Gash (1979) and Gash et al. ( 1980 ) made the assumption of one storm per rainday. This has the obvious advantage that, once a value has been obtained for E/R, the model can subsequently be run on the widely available daily rainfall data. Pearce and Rowe (1981) found that this assumption was inadequate for the rainfall climate of the South Island of New Zealand, where storms TABLE 1 The analytical forms for the components of interception loss a Component of interception loss
Formulation
For m small storms with PG < P~.
(1--p-pt)
Wetting up the canopy in n large storms with Pc; > P~; Evaporation from saturated canopy during rainfall
n(1-p-pt)P(;-nS
m
~ P(:j j=l
Evaporation after rainfall ceases for n large storms Evaporation from trunks in q storms that fill the storage Evaporation from trunks in m + n - q storms that do not fill the storage Pd defined as the amount of rain necessary to saturate the canopy
n
£= ~ ( P G j - P ; ) Rj=~ nS qSt rn+n--q
Pt
~
j=l
P(~j
P~= (-/~S/E)ln[1-
(/~/R)(1-p-pt)
-~ ]
aThe simpler form of the stemflow formulation (Gash, 1979 ) has been used, rather than the more complex formulation introduced by Gash et al. (1980) to model the evaporation from the trunks in a forest with high stemflow and long duration storms.
281 frequently exceed 24 hours duration. However, in the tropics where rain typically falls in short intense convective storms it is more likely to be a reasonable assumption and has been retained in the present analysis. To model the evaporation from a dense young spruce plantation in Plynlimon, central Wales, Gash et al. ( 1980 ) introduced a more complex formulation for the evaporation from the trunks which accounted for the high stemflow and long duration storms present at that site. As the stemflow at the present site is low and the storms generally of short duration, the original simpler formulation tested against data from mature pine forest at Thetford, East Anglia (where stemflow was also low and storms were of shorter duration), has been used in this analysis. SITE The experimental area described in this paper forms part of the micrometeorological site described by Shuttleworth et al. (1984a) and by Lloyd and Marques (1988). It is situated at 02 ° 57' S, 59 ° 57'W in the Reserva Florestal Ducke, 25 km from Manaus, Amazonas, Brazil. It is typical of undisturbed natural Amazonian terra firme rainforest, extending with no obvious sub-storeys to a height of approximately 35 m with occasional emergent trees reaching 40 m. The plant density is some 3000 stems h a - 1but less than 10% have girths of greater than 0.2 m. INSTRUMENTATION Two automatic weather stations (Didcot Instruments, Abingdon, Gt. Britain) were mounted on a 45 m tower above the forest. Measurements of solar and net radiation, temperature, aspirated wet-bulb temperature and windspeed were made every five minutes and recorded on magnetic tape. Readings from the two stations were later averaged to produce a single set of quality controlled hourly average values. The measurements were made for the period 3 September 1983-21 August 1985. Complete loss of data occurred on 19 days during this period. During the period 26 March 1984-22 June 1984 the polythene domes on both the net radiometers initially clouded and later cracked through prolonged exposure to solar radiation. The net radiation measurement over this period was not considered to be reliable and an estimate of net radiation based on the measured solar radiation was substituted. The form of the expression used and its derivation is described in Appendix 1. Interception loss was determined as the measured difference between gross rainfall and throughfall plus stemflow. Full details of the instrumentation have been described by Lloyd and Marques ( 1988 ). Gross rainfall was measured by one 203-ram diameter 0.25 mm tipping bucket raingauge situated at the top of the tower. Additional measurements were made at a site 100 m from the tower
282 on a small platform erected at the top of a tree, the crown of which was missing. During the period 3 October 1983-1 June 1984, throughfall was measured by fourteen 203-mm diameter, 0.5 mm tipping bucket raingauges. These were randomly relocated every week along a 100 m transect (marked at 1 m intervals) which was situated close to, and between, the gross rainfall measurements. The weekly accumulated tips were recorded on separate counters. The rims of the raingauges were fitted with extensions to minimise splash-out. No throughfall was measured between 1 June 1984 and 5 July 1984, due to the failure of the counter system. From 5 July 1984 to 21 August 1985, the above system of fourteen tipping bucket raingauges was increased to sixteen gauges and augmented by thirtysix bottle gauges. For this period the tipping bucket gauges were fixed in random positions alongside the transect line and their tips accumulated and stored every 30 minutes on two 12-channel solid-state data loggers (Computing Techniques, Gt. Britain). The 100 m transect line was replicated by four more parallel transect lines forming a 100 m × 4 m random grid with 505 sampling positions. On this grid the thirty-six bottle gauges, each with a 127-mm diameter copper funnel, were randomly relocated every week. These funnels were of sufficiently steep an angle to prevent splash-out. During the period 14 March 1985-13 May 1985, the bottle gauges were relocated after every storm. Lloyd and Marques (1988) give further details of these instruments and the errors and spatial variability associated with this array of bottle gauges. Stemflow was measured on nineteen adjacent trees within the middle of the random grid for the period 20 August 1984-21 August 1985. The method of obtaining stemflow, its errors and variability are detailed in Lloyd and Marques (1988). Six of the stemflow measurements were recorded on the remaining channels of the solid-state loggers described above, the other thirteen stemflows were collected in 20 1 plastic bottles. These bottle stemflow totals were measured every week, except for the period 14 March 1985-13 May 1985 when the totals were measured after every storm. RESULTS
Total interception loss The estimate of total interception loss was based on the two years of gross rainfall and throughfall measurements recorded between 3 September 1983 and 21 August 1985. To compare the measured interception loss with the modelled results, periods were removed from the data set when data pertinent to either result were missing. The remaining data set had 625 days of data. Stemflow was only measured during the second year of the experiment, but its relatively small contribution to the water balance justified it being simulated for the first year. The increase in the reliability of the estimate of total
283
4000-
3000 i
Gross~
2000j
~
i i
10001 i
0
,
/
100
I
"
interception oss
200
300 400 Number of days of data
500
600
Fig. 1. Cumulative gross rainfall and measured interception loss plotted against number of days of complete data, starting on 3rd September 1983 and finishing on 21st August 1985. The error bands on the interception loss are also shown ( .... ). interception loss gained from using two years of gross rainfall and throughfall data was felt to outweigh the small loss of accuracy such a simulation would cause. Consequently, stemflow measurements were taken as 1.8 + 1% of gross rainfall for the first year, this figure being the overall estimate gained from the measurements of stemflow between 20 August 1984 and 21 August 1985. The gross rainfall recorded in the 625 days of data was 4804 mm. Total measured throughfall was 4286 mm with a standard error of 170 mm. Throughfall was therefore 89 +_3.5% of gross rainfall. Total stemflow was 90 mm of which 49 mm was simulated data. The total interception loss from these measurements was 428 mm with a standard error of 173 mm which is 8.9 + 3.6% of gross rainfall. The results are plotted in Fig. 1.
Canopy capacity The canopy capacity is usually derived from an analysis of separate storms using the method of Leyton et al. (1967). A line of slope (1 - P t ) is drawn to envelop all the points on a plot of gross rainfall versus throughfall for individual storms. Such a line is assumed to go through only those points representing conditions with minimal evaporation during a storm. The canopy capacity is then given by the intercept of this line with the throughfall axis.
284 The method is appropriate where spatial variability of throughfall measurements is relatively low, e.g. dense plantation coniferous forests. However, with the high spatial variability of throughfall encountered in this particular tropical rainforest (see Lloyd and Marques, 1988), the above method was found to be vague and subjective in its derivation of the canopy capacity, and therefore a more objective method was used. Separate linear regressions of gross rainfall versus throughfall for individual small storms were calculated for each of the 16 fixed tipping bucket raingauges. Individual storms were defined as periods of continuous rain with at least six dry hours separation. These regressions gave a mean slope of 0.92 + 0.12 and a mean intercept of 0.65 + 0.31 mm. This regression produces a value of 0.70 mm of rainfall for zero throughfall. This figure is not equivalent to the canopy capacity, but must be corrected to take account of evaporation during rainfall. Applying the argument given by Gash (1979), and the values of the parameters either implied by the regressions or derived later in this section, gives a corrected value of S equal to 0.74 mm.
Free throughfall coefficient The free throughfall coefficient, p, is an estimate of that fraction of gross rainfall which arrives directly at the soil surface without striking any of the vegetation surfaces. This was determined by using an anascope, similar to that used by Ford (1976), to gain point observations of the canopy cover. These observations were made at each of the 505 sampling positions within the random grid transect area (see Lloyd and Marques, 1988). Of the 505 observations, 40 were judged to be clear sky, implying a free throughfall coefficient of 0.08 with a standard error of 0.01.
Stemflow parameters A similar method to that used for estimating canopy capacity was adopted for evaluating the trunk storage capacity, St, and the proportion of rainfall which is diverted onto the trunks, Pt. The variability of stemflow in this tropical rainforest is also very high, although the overall contribution is relatively small (Lloyd and Marques, 1988). Fifty-two storms were identified for use in this analysis. No individual tree had measurements for all these storms, the worst tree data set being twelve storms and the best being thirty-four storms. The mean number of storms per regression was twenty-two. Separate linear regressions of stemflow versus gross rainfall were formed for each of the nineteen trees. The intercepts of these regressions are estimates of the trunk capacities and the gradients are estimates of the proportion of rainfall diverted to the trunks. By averaging both the set of intercepts and the set of gradients, the stemflow equation is given by
285 S f = 0 . 0 3 6 ( + 0 . 0 0 6 ) PG - 0 . 1 5 ( + 0 . 0 8 )
(3)
where P c is gross rainfall. Values of 0.036 ( _+0.006) for Pt and 0.15 mm ( + 0.08) for St were therefore used as stemflow parameters in the model.
Aerodynamic resistance In the absence of experimental values, ra has often been computed as a function of windspeed, vegetation height, roughness length and zero plane displacement. Such a procedure in this rainforest would lead to a value for f of 29.2 in the eq. 2. However, at this site atmospheric turbulence measurements are available and f can be estimated directly from m o m e n t u m transfer. In a parallel paper, Shuttleworth (1988) has used these measurements to derive a value of [= 34.2. A standard error of 4.7 about this value was estimated from analysis of the same data and these values are used here. MODELLING
Application of the Rutter model The Rutter model was applied to the automatic weather station data using the state parameters given in the previous section. The results are shown in Fig. 2 (a). The model estimated a total loss of 605 mm, equal to 12.6% of gross rainfall. The model also estimated throughfall to be 84.5% of gross rainfall, and stemflow to be 2.9% of gross rainfall.
Application of Gash 's analytical model The analytical model was applied to the same data set as the Rutter interception model using the same state parameters. As in previous applications of the analytical model (Gash, 1979; Gash et al., 1980), saturated conditions were arbitrarily defined as occurring when the hourly rainfall was greater than 0.5 mm (i.e. two bucket tips). The average evaporation and rainfall rate onto a saturated canopy were then used to estimate the total evaporation for each month. The results are shown in Fig. 2 (b). The model estimated a total loss of 543 mm or 11.3% of gross rainfall, which is also within the error bands of the measurement. The overall average evaporation and rainfall rate for saturated canopy conditions were E = 0 . 2 1 and /~=5.15 mm h -1 respectively. It was calculated that 49% of the evaporation was the result of drying out after rainfall and 34% the result of evaporation from a saturated canopy during rainfall. The remaining 17% was accounted for by wetting up the canopy (1%), small storms (7%) and trunk evaporation (9%). Saturated trunks accounted for 8% of the trunk evaporation.
286
700 E
(a)
Error
limits
600 500 400
"~ 300
200100-
j
Putter 160
Goo!
~g
260
360
460
(b)
560
Error limits
":
• f!
.....t!
500 i 400J
660
Measured
L
Analytic
~°°°~
2~
360
45o
56o
ado
Number of days of data
Fig. 2. Cumulative measured interception loss ( ) and cumulative interception loss as estimated ( - - - ) by (a) the Rutter model and (b) Gash's analytical model, against number of days of complete data.
The year-to-year variation in interception loss can be assessed by applying the analytical model to the daily rainfall totals measured at the Reserva Ducke climate station. The model was applied to the period 1971 to 1983 inclusive, using the overall average values of E = 0.21 a n d / ~ = 5.15 mm h -~, and the state parameters derived for the micrometeorological tower site. The results are shown in Table 2. The annual rainfall for this period ranges between 1901 mm and 2712 mm with an average of 2391 mm. The estimated interception loss varies between 10.0% and 12.2% of the rainfall with an average of 11.1%. The highest percentage interception loss occurs with the lowest annual rainfall and vice versa.
Error analysis Both the measurement data set and the model output have errors associated with them. The measurement data set error limits are largely due to the effects
292
11.2
Percentage loss
2607
1971
Year
Interception loss (mm)
Rainfall (mm)
given
11.2
301
2680
1972
11.9
295
2482
1973
12.2
278
2274
1974
12.3
288
2351
1975
10.4
274
2635
1976
11.8
287
2435
1977
11.1
251
2257
1978
10.3
278
2712
1979
12.6
239
1901
1980
11.4
257
2258
1981
10.5
263
2497
1982
12.1
242
1996
1983
11.4
273
2391
Mean
0.2
6
70
Standard deviation
The annual interception loss for the Reserva Ducke Forest, estimated using the analytical model applied to the daily rainfall from the Reserva Ducke climate station and the model parameters derived during the study period. The means and the standard deviation of the means are also
TABLE 2
b~
288 of small samples in assessing very high spatial variability. This uncertainty or "error" results in the cumulative measured throughfall being subject to large positive and negative fluctuations. For example, in Fig. 2 it can be seen that during the period from 2 January to 30 January 1985 (days 425-453 in Fig. 2) the measured interception loss was negative. Given the statistical distribution of the throughfall (see Lloyd and Marques, 1988) such fluctuation should not be unexpected. While over a long period these random fluctuations should cancel, as can be seen from Fig. 2 the measurement of cumulative interception loss is inevitably less smooth than the modelled estimate. The errors in the models are the result of errors inherent in the physical description of the models, together with the errors incurred in the measurement of the state parameters and the driving variables. The overall error in the model is dominated by the effect of errors in the state parameters. By using the method of Rosenblueth (1975), individual contributions to the overall error, resulting from the error in each of the parameters S, p, Pt, St and f, were combined to estimate the standard error in the models' outputs. The modelled interception loss over the two year measurement period, together with its standard error for both of the models is: Rutter: 605 + 127 mm (12.1 + 2.6% of gross rainfall) Analytic: 543 _+103 mm (11.3 _+2.2% of gross rainfall) Standard difference of means tests were performed between measured and modelled interception loss on both models and neither were significantly different from the measurements at the 10% level. The error analysis above does not include the possible error incurred through using assumed parameter values for the drainage function. The leaves of tropical rainforest trees are very different from the needles of the pine trees used to derive the original values of the drainage function. For example, many species of tropical trees have evolved the ability to repel and shed water rapidly from their smooth leaf surfaces via drip points (Herwitz, 1987 ). It might therefore be expected that the drainage from a tropical forest would be more rapid than from a stand of pine trees. The sensitivity of the intercetJtion loss to change in the drainage parameters can be seen in Fig. 3 for a typical month's data. As D~ and b increase, the rate of drip increases until the limit, where the depth of water on the canopy is reduced to S at the end of each time-step and no build-up of water is allowed on the canopy. This is equivalent to the assumption in the analytical model that the canopy remains at saturation during a storm and drip ceases at the end of the storm. With these limiting values of D~ and b in the Rutter model, the estimated evaporation is reduced by 7% and the difference between the Rutter and analytical model estimates becomes less than 5% of the estimated loss.
289
25 0
--
20
¢.
2 ,.
10
_= ..~ g
b=5.25
e-
i
2
~, ' g ' ~ Drainage paramoter
' Ds
1'o ' f2 mm.min 1
i
i
{~1o-~1
25 o
20
e-
"~
15-
lODs = 0 . 0 0 1 4
5~
0-
.~ -5 1'0
2'0
3'0 Drainage
4'0 parameter
5'0
6'0
7'0
b
Fig. 3. Percentage change in the interception loss for a typical month (May 1985) as estimated by the Rutter model, due to variation in the drainage parameters b and D~. DISCUSSION AND CONCLUSIONS
The interception loss found at this site, although of similar absolute magnitude to those found in forests in temperate latitudes, is a relatively small percentage of the gross rainfall. The m e a s u r e m e n t of interception loss as the small difference between gross and net rainfall is therefore inevitably subject to large relative error. This is exacerbated by the problem of sampling throughfall in a mixed forest, which is inherently more variable t h a n is found in temperate forests. These problems have been discussed in detail by Jackson (1971) and Lloyd and Marques (1988). The problem of small-scale variability in throughfall can be overcome by the use of a plastic sheet net rainfall gauge of the type described by Calder and Rosier (1976) which, apart from excluding the short vegetation, gives a complete sample over a small area. Calder et al. (1986) used two plastic sheet gauges, each of the order of 40 m 2 in area, to
290 measure net rainfall in an area of secondary rainforest in Java. The rainforest at this site had a higher stem density and a narrower distribution of stem diameters than the primary rainforest of the Reserva Ducke. For such a method to sample adequately the net rainfall in the Reserva Ducke, where the dominant trees have a separation of tens of metres, either the gauge would need to be very large in area or several smaller replicates would be required. The experience of operating a 90 m 2 net rainfall gauge at this site was that the plastic required almost daily maintenance to repair damage by insects. In addition there were considerable problems in creating a measuring system which could cope with and measure accurately the large peak flow rates encountered during intense storms. Because of these problems, the net rainfall results were not used. It must therefore be accepted that there are relatively large errors in the measurement of the interception loss, and similarly large errors in the derivation of the forest structure parameters, particularly the canopy capacity. This error in the evaluation of the canopy capacity accounts for 84% of the error in the model calculation. However, the maximum difference between the modelled and measured interception loss is less than 4% of the total measured rainfall. An error of this size will normally be less than, or comparable with, other errors involved in drawing up a water balance. Neither of the modelled losses are significantly different from the measured interception loss and both models can therefore be said to have performed adequately. It is interesting to compare the values of the major model parameters found at the present site with some previous values found in temperate forests. Gash et al. (1980) comparing data from four coniferous forest sites in Great Britain found values of S ranging between 0.8 and 1.2 mm, of/~ between 0.13 and 0.33 mm h - 1, and of/~ between 1.2 and 1.8 mm h - 1. The equivalent values found in the present study being 0.74 mm, 0.21 mm h-1 and 5.4 mm h - ' respectively. The canopy capacity is slightly smaller, perhaps reflecting the observation by Herwitz (1987) that films of water of an even thickness are not established on tropical leaf surfaces but instead retract into bead-like droplets. These droplets then coalesce and are rapidly shed from the leaf surface. Such action would lead to a lower canopy capacity than would be expected from consideration of the leaf areda alone. The values of S and St found here are also less than those found by Herwitz (1985) in a study of individual trees. He found that between 1.6 and 6.8 mm of water were required to completely saturate all surfaces of the canopy and trunks, and that more than half of this was a result of trunk storage. The trunk storage values were obtained through oven-drying whereas observation indicated that the trunks were never subjected to these conditions in the very humid atmosphere of this rainforest. Herwitz also commented that only in large storms ( > 10 mm) do all the upper and lower leaf surfaces become wetted and the bark totally saturated. Clearly the model of constant canopy and trunk storage capacities used in the present analysis is a simplification
291 and in reality both may vary with the size of the storm. Nevertheless the performance of both models using the presently defined storage capacities is adequate and it does not therefore seem justified, at this stage, to introduce the additional complexity of dynamic storage capacities. Similarly, it could be argued that the drainage formulation used in the Rutter model should be simplified as suggested by Aston (1979). As a result of his experiments, Aston suggested that the modelling of the interception process be simplified so as not to allow any build up of water on the canopy (effectively the assumption in the analytical model). Making this assumption would reduce the loss calculated by the Rutter model from 605 mm to 564 mm, compared with the estimate of 543 mm from the analytical model and the measured value of 428 mm. Given the lack of certainty in the drainage parameters from tropical forest, this simplification would appear to be sensible. While the value of/~ derived from the meteorological measurements is similar to those found in temperate latitudes, the value of/~ is almost a factor of five higher. It is this high rainfall rate which causes the comparatively low percentage interception loss. A given quantity of rain falling on this tropical forest will take one fifth of the time compared to the same amount of rain falling on a forest in a temperate maritime climate. The time for evaporation during storms and the fractional interception loss are correspondingly reduced. ACKNOWLEDGEMENTS The results presented here were obtained as part of an extensive programme of research into Amazonian micrometeorology supported by the Natural Environment Research Council, Gt. Britain, the Conselho Nacional de Desenvolvimento Cientifico et Tecnologico (CNPq), Brazil and the British Council. The authors are pleased to acknowledge this support. We also thank our colleagues in the Ciencas do Ambiente section of the Instituto National de Pesquisas da Amazonia for their help in data collection and equipment maintenance. APPENDIX Trends in the linear correlation between net and solar radiation
The physics of radiation exchange is such that it is possible to establish an approximate linear relationship between the net radiation, RN, and solar radiation, SR, measured above a stand of vegetation with the form
292
RN =c+mSR
(A1)
see for example Shuttleworth et al. (1984b). In this expression the intercept, c, provides a measure of net longwave exchange, while the slope, m, is largely, but not entirely, related to average albedo. The data given by the automatic weather stations mounted above the forest in the present study provide hourly average measurements of net and solar radiation. Intercomparison studies between the two stations suggest that these two radiation measurements could be subject to a systematic error as large as 5% or 5 W m -2, whichever is greater. In addition, individual hourly measurements exhibit a much greater random variation of the order 10-12%. This is because the hourly measurements are not true average values, rather they are the average of twelve instantaneous measurements made at five minute intervals. Any timing differences between the two stations can therefore easily give significant differences, particularly in conditions of rapidly changing cloud cover. An analysis was made of these radiation data. This comprised making a simple linear regression between measured net and solar radiation for all the hourly average values available in each of the 25 months for which automatic weather station data were taken. No relationship was possible for the months April and May 1984, and only a relationship of reduced significance found for June 1984. Over most of this period the radiation measurement was unreliable, see the section on 'instrumentation'. The values of c and m, in eq. A1, are plotted in Figs. A l ( a ) and A l ( b ) together with their estimated error. The illustrated errors are the statistical estimates generated in the regression procedure, and are therefore arguably a realistic estimate of the likely errors involved in describing the relative variation in monthly estimates. It must be remembered that, because of the systematic errors quoted above, they do not represent the error in the absolute value of c and m. Accepting the quoted systematic errors, and combining them in quadrature, implies that all the values of c could be in systematic error by around 7 W m -2, and all the values of m could be in systematic error by as much as 7%. The resulting values of c and m indicate a significant yearly trend, which appears to be related to the annual variation in rainfall (and presumably cloudiness) at this site, see Fig. A1 (c). The yearly cycle in the offset and gradient in eq. A1 are adequately described by the expressions c = - 1 6 + 7 cos (27C[ND --31]/365)
(A2)
m=0.782-0.028 cos (2~[ND --31]/365)
(A3)
where ND is the day number in the year (it is acceptable to ignore the fact that 1984 was a leap year in quoting these expressions. Clearly the comments re-
293 g" IE
I
[
I
I
¢o -20
o (3 -40
1.0
0.5
"~ 400
=o ~. 200
L_
i
o 1983
1984
1985
Fig. A1. The variation over the measurement period of the coefficients (a) c and (b) m in eq. A1, relating net to solar radiation and (c) the measured rainfall, over the same period.
lating to systematic errors in the individual values of c and m given in the previous paragraph also apply to eqs. A2 and A3. In the analysis given elsewhere in this paper, eq. A1, with the annual variation in c and rn described by eqs. A2 and A3, is used to provide an estimate of net radiation for those periods when the net radiation measurement was not reliable, but a measurement of solar radiation is available. REFERENCES
Aston, A.R., 1979. Rainfall interception by eight small trees. J. Hydrol., 42: 383-396. Bathurst, J.C., 1986. Physically-based distributed modelling of an upland catchment using the Syst~me Hydrologique Europ~en. J. Hydrol., 87: 79-102.
294 Calder, I.R., 1977. A model of transpiration and interception loss from a spruce forest in Plynlimon, Central Wales. J. Hydrol., 33: 247-265. Calder, I.R. and Rosier, P.T.W., 1976. The design of large plastic-sheet net rainfall gauges. J. Hydrol., 30: 403-405. Calder, I.R., Wright, I.R. and Murdiyarso, D., 1986. A study of evaporation from tropical rain forest. J. Hydrol., 89: 13-31. Dolman, A.J., 1987. Summer and winter rainfall interception in an oak forest. Predictions with an analytical and a numerical simulation model. J. Hydrol., 90: 1-9. Eagleson, P.S., 1986. The emergence of global-scale hydrology. Water Resour. Res., 22: 65-145. Ford, E.D., 1976. The canopy of a Scots pine forest: description of a surface of complex roughness. Agric. Meteorol., 17: 9-32. Gash, J.H.C., 1979. An analytical model of rainfall interception in forests. Q.J.R. Meteorol. Soc., 105: 43-55. Gash, J.H.C. and Morton, A.J., 1978. An application of the Rutter model to the estimation of the interception loss from Thetford Forest. J. Hydrol., 38: 49-58. Gash, J.H.C., Wright, I.R. and Lloyd, C.R., 1980. Comparative estimates of interception loss from three coniferous forests in Great Britain. J. Hydrol., 48: 89-105. Herwitz, S.R., 1985. Interception storage capacities of tropical rainforest canopy trees. J. Hydrol., 77: 237-252. Herwitz, S.R., 1987. Raindrop impact and water flow on the vegetative surfaces of trees and the effects on stemflow and throughfall generation. Earth Surface Processes and Landforms, 12: 425-432. Jackson, I.J., 1971. Problems of throughfall and interception assessment under tropical forest. J. Hydrol., 12: 234-254. Leyton, L., Reynolds, E.R.C. and Thompson, F.B., 1967. Rainfall in forest and moorland. In: W.E. Sopper and H.W. Lull (Editors), Int. Symp. on Forest Hydrology, Pergamon Press, Oxford, pp. 163-178. Lloyd, C.R. and Marques, A. de 0., 1988. Spatial variability of throughfall and stemflow measurements in Amazonian rainforest. Agric. For. Meteorol., 42: 63-73. Pearce, A.J. and Rowe, L.K., 1981. Rainfall interception in a multi-storied, evergreen mixed forest: estimates using Gash's analytical model. J. Hydrol., 49: 341-353. Rosenblueth, E., 1975. Point estimates for probability moments. Proc. Natl. Acad. Sci. U.S.A. Vol. 72, No. 10: 3812-3814. Rutter, A.J., Kershaw, K.A., Robins, P.C. and Morton, A.J., 1971. A predictive model of rainfall interception in forests, I. Derivation of the model from observations in a stand of Corsican pine. Agric. Meteorol., 9: 367-384. Rutter, A.J., Morton, A.J. and Robins, P.C., 1975. A predictive model of rainfall interception in forests, II. Generalization of the model and comparison with observations in some coniferous and hardwood stands. J. Appl. Ecol., 12: 367-380. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J., Roberts, J., Marques, A. de O., Fisch, G., Silva, V. de P., Ribeiro, M.N.G., Molion, L.C.B., de Sa, L.D.A., Nobre, J.C., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984a. Eddy correlation measurements of energy partition for Amazonian forest. Q.J.R. Meteorol. Soc., 110: 1143-1162. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J., Roberts, J., Marques, A. de 0., Fisch, G., Silva, V. de P., Ribeiro, M.N.G., Molion, L.C.B., de Sa, L.D.A., Nobre, J.C., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984b. Observations of radiation exchange above and below Amazonian forest. Q.J.R. Meteorol. Soc., 110:1163-1169. Shuttleworth, W.J., 1988. Evaporation from Amazonian ~ain forest. Proc. R. Soc. London, Ser. B, 233: 321-346.
277
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
THE M E A S U R E M E N T A N D M O D E L L I N G OF R A I N F A L L INTERCEPTION BY AMAZONIAN RAIN FOREST
C.R. LLOYD, J.H.C. GASH and W.J. SHUTTLEWORTH
Institute of Hydrology, Wallingford, OXIO 8BB (Gt. Britain) A. DE O. MARQUES F ~
Instituto Nacional de Pesquisas da Amazonia, CP 478, Manaus, Am. (Brazil) (Received December 16, 1987; revision accepted March 18, 1988)
ABSTRACT Lloyd, C.R., Gash, J.H.C., Shuttleworth, W.J. and Marques F., A. de O., 1988. The measurement and modelling of rainfall interception by Amazonian rain forest. Agric. For. Meteorol., 43: 277294. Measurements of the evaporation of rainfall intercepted by Amazonian rain forest were compared with estimates made by two models, the Rutter model and Gash's analytical model, applied to meteorological measurements made with automatic weather stations mounted above the forest. Neither of the model estimates of interception loss was significantly different from measured interception loss, which amounted to 8.9% of the measured rainfall.
INTRODUCTION
There is much concern about the environmental effects of deforestation in the humid tropics. Clearing an area of forest will almost certainly affect its local hydrology in terms of the volume and timing of run-off. If the area is sufficiently large, changes in the surface energy balance may also result in changes in climate. These changes may extend to other regions far beyond the former forest. The sensitivity of climate to changes in vegetation can be predicted using global circulation models (Eagleson, 1986 ), multi-layer models of the Earth's atmosphere which run on a timestep of typically ten minutes. These models require a representation of the surface energy balance, at the same time-scale, which can predict the surface fluxes from the meteorological variables generated by the model. In contrast, the local effects on run-off can be predicted by catchment models for which daily climatological measurements may be adequate. There is thus a requirement for a description of forest evaporation both on the ten minute and on the daily time-scale. Studies of forests in temperate regions have shown that interception loss, the evaporation which 0168-1923/88/$03.50
© 1988 Elsevier Science Publishers B.V.
278 results from rainfall intercepted by the forest canopy and evaporated before reaching the ground, is an important component of forest evaporation. Measurements and models of the interception loss from tropical forest are therefore an essential prerequisite to any quantitative prediction of the effects of deforestation. In this paper two appropriate models for estimating the evaporation of intercepted rainfall are tested against measurements made in Amazonian rain forest. The Rutter model (Rutter et al., 1971, 1975) calculates a running balance of the amount of water on the canopy, with evaporation being estimated from the meteorological variables and forest stand parameters. It is usually run with hourly meteorological data. The model has been successfully tested against data from coniferous plantation forest in Great Britain (Gash and Morton, 1978; Gash et al., 1980) and forms the basis of Calder's (1977) interception model and the interception component of the Syst~me Hydrologique Europ~en (Bathurst, 1986). Gash's analytical model (Gash, 1979) is a storm-based simplification of the Rutter model which, if calibrated using hourly meteorological data, can then be run on daily rainfall values. The model has been successfully tested against data from coniferous plantation forest in Great Britain (Gash et al., 1980), from an oak plantation in The Netherlands (Dolman, 1987) and from mixed evergreen forest in New Zealand (Pearce and Rowe, 1981). Both physically-based models have empiricism restricted as far as possible to the values of parameters whose physical significance is understood. Provided that appropriate values of these model parameters can be derived or estimated, then the models should be generally applicable and not limited to the sites for which they were originally derived. It is a major test of this modelling philosophy to determine whether these models, which were originally tested against data from temperate mono-culture plantations, can successfully estimate the evaporation from tropical rain forest. THEORY The Rutter model
Full details of the Rutter model have been given by Rutter et al. ( 1971, 1975 ). It is essentially a numerical computer model which calculates a running balance of the depth of water on the forest canopy and tree trunks. The model requires the following state parameters: S--- canopy storage capacity, the depth of water left on the canopy in conditions of zero evaporation, when rain and throughfall have ceased; p = free throughfall coefficient, the proportion of rain which falls to the ground without striking the~anopy; St = trunk water capacity; pt =proportion of rain diverted to the trunks. When the depth of water on the canopy, C, exceeds the canopy capacity the drainage rate, D, is calculated from the relationship
279
D=D~ exp[b(C-S) ]
(1)
There is thus a requirement in eq. 1 for values of D~, the drainage rate when C = S and b, which defines the rate of increase in drainage with depth of water on the canopy. The values used in the following analysis were those derived by Rutter et al. (1971) for a Corsican pine canopy modified by the ratio of the rain forest canopy capacity to the Corsican pine canopy capacity as suggested by Rutter et al. (1975). The values for D~ and b were 0.0014 mm min -~ and 5.25 respectively. In the version of the model used here no drainage is allowed when the canopy is unsaturated, ie C< S. This condition complies with the definition of the canopy capacity and avoids the weakness in the drainage equation, noted by Calder (1977), of predicting small but finite drainage from a dry canopy. Evaporation from a saturated canopy is calculated from the appropriate form of the Penman-Monteith equation, with the surface resistance set to zero. When C is less than S (indicating a partially wet canopy with no drainage ), the evaporation is reduced in proportion to the calculated value of C/S. The model is driven by hourly values of rainfall, but in addition the evaporation calculation requires hourly values of net radiation, temperature, humidity and windspeed. The aerodynamic resistance to the transport of water vapour, ra is calculated from
ra =f/U
(2)
where u is windspeed and f is a constant (Rutter et al., 1971 ). The original version of the Rutter model divided each hour into six minute periods, using analytical integrations of the model equations as smoothing functions. In the present version this has been abandoned in favour of a simpler numerical integration using the original equations. Tests using the data presented by Gash et al. (1980) showed that with a timestep of two minutes there was negligible difference between the two methods. The model has also been modified to remove the systematic increase in the duration of storms caused by the procedure of spreading each hour's rainfall equally over the whole hour. On average there will be as many storms which start (or end) less than halfway through an hour, as there will be storms which start (or end) more than halfway through an hour; so the effect of spreading the rain equally over the whole hour will, on average, be to increase the length of storms by one hour. In the tropics where storms are characteristically of short duration this may result in a significant over-estimation of interception loss by the model. The modification restricted the rainfall to the second half of any hour with rain which was preceded by a dry hour, and to the first half of any hour with rain which was followed by a dry hour.
28O
Gash's analytical model Gash's analytical model (Gash, 1979), considers rainfall to occur in a series of discrete storms each of which comprises a period of wetting up, a period of saturation and a period of drying out. The canopy is assumed to have sufficient time to dry between storms. The model is fundamentally a simplification of the Rutter model. It requires the same state variables S, p, St and Pt, and in addition E/R, the ratio of the mean evaporation rate to the mean rainfall rate for hours when rain is falling onto a saturated canopy. Interception loss is then calculated as the sum of the components given in Table 1. Where hourly meteorological data are available these can be used to derive E and/~ by applying the Penman-Monteith equation to those hours with the rainfall above a certain threshold, which are considered to represent saturated conditions. The derived values of E/R can then be applied to the rainfall data recalculated as storm totals, or be used to extrapolate the results to other sites where only rainfall data are available. In applying the model to data from Great Britain, Gash (1979) and Gash et al. ( 1980 ) made the assumption of one storm per rainday. This has the obvious advantage that, once a value has been obtained for E/R, the model can subsequently be run on the widely available daily rainfall data. Pearce and Rowe (1981) found that this assumption was inadequate for the rainfall climate of the South Island of New Zealand, where storms TABLE 1 The analytical forms for the components of interception loss a Component of interception loss
Formulation
For m small storms with PG < P~.
(1--p-pt)
Wetting up the canopy in n large storms with Pc; > P~; Evaporation from saturated canopy during rainfall
n(1-p-pt)P(;-nS
m
~ P(:j j=l
Evaporation after rainfall ceases for n large storms Evaporation from trunks in q storms that fill the storage Evaporation from trunks in m + n - q storms that do not fill the storage Pd defined as the amount of rain necessary to saturate the canopy
n
£= ~ ( P G j - P ; ) Rj=~ nS qSt rn+n--q
Pt
~
j=l
P(~j
P~= (-/~S/E)ln[1-
(/~/R)(1-p-pt)
-~ ]
aThe simpler form of the stemflow formulation (Gash, 1979 ) has been used, rather than the more complex formulation introduced by Gash et al. (1980) to model the evaporation from the trunks in a forest with high stemflow and long duration storms.
281 frequently exceed 24 hours duration. However, in the tropics where rain typically falls in short intense convective storms it is more likely to be a reasonable assumption and has been retained in the present analysis. To model the evaporation from a dense young spruce plantation in Plynlimon, central Wales, Gash et al. ( 1980 ) introduced a more complex formulation for the evaporation from the trunks which accounted for the high stemflow and long duration storms present at that site. As the stemflow at the present site is low and the storms generally of short duration, the original simpler formulation tested against data from mature pine forest at Thetford, East Anglia (where stemflow was also low and storms were of shorter duration), has been used in this analysis. SITE The experimental area described in this paper forms part of the micrometeorological site described by Shuttleworth et al. (1984a) and by Lloyd and Marques (1988). It is situated at 02 ° 57' S, 59 ° 57'W in the Reserva Florestal Ducke, 25 km from Manaus, Amazonas, Brazil. It is typical of undisturbed natural Amazonian terra firme rainforest, extending with no obvious sub-storeys to a height of approximately 35 m with occasional emergent trees reaching 40 m. The plant density is some 3000 stems h a - 1but less than 10% have girths of greater than 0.2 m. INSTRUMENTATION Two automatic weather stations (Didcot Instruments, Abingdon, Gt. Britain) were mounted on a 45 m tower above the forest. Measurements of solar and net radiation, temperature, aspirated wet-bulb temperature and windspeed were made every five minutes and recorded on magnetic tape. Readings from the two stations were later averaged to produce a single set of quality controlled hourly average values. The measurements were made for the period 3 September 1983-21 August 1985. Complete loss of data occurred on 19 days during this period. During the period 26 March 1984-22 June 1984 the polythene domes on both the net radiometers initially clouded and later cracked through prolonged exposure to solar radiation. The net radiation measurement over this period was not considered to be reliable and an estimate of net radiation based on the measured solar radiation was substituted. The form of the expression used and its derivation is described in Appendix 1. Interception loss was determined as the measured difference between gross rainfall and throughfall plus stemflow. Full details of the instrumentation have been described by Lloyd and Marques ( 1988 ). Gross rainfall was measured by one 203-ram diameter 0.25 mm tipping bucket raingauge situated at the top of the tower. Additional measurements were made at a site 100 m from the tower
282 on a small platform erected at the top of a tree, the crown of which was missing. During the period 3 October 1983-1 June 1984, throughfall was measured by fourteen 203-mm diameter, 0.5 mm tipping bucket raingauges. These were randomly relocated every week along a 100 m transect (marked at 1 m intervals) which was situated close to, and between, the gross rainfall measurements. The weekly accumulated tips were recorded on separate counters. The rims of the raingauges were fitted with extensions to minimise splash-out. No throughfall was measured between 1 June 1984 and 5 July 1984, due to the failure of the counter system. From 5 July 1984 to 21 August 1985, the above system of fourteen tipping bucket raingauges was increased to sixteen gauges and augmented by thirtysix bottle gauges. For this period the tipping bucket gauges were fixed in random positions alongside the transect line and their tips accumulated and stored every 30 minutes on two 12-channel solid-state data loggers (Computing Techniques, Gt. Britain). The 100 m transect line was replicated by four more parallel transect lines forming a 100 m × 4 m random grid with 505 sampling positions. On this grid the thirty-six bottle gauges, each with a 127-mm diameter copper funnel, were randomly relocated every week. These funnels were of sufficiently steep an angle to prevent splash-out. During the period 14 March 1985-13 May 1985, the bottle gauges were relocated after every storm. Lloyd and Marques (1988) give further details of these instruments and the errors and spatial variability associated with this array of bottle gauges. Stemflow was measured on nineteen adjacent trees within the middle of the random grid for the period 20 August 1984-21 August 1985. The method of obtaining stemflow, its errors and variability are detailed in Lloyd and Marques (1988). Six of the stemflow measurements were recorded on the remaining channels of the solid-state loggers described above, the other thirteen stemflows were collected in 20 1 plastic bottles. These bottle stemflow totals were measured every week, except for the period 14 March 1985-13 May 1985 when the totals were measured after every storm. RESULTS
Total interception loss The estimate of total interception loss was based on the two years of gross rainfall and throughfall measurements recorded between 3 September 1983 and 21 August 1985. To compare the measured interception loss with the modelled results, periods were removed from the data set when data pertinent to either result were missing. The remaining data set had 625 days of data. Stemflow was only measured during the second year of the experiment, but its relatively small contribution to the water balance justified it being simulated for the first year. The increase in the reliability of the estimate of total
283
4000-
3000 i
Gross~
2000j
~
i i
10001 i
0
,
/
100
I
"
interception oss
200
300 400 Number of days of data
500
600
Fig. 1. Cumulative gross rainfall and measured interception loss plotted against number of days of complete data, starting on 3rd September 1983 and finishing on 21st August 1985. The error bands on the interception loss are also shown ( .... ). interception loss gained from using two years of gross rainfall and throughfall data was felt to outweigh the small loss of accuracy such a simulation would cause. Consequently, stemflow measurements were taken as 1.8 + 1% of gross rainfall for the first year, this figure being the overall estimate gained from the measurements of stemflow between 20 August 1984 and 21 August 1985. The gross rainfall recorded in the 625 days of data was 4804 mm. Total measured throughfall was 4286 mm with a standard error of 170 mm. Throughfall was therefore 89 +_3.5% of gross rainfall. Total stemflow was 90 mm of which 49 mm was simulated data. The total interception loss from these measurements was 428 mm with a standard error of 173 mm which is 8.9 + 3.6% of gross rainfall. The results are plotted in Fig. 1.
Canopy capacity The canopy capacity is usually derived from an analysis of separate storms using the method of Leyton et al. (1967). A line of slope (1 - P t ) is drawn to envelop all the points on a plot of gross rainfall versus throughfall for individual storms. Such a line is assumed to go through only those points representing conditions with minimal evaporation during a storm. The canopy capacity is then given by the intercept of this line with the throughfall axis.
284 The method is appropriate where spatial variability of throughfall measurements is relatively low, e.g. dense plantation coniferous forests. However, with the high spatial variability of throughfall encountered in this particular tropical rainforest (see Lloyd and Marques, 1988), the above method was found to be vague and subjective in its derivation of the canopy capacity, and therefore a more objective method was used. Separate linear regressions of gross rainfall versus throughfall for individual small storms were calculated for each of the 16 fixed tipping bucket raingauges. Individual storms were defined as periods of continuous rain with at least six dry hours separation. These regressions gave a mean slope of 0.92 + 0.12 and a mean intercept of 0.65 + 0.31 mm. This regression produces a value of 0.70 mm of rainfall for zero throughfall. This figure is not equivalent to the canopy capacity, but must be corrected to take account of evaporation during rainfall. Applying the argument given by Gash (1979), and the values of the parameters either implied by the regressions or derived later in this section, gives a corrected value of S equal to 0.74 mm.
Free throughfall coefficient The free throughfall coefficient, p, is an estimate of that fraction of gross rainfall which arrives directly at the soil surface without striking any of the vegetation surfaces. This was determined by using an anascope, similar to that used by Ford (1976), to gain point observations of the canopy cover. These observations were made at each of the 505 sampling positions within the random grid transect area (see Lloyd and Marques, 1988). Of the 505 observations, 40 were judged to be clear sky, implying a free throughfall coefficient of 0.08 with a standard error of 0.01.
Stemflow parameters A similar method to that used for estimating canopy capacity was adopted for evaluating the trunk storage capacity, St, and the proportion of rainfall which is diverted onto the trunks, Pt. The variability of stemflow in this tropical rainforest is also very high, although the overall contribution is relatively small (Lloyd and Marques, 1988). Fifty-two storms were identified for use in this analysis. No individual tree had measurements for all these storms, the worst tree data set being twelve storms and the best being thirty-four storms. The mean number of storms per regression was twenty-two. Separate linear regressions of stemflow versus gross rainfall were formed for each of the nineteen trees. The intercepts of these regressions are estimates of the trunk capacities and the gradients are estimates of the proportion of rainfall diverted to the trunks. By averaging both the set of intercepts and the set of gradients, the stemflow equation is given by
285 S f = 0 . 0 3 6 ( + 0 . 0 0 6 ) PG - 0 . 1 5 ( + 0 . 0 8 )
(3)
where P c is gross rainfall. Values of 0.036 ( _+0.006) for Pt and 0.15 mm ( + 0.08) for St were therefore used as stemflow parameters in the model.
Aerodynamic resistance In the absence of experimental values, ra has often been computed as a function of windspeed, vegetation height, roughness length and zero plane displacement. Such a procedure in this rainforest would lead to a value for f of 29.2 in the eq. 2. However, at this site atmospheric turbulence measurements are available and f can be estimated directly from m o m e n t u m transfer. In a parallel paper, Shuttleworth (1988) has used these measurements to derive a value of [= 34.2. A standard error of 4.7 about this value was estimated from analysis of the same data and these values are used here. MODELLING
Application of the Rutter model The Rutter model was applied to the automatic weather station data using the state parameters given in the previous section. The results are shown in Fig. 2 (a). The model estimated a total loss of 605 mm, equal to 12.6% of gross rainfall. The model also estimated throughfall to be 84.5% of gross rainfall, and stemflow to be 2.9% of gross rainfall.
Application of Gash 's analytical model The analytical model was applied to the same data set as the Rutter interception model using the same state parameters. As in previous applications of the analytical model (Gash, 1979; Gash et al., 1980), saturated conditions were arbitrarily defined as occurring when the hourly rainfall was greater than 0.5 mm (i.e. two bucket tips). The average evaporation and rainfall rate onto a saturated canopy were then used to estimate the total evaporation for each month. The results are shown in Fig. 2 (b). The model estimated a total loss of 543 mm or 11.3% of gross rainfall, which is also within the error bands of the measurement. The overall average evaporation and rainfall rate for saturated canopy conditions were E = 0 . 2 1 and /~=5.15 mm h -1 respectively. It was calculated that 49% of the evaporation was the result of drying out after rainfall and 34% the result of evaporation from a saturated canopy during rainfall. The remaining 17% was accounted for by wetting up the canopy (1%), small storms (7%) and trunk evaporation (9%). Saturated trunks accounted for 8% of the trunk evaporation.
286
700 E
(a)
Error
limits
600 500 400
"~ 300
200100-
j
Putter 160
Goo!
~g
260
360
460
(b)
560
Error limits
":
• f!
.....t!
500 i 400J
660
Measured
L
Analytic
~°°°~
2~
360
45o
56o
ado
Number of days of data
Fig. 2. Cumulative measured interception loss ( ) and cumulative interception loss as estimated ( - - - ) by (a) the Rutter model and (b) Gash's analytical model, against number of days of complete data.
The year-to-year variation in interception loss can be assessed by applying the analytical model to the daily rainfall totals measured at the Reserva Ducke climate station. The model was applied to the period 1971 to 1983 inclusive, using the overall average values of E = 0.21 a n d / ~ = 5.15 mm h -~, and the state parameters derived for the micrometeorological tower site. The results are shown in Table 2. The annual rainfall for this period ranges between 1901 mm and 2712 mm with an average of 2391 mm. The estimated interception loss varies between 10.0% and 12.2% of the rainfall with an average of 11.1%. The highest percentage interception loss occurs with the lowest annual rainfall and vice versa.
Error analysis Both the measurement data set and the model output have errors associated with them. The measurement data set error limits are largely due to the effects
292
11.2
Percentage loss
2607
1971
Year
Interception loss (mm)
Rainfall (mm)
given
11.2
301
2680
1972
11.9
295
2482
1973
12.2
278
2274
1974
12.3
288
2351
1975
10.4
274
2635
1976
11.8
287
2435
1977
11.1
251
2257
1978
10.3
278
2712
1979
12.6
239
1901
1980
11.4
257
2258
1981
10.5
263
2497
1982
12.1
242
1996
1983
11.4
273
2391
Mean
0.2
6
70
Standard deviation
The annual interception loss for the Reserva Ducke Forest, estimated using the analytical model applied to the daily rainfall from the Reserva Ducke climate station and the model parameters derived during the study period. The means and the standard deviation of the means are also
TABLE 2
b~
288 of small samples in assessing very high spatial variability. This uncertainty or "error" results in the cumulative measured throughfall being subject to large positive and negative fluctuations. For example, in Fig. 2 it can be seen that during the period from 2 January to 30 January 1985 (days 425-453 in Fig. 2) the measured interception loss was negative. Given the statistical distribution of the throughfall (see Lloyd and Marques, 1988) such fluctuation should not be unexpected. While over a long period these random fluctuations should cancel, as can be seen from Fig. 2 the measurement of cumulative interception loss is inevitably less smooth than the modelled estimate. The errors in the models are the result of errors inherent in the physical description of the models, together with the errors incurred in the measurement of the state parameters and the driving variables. The overall error in the model is dominated by the effect of errors in the state parameters. By using the method of Rosenblueth (1975), individual contributions to the overall error, resulting from the error in each of the parameters S, p, Pt, St and f, were combined to estimate the standard error in the models' outputs. The modelled interception loss over the two year measurement period, together with its standard error for both of the models is: Rutter: 605 + 127 mm (12.1 + 2.6% of gross rainfall) Analytic: 543 _+103 mm (11.3 _+2.2% of gross rainfall) Standard difference of means tests were performed between measured and modelled interception loss on both models and neither were significantly different from the measurements at the 10% level. The error analysis above does not include the possible error incurred through using assumed parameter values for the drainage function. The leaves of tropical rainforest trees are very different from the needles of the pine trees used to derive the original values of the drainage function. For example, many species of tropical trees have evolved the ability to repel and shed water rapidly from their smooth leaf surfaces via drip points (Herwitz, 1987 ). It might therefore be expected that the drainage from a tropical forest would be more rapid than from a stand of pine trees. The sensitivity of the intercetJtion loss to change in the drainage parameters can be seen in Fig. 3 for a typical month's data. As D~ and b increase, the rate of drip increases until the limit, where the depth of water on the canopy is reduced to S at the end of each time-step and no build-up of water is allowed on the canopy. This is equivalent to the assumption in the analytical model that the canopy remains at saturation during a storm and drip ceases at the end of the storm. With these limiting values of D~ and b in the Rutter model, the estimated evaporation is reduced by 7% and the difference between the Rutter and analytical model estimates becomes less than 5% of the estimated loss.
289
25 0
--
20
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2
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' Ds
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i
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5~
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.~ -5 1'0
2'0
3'0 Drainage
4'0 parameter
5'0
6'0
7'0
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Fig. 3. Percentage change in the interception loss for a typical month (May 1985) as estimated by the Rutter model, due to variation in the drainage parameters b and D~. DISCUSSION AND CONCLUSIONS
The interception loss found at this site, although of similar absolute magnitude to those found in forests in temperate latitudes, is a relatively small percentage of the gross rainfall. The m e a s u r e m e n t of interception loss as the small difference between gross and net rainfall is therefore inevitably subject to large relative error. This is exacerbated by the problem of sampling throughfall in a mixed forest, which is inherently more variable t h a n is found in temperate forests. These problems have been discussed in detail by Jackson (1971) and Lloyd and Marques (1988). The problem of small-scale variability in throughfall can be overcome by the use of a plastic sheet net rainfall gauge of the type described by Calder and Rosier (1976) which, apart from excluding the short vegetation, gives a complete sample over a small area. Calder et al. (1986) used two plastic sheet gauges, each of the order of 40 m 2 in area, to
290 measure net rainfall in an area of secondary rainforest in Java. The rainforest at this site had a higher stem density and a narrower distribution of stem diameters than the primary rainforest of the Reserva Ducke. For such a method to sample adequately the net rainfall in the Reserva Ducke, where the dominant trees have a separation of tens of metres, either the gauge would need to be very large in area or several smaller replicates would be required. The experience of operating a 90 m 2 net rainfall gauge at this site was that the plastic required almost daily maintenance to repair damage by insects. In addition there were considerable problems in creating a measuring system which could cope with and measure accurately the large peak flow rates encountered during intense storms. Because of these problems, the net rainfall results were not used. It must therefore be accepted that there are relatively large errors in the measurement of the interception loss, and similarly large errors in the derivation of the forest structure parameters, particularly the canopy capacity. This error in the evaluation of the canopy capacity accounts for 84% of the error in the model calculation. However, the maximum difference between the modelled and measured interception loss is less than 4% of the total measured rainfall. An error of this size will normally be less than, or comparable with, other errors involved in drawing up a water balance. Neither of the modelled losses are significantly different from the measured interception loss and both models can therefore be said to have performed adequately. It is interesting to compare the values of the major model parameters found at the present site with some previous values found in temperate forests. Gash et al. (1980) comparing data from four coniferous forest sites in Great Britain found values of S ranging between 0.8 and 1.2 mm, of/~ between 0.13 and 0.33 mm h - 1, and of/~ between 1.2 and 1.8 mm h - 1. The equivalent values found in the present study being 0.74 mm, 0.21 mm h-1 and 5.4 mm h - ' respectively. The canopy capacity is slightly smaller, perhaps reflecting the observation by Herwitz (1987) that films of water of an even thickness are not established on tropical leaf surfaces but instead retract into bead-like droplets. These droplets then coalesce and are rapidly shed from the leaf surface. Such action would lead to a lower canopy capacity than would be expected from consideration of the leaf areda alone. The values of S and St found here are also less than those found by Herwitz (1985) in a study of individual trees. He found that between 1.6 and 6.8 mm of water were required to completely saturate all surfaces of the canopy and trunks, and that more than half of this was a result of trunk storage. The trunk storage values were obtained through oven-drying whereas observation indicated that the trunks were never subjected to these conditions in the very humid atmosphere of this rainforest. Herwitz also commented that only in large storms ( > 10 mm) do all the upper and lower leaf surfaces become wetted and the bark totally saturated. Clearly the model of constant canopy and trunk storage capacities used in the present analysis is a simplification
291 and in reality both may vary with the size of the storm. Nevertheless the performance of both models using the presently defined storage capacities is adequate and it does not therefore seem justified, at this stage, to introduce the additional complexity of dynamic storage capacities. Similarly, it could be argued that the drainage formulation used in the Rutter model should be simplified as suggested by Aston (1979). As a result of his experiments, Aston suggested that the modelling of the interception process be simplified so as not to allow any build up of water on the canopy (effectively the assumption in the analytical model). Making this assumption would reduce the loss calculated by the Rutter model from 605 mm to 564 mm, compared with the estimate of 543 mm from the analytical model and the measured value of 428 mm. Given the lack of certainty in the drainage parameters from tropical forest, this simplification would appear to be sensible. While the value of/~ derived from the meteorological measurements is similar to those found in temperate latitudes, the value of/~ is almost a factor of five higher. It is this high rainfall rate which causes the comparatively low percentage interception loss. A given quantity of rain falling on this tropical forest will take one fifth of the time compared to the same amount of rain falling on a forest in a temperate maritime climate. The time for evaporation during storms and the fractional interception loss are correspondingly reduced. ACKNOWLEDGEMENTS The results presented here were obtained as part of an extensive programme of research into Amazonian micrometeorology supported by the Natural Environment Research Council, Gt. Britain, the Conselho Nacional de Desenvolvimento Cientifico et Tecnologico (CNPq), Brazil and the British Council. The authors are pleased to acknowledge this support. We also thank our colleagues in the Ciencas do Ambiente section of the Instituto National de Pesquisas da Amazonia for their help in data collection and equipment maintenance. APPENDIX Trends in the linear correlation between net and solar radiation
The physics of radiation exchange is such that it is possible to establish an approximate linear relationship between the net radiation, RN, and solar radiation, SR, measured above a stand of vegetation with the form
292
RN =c+mSR
(A1)
see for example Shuttleworth et al. (1984b). In this expression the intercept, c, provides a measure of net longwave exchange, while the slope, m, is largely, but not entirely, related to average albedo. The data given by the automatic weather stations mounted above the forest in the present study provide hourly average measurements of net and solar radiation. Intercomparison studies between the two stations suggest that these two radiation measurements could be subject to a systematic error as large as 5% or 5 W m -2, whichever is greater. In addition, individual hourly measurements exhibit a much greater random variation of the order 10-12%. This is because the hourly measurements are not true average values, rather they are the average of twelve instantaneous measurements made at five minute intervals. Any timing differences between the two stations can therefore easily give significant differences, particularly in conditions of rapidly changing cloud cover. An analysis was made of these radiation data. This comprised making a simple linear regression between measured net and solar radiation for all the hourly average values available in each of the 25 months for which automatic weather station data were taken. No relationship was possible for the months April and May 1984, and only a relationship of reduced significance found for June 1984. Over most of this period the radiation measurement was unreliable, see the section on 'instrumentation'. The values of c and m, in eq. A1, are plotted in Figs. A l ( a ) and A l ( b ) together with their estimated error. The illustrated errors are the statistical estimates generated in the regression procedure, and are therefore arguably a realistic estimate of the likely errors involved in describing the relative variation in monthly estimates. It must be remembered that, because of the systematic errors quoted above, they do not represent the error in the absolute value of c and m. Accepting the quoted systematic errors, and combining them in quadrature, implies that all the values of c could be in systematic error by around 7 W m -2, and all the values of m could be in systematic error by as much as 7%. The resulting values of c and m indicate a significant yearly trend, which appears to be related to the annual variation in rainfall (and presumably cloudiness) at this site, see Fig. A1 (c). The yearly cycle in the offset and gradient in eq. A1 are adequately described by the expressions c = - 1 6 + 7 cos (27C[ND --31]/365)
(A2)
m=0.782-0.028 cos (2~[ND --31]/365)
(A3)
where ND is the day number in the year (it is acceptable to ignore the fact that 1984 was a leap year in quoting these expressions. Clearly the comments re-
293 g" IE
I
[
I
I
¢o -20
o (3 -40
1.0
0.5
"~ 400
=o ~. 200
L_
i
o 1983
1984
1985
Fig. A1. The variation over the measurement period of the coefficients (a) c and (b) m in eq. A1, relating net to solar radiation and (c) the measured rainfall, over the same period.
lating to systematic errors in the individual values of c and m given in the previous paragraph also apply to eqs. A2 and A3. In the analysis given elsewhere in this paper, eq. A1, with the annual variation in c and rn described by eqs. A2 and A3, is used to provide an estimate of net radiation for those periods when the net radiation measurement was not reliable, but a measurement of solar radiation is available. REFERENCES
Aston, A.R., 1979. Rainfall interception by eight small trees. J. Hydrol., 42: 383-396. Bathurst, J.C., 1986. Physically-based distributed modelling of an upland catchment using the Syst~me Hydrologique Europ~en. J. Hydrol., 87: 79-102.
294 Calder, I.R., 1977. A model of transpiration and interception loss from a spruce forest in Plynlimon, Central Wales. J. Hydrol., 33: 247-265. Calder, I.R. and Rosier, P.T.W., 1976. The design of large plastic-sheet net rainfall gauges. J. Hydrol., 30: 403-405. Calder, I.R., Wright, I.R. and Murdiyarso, D., 1986. A study of evaporation from tropical rain forest. J. Hydrol., 89: 13-31. Dolman, A.J., 1987. Summer and winter rainfall interception in an oak forest. Predictions with an analytical and a numerical simulation model. J. Hydrol., 90: 1-9. Eagleson, P.S., 1986. The emergence of global-scale hydrology. Water Resour. Res., 22: 65-145. Ford, E.D., 1976. The canopy of a Scots pine forest: description of a surface of complex roughness. Agric. Meteorol., 17: 9-32. Gash, J.H.C., 1979. An analytical model of rainfall interception in forests. Q.J.R. Meteorol. Soc., 105: 43-55. Gash, J.H.C. and Morton, A.J., 1978. An application of the Rutter model to the estimation of the interception loss from Thetford Forest. J. Hydrol., 38: 49-58. Gash, J.H.C., Wright, I.R. and Lloyd, C.R., 1980. Comparative estimates of interception loss from three coniferous forests in Great Britain. J. Hydrol., 48: 89-105. Herwitz, S.R., 1985. Interception storage capacities of tropical rainforest canopy trees. J. Hydrol., 77: 237-252. Herwitz, S.R., 1987. Raindrop impact and water flow on the vegetative surfaces of trees and the effects on stemflow and throughfall generation. Earth Surface Processes and Landforms, 12: 425-432. Jackson, I.J., 1971. Problems of throughfall and interception assessment under tropical forest. J. Hydrol., 12: 234-254. Leyton, L., Reynolds, E.R.C. and Thompson, F.B., 1967. Rainfall in forest and moorland. In: W.E. Sopper and H.W. Lull (Editors), Int. Symp. on Forest Hydrology, Pergamon Press, Oxford, pp. 163-178. Lloyd, C.R. and Marques, A. de 0., 1988. Spatial variability of throughfall and stemflow measurements in Amazonian rainforest. Agric. For. Meteorol., 42: 63-73. Pearce, A.J. and Rowe, L.K., 1981. Rainfall interception in a multi-storied, evergreen mixed forest: estimates using Gash's analytical model. J. Hydrol., 49: 341-353. Rosenblueth, E., 1975. Point estimates for probability moments. Proc. Natl. Acad. Sci. U.S.A. Vol. 72, No. 10: 3812-3814. Rutter, A.J., Kershaw, K.A., Robins, P.C. and Morton, A.J., 1971. A predictive model of rainfall interception in forests, I. Derivation of the model from observations in a stand of Corsican pine. Agric. Meteorol., 9: 367-384. Rutter, A.J., Morton, A.J. and Robins, P.C., 1975. A predictive model of rainfall interception in forests, II. Generalization of the model and comparison with observations in some coniferous and hardwood stands. J. Appl. Ecol., 12: 367-380. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J., Roberts, J., Marques, A. de O., Fisch, G., Silva, V. de P., Ribeiro, M.N.G., Molion, L.C.B., de Sa, L.D.A., Nobre, J.C., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984a. Eddy correlation measurements of energy partition for Amazonian forest. Q.J.R. Meteorol. Soc., 110: 1143-1162. Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., Moore, C.J., Roberts, J., Marques, A. de 0., Fisch, G., Silva, V. de P., Ribeiro, M.N.G., Molion, L.C.B., de Sa, L.D.A., Nobre, J.C., Cabral, O.M.R., Patel, S.R. and de Moraes, J.C., 1984b. Observations of radiation exchange above and below Amazonian forest. Q.J.R. Meteorol. Soc., 110:1163-1169. Shuttleworth, W.J., 1988. Evaporation from Amazonian ~ain forest. Proc. R. Soc. London, Ser. B, 233: 321-346.