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Hydrology of tile drainage runoff
Phys. Chem. Eurtk (Bj, Vol. 26, No. 7-8, pp.623-627, 2001 0 2001 Elsevier Science Ltd. All rights reserved 1464-1909/01/$ - see front matter
Pergamon
PII:
S1464-1909(01)00059-4
Hydrology of Tile Drainage Runoff F. Dolezal’, Z. Kulhavy’, M. Soukup’ and R. Kodesova2 ‘Research
Institute
for Soil and Water Conservation,
Zabovreska
250, 156 27 Praha 5 - Zbraslav,
Czech Republic
2Proutena 423, 149 00 Praha 4, Czech Republic
Abstract. The paper is focused on the statistical analysis of drainage runoff. The probability-of-exceedance (POE) curves of drainage runoff typically consist of three parts. The first part, a low-discharge domain, reflects the local hydrogeology of the drained land, provided that the drains are in contact with a permanent aquifer; otherwise the discharges in this part are zero. The second part comprises the cases when the soil profile itself is being drained, while in the third part the discharges are limited from above by the hydraulic capacity of the drainage system. The mechanisms behind the shape of the POE-curve are analysed. In the range of medium discharges, the rate of decline of the discharge depends on the discharge itself in an approximately linear manner and can be physically interpreted. An approximation of the middle part of the POE-curve, using the logarithmic Gumbel distribution, is proposed. Empirical POE-curves have been derived from the data measured on three different sites. Their shapes, as well as the shapes of synthetic POE-curves obtained from DRAINMOD simulation with a generated loo-year weather input, are in qualitative accordance with the stated hypotheses. The maximum observed discharges are near to their physical limits. The specific drainage runoff from a drained ploughed land is considerably higher than the total specific runoff from an undrained forested area. 0 2001 Elsevier Science Ltd. All rights reserved
1 Introduction The drainage runoff is a specific, directly measurable component of the catchment water balance. Its role and significance varies considerably, depending on the local climate, soils, hydrogeology and orography. This paper deals with the hydrological role of underground (tile or plastic pipe) drainage systems on agricultural lands in foothill zones of Central Europe and is mainly focused on
the stochastic aspect of drainage runoff. The main practical focus is on flood problems (cf. Fidler and Soukup, 1998).
2 Theory 2.1 Stochastic analysis of drainage runoff The drainage runoff probability-of-exceedance curves (referred to below as POE-curves) are often presented in terms of instantaneous or average daily runoff rates, rather than of peak flows (cf. Shkinkis, 1974, p. 285). The PoEcurves are most advantageously plotted as flow rates (vertical axis, linear scale) vs. probabilities of exceedance (horizontal axis, logarithmic scale). All statements about the shape of the POE-curves below refer to this way of plotting. The POE-curves of instantaneous of average daily discharges are typically composed of three parts. At low or zero discharges, the hydrogeology of the drained land is a decisive factor. The drainage system may drain a perennial aquifer, in which case the drainage runoff is almost uniform in time and virtually never ceases. If no such aquifer is around, the drainage runoff is ephemeral. In the former case, there is a certain non-zero discharge of which the POE is unity and the POE-curve in the domain of low discharges is concave downwards or approximately linear. In the latter case, the zero discharge has a certain non-zero probability of non-exceedance, i.e., a part of the POE-curve coincides with the x-axis. The second parts of POE-curves comprise medium discharges which result from abstraction of water from the soil profile itself. This parts of the POE-curves are usually concave upwards and can be approximated with a suitable theoretical distribution, e.g, with the logarithmic Gumbel (Cunnane, 1989). Finally, the third part of the POE-curve, the one which accounts for the highest discharges, is
624
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
Table 1. Basic characteristicsof experimental catchments Name of catchment: Average latitude:
Cerhovicky potok 490 51’E
Cemici 49’ 37’ N
Krepelka 50” 29’ N
Average longitude: Altitude (m):
13’ 50’ E 390 - 572
WWE 460 - 561
360 - 410
7.31 18%
1.42
2.0
65 %
7.5%
% forest:
22%3 61 %
14% 19%
20 % 5%
Average annual precipitation (mm):*)
617, Holoubkov 1901-50
Average annual air temperature(“C): *)
7.5, Jince 1901-50 S7 - 40.5 ha S8 - 23.5 ha
722, Cechtice 1961-95 7.5, Cechtice 1961-95
742, Hronov 1901-50 7.3, Broumov 1901-50
Sl - 0.605 ha S2-1.815ha
0.80 ha
Area (km*): % arable land: % grassland:
Drainage systems studied:
1992 - 2000 weatheredparagneiss
1986 - 2000 weatheredschist Parent rock: ‘) Including the set-asideland. *) According to the weather station and period indicated Measurementperiod:
influenced by the hydraulic capacity of the drainage system. It is usually concave downwards and its slope approaches zero. When the data are available for a longer period, it is possible to estimate a POE-curve for annual maxima, for peak-over-threshold flows or even for monthly maxima, even though the latter are not strictly stationary. The PoEcurves of monthly, annual or other maxima are composed of the same three parts as above but larger parts of them belong to the domains of high and medium discharges, while the domain of low discharges is less pronounced or is completely lacking.
2.2 Drainage hydraulics The hydrological analysis of a drainage system requires that the drainage hydraulics is understood. Suitable equations are those derived by Kirkham et al., namely, for a steady flow of groundwater towards the drains (cf. van Schilfgaarde, 1974, p. 204): q = K h,,, F(L,r, D)
16’ 14’ E
(1)
where q (m.d-‘) is the specific drainage runoff, K (m.d-‘) is the hydraulic conductivity of the soil, h,,, (m) is the groundwater table elevation above the level of drains taken in the mid-distance between the drains and F (mm’)is a geometrical factor which depends on the drain spacing L (m), the effective drain radius r (m) and the effective depth D (m) of an impermeable bedrock below the level of drains. It follows from (1) that the drainage runoff depends linearly on the groundwater table elevation. An analogous equation for unsteady drainage after a rain event (cf. van Schilfgaarde, 1974, p. 256) is:
where h,,,,, (m) is h,,, at t = 0, t (d) is the time elapsed since the rain cessation, f (m3.m”) is the drainable porosity of the
1965 - 1982 loess loam over sandstone
soil and G (m-l) is another geometrical factor. If the relation between q and h,,, can be approximated as (l), the rate of the drainage runoff decline will be: dq dt=
-- KG
(3)
f4
In other words, the slope of the plot of dq/dt vs. q or dQ/dt vs. Q, where Q (m3.s-‘) is the drain discharge, gives the ratio KG/J also referred to as the drainage intensity factor. At very high discharges, the flow regime in the critical point of the system can be regarded as a full-profile pipe flow. Smedema and Rycroft (1983, p. 158) give approximate formulae for the quasi-steady discharge Q (m3.s-‘) in smooth pipes: Q =89d2,7’ie,s7 (4) and in corrugated plastic pipes: Q = 38d2,67iO,sO (5) where d(m) is the inner diameter of the drain and i (m.m-‘) is the drain slope. The drainage flow hydraulics is, in our context, regarded as a tool which helps us to explain the POE curves. An attempt in this direction was made, e.g., by Fidler (cf. Benetin et al., 1987, pp. 206-209).
3 Experimental
sites and methodology
The characteristics of experimental sites are given in Table 1. The instantaneous as well as the average daily runoff rates are available for the Cerhovicky potok and the Cemici catchments while only the instantaneous rates sampled once per day are available for the Krepelka catchment. Synthetic POE-curves were produced by DRAINMOD (cf. Skaggs, 1980), a simulation model of soil water flow in which the processes in the unsaturated part of the soil are treated as sequences of steady states. The input parameters corresponded approximately to the Cemici catchment but
625
E Dolezal et al.: Hydrology of Tile Drainage Runoff
.-
2.5
_..__._,,.,___
-
.._-,_
-_-
.._. -
..___ -
..-...-
-
..-.-........- __
Q“.ma 3 2.0 2 i
!
g
j
6
I I,0 / / ;
il.5
1
'
ci 0.5 ; I
03
0.0 1
0 0,001
0.01
O,l Probabilityof excaedanca
0.ooo1
1
caG&aU.
Th
WC&W
inpur 10 IXMXMUB
0.01
0.1
1
Probabilityof exceadance
Fig.1. Empirical probability-of-exceedance curves for the instantaneous (Q) rtnh ti average &aiIy {QJ &r& &&harges ia he Cemici catch* draima_e system%1~t’Mtt*n~r.
wert nti
0,001
Fig.2. Empirical probability-of-exceedancecurves for the sampled daily (Qj, tfte maximum monthly (C&&J and tie maximum annual (QY.& $cllir~~ha~J~~.~~~~~i~,~~,~!
was
loo-year daily data series generated by WXGEN (cf. Sharpley and Williams, 1990), a stochastic weather generator in which the sequence of wet and dry days is simulated as a first-order Markovian process, while the daiIy precipitation sums on wet days and daily tenperamres, solar radiation sums, air humidities and wind speeds on all days are generated as autocorrelated random prescribed These processes with characteristics. characteristics were derived from observed weather stati& in adjacent weather stations. a
4 Results and discussion 4.1 Empirical POE-curves The POE-curves of instantaneous and average daily drainage discharges for the Cemici-Sl site are presented in Fig. 1. Similar POE-curves were obtained for the other sites. The average daily discharges are, at the same probability of exceedance, perceptibly lower than the instantaneous discharges. In general, the shape of the POE-curves follows the trends outlined in the theoretical part above. The zigzagbenavrour o? tie ‘ms~raneous tir&arge curve ‘mFtg. 1 is an artifact caused by physical insufficiency of the Vnotch flowmeter used. The POE-curve for sampled daily discharges in the Krepelka catchment is compared with the curves far monully anct annua1 maxima iaF&.ZAuI%ree curves entire1~ belong to tie domam of me&mu &ss&rges as discussed above. The high-discharge domain is not cl&~ indicated, exe+, perhaps, for the e.uNe of daily discharges.
0.caJ1
0,001
0.01
O,l
1
PMabiJ@nta,.CS&W
Fig.3. Empirical probability-of-exceedancecurves for the sampled daily (Krepelka) or the average daily (all other sites) specific drainage runoff rates - comparisonof different sites.
0.10 O,W 0.08 0.07 f =
0.06
=
0.05
3
w‘l 0.03 cm! 0.01 o,w 0.1
Probability of exceedance
1
Fig.4. Empirical probability-of-exceedancecurves for the sampled daily (K1qA9.a~ M ti Wage daily (at%tier sties) specific drainage runoff rams - compsr&on of di&renr sites. This is a blown-up porrion of- Fig. 3 showing the domain of low discharges.
626
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
% r: P -
I 1 a”- 0,8 ci &
2
___.
1.8
-.
,
1.8 1.4 1.2
ti
L E’ 0.8 0.4
E ‘@
l 0.8
”
0.8
=
0,4
0.2 0 o.oow1
o.ow1
0,001
0,Ol
O,l
1
0
0.1
0.3
0.2
0.4
0.5
0.8
qd,stream (Us/ha)
Probability of exceedance
Fig.5. Synthetic probability-of-exceedance curves for the average daily (QJ, the maximum monthly (Q,,,,,,,& and the maximum annual (QY.,,& drain discharges. The curves were obtained from a DRAMMOD simulation with the input parameters approximating the Cernici-Sl site and a loo-year daily weather data seriesgeneratedby WXGEN.
Fig.6. A comparison of the average daily specific drainage runoff rate (Cerhovicky potok, drainage system S7, 40.5 ha) with the average daily specific stream runoff rate (profile B I, 3 I5 ha) upstreamof the S7 outlet. The straight line indicatesa hypotheticalequality of the two runoff rates.
Comparisons between different sites are only possible in terms of the specific runoff rate, i.e., the discharge divided by the contributing area, which is taken as the nominal area of the drained land. The resulting POE-curves for daily (average or sampled) specific drainage runoff rates are displayed in Fig. 3. A blown-up portion of the same figure for lowest discharges is presented in Fig. 4. At first glance, all curves in Fig. 3 are similar to each other, but the Krepelka site, on which the underlying rock is permeable sandstone, undergoes periods without any drainage runoff, while the CerniciS2 site, which drains a permanent spring, has always non-zero discharges (see Fig. 4). The latter is the only site which reveals a clearly pronounced non-zero low-discharge domain of the POE curve (up to about 0.8 l/s/ha). The medium-discharge domain of the CemiciS2 curve has a considerably larger slope than the lowdischarge domain which indicates that the mechanisms of drainage are different. These processes may be analysed using (2) and (3) above. The uppermost part of the CerniciS2 curve may already be regarded as belonging to the highdischarge domain.
empirical curves in Fig. 3 are qualitatively similar to the synthetic curves in Fig. 5. The upper limit of simulated discharges (1.45 1.i’) is considerably lower than the upper limit of measured discharges in Cemici-Sl (4.17 1.~~‘,see Fig. 1 and Table 2). Table 2 presents an approximate calculation of the possible upper limits of the drainage runoff based on the formulae given above. The results are only rough approximations because the soil and drain pipe properties are not accurately known and the assumed hydraulic scenarios may not be
‘4.2 Model calculations Synthetic POE-curves are presented in Fig. 5. They are far from fitting the measured data, because the DRAINMOD model has not been calibrated, but are deemed to be qualitatively correct because the physical processes simulated by DRAINMOD correspond more or less to the processes which really occur in the field. The synthetic POE-curves reveal well-developed high-discharge domains as discussed above. These domains are lacking or uncertain in most empirical POE-curves, because the latter are usually based on only few years of measured data. Otherwise, the
Table 2 Estimation of upper limits of the drain discharge (Q) and the specific runoff rate (q) Site: Area (ha):
Cemici Sl
Cemici S2
0.605
I.815
Cerhovicky potok 40.5
a) Limitation by drain pipe hydraulics: Pipe material:
plastic
Drain diameter d(m):
0.09 m
plastic 0.065 m
smooth 0.2 m
Drain slope i: Q (1,s’) =
0.025 9.70
0.0452 5.47
0.043 188.91
q (I.$-‘.ha”) =
16.03
3.01
4.66
b) Limitation by groundwaterhydraulics: Drain spacingL (m): Hydraulic conductivityK(m.d-‘): Groundwatertable elevation h, (m):
I3
I3
11
0.7
0.8
0.4
I.0
1.0
1.0
Eff. drain radius r(m): Geom. factor F (m-l): Q (1,s”) = q (I.s”.ha-‘) =
0.02 0.04532 2.22 367
0.02 0.04532 762 4.20
0.02 0.05529 103.67 2.56
c) Actually observedinstantaneousmaxima: Q (Is“) = 4.17 4.17
112.68
q (I.s“.ha-‘) =
2.78
6.90
2.30
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
exactly the same as in reality. Nonetheless, these results suggest that the observed maximum discharges from the drainage systems studied are near to their physical limits.
621
paper is probably the first attempt to identify different parts of the POE curves and to analyse the mechanisms behind them. The analysis presented above suggests that this approach is correct and should be pursued further.
4.3 Comparison with stream runoff Fig. 06 coqpares tie averape b6ly sped% hr&mage mnc% (Cerhovicky potok, S7) with the average daily specific runoff in the stream (the Cerhovicky potok itself) at a profile (Bl) upstream of the S7 outlet. Bl is fed by the uppemnodg. un&tim& an& -mutiny -&r&e& pzrh. ti %fe catchment. Fig. 6 suggests that the specific drainage runoff from ploughed land is higher than the total specific runoff from an undrained and forested area. However, the actual contributing area of the drainage system may be much larger than its nominal area\ extent and is very ti%icuIrt to delineate.
5 Conclusions The tile drainage runoff is an important part of hydrological balance but is difficult to quantify, especially in foothill regions where the local conditions vary on an extremely short spatial scale. The quantification of the role which the drainage runoff plays during floods and droughts requires, amorg, otier aspecti_, SAaS&e pro&aMJ?y of exceedance curvces jtie POE-curves) 0Etie brainage rrrnopEIue &Aieh. While this approach as such is not completely new, this
Acknowledgement. The research was partly financed by the National Aqxq +& %z&ss!!~.~~Qx.~~x.assh as aqrx+&w. V&T!! Ep QQ@USS&
and 6y the Grant Agency or-tie Gecri RepubrSi: as a pro~&cf no. 103/99/1470. Technical assistance of A. Eichler, K. Mimrova, E. Pilna, P. Hospodka, P. Prazak and others is greatly acknowledged.
References Benetin, J., Dvorak, J., Fidler, J., and Kabina, P., Drainage (in Czech and Slovak), Prlroda, Bratislava, 1987. Cumxxke, C., Stattstical dtstrihutians far flood Jiie~uency analysis,
Operational Hydrology Report No. 33, WMO, Geneva, IY89. Fidler, J. and Soukup, M., The share of runoff from drainages in the size of flood discharge (in Czech), Rostlinna vyroba, h&237-241, 1998. Sharpley, A.N., and Williams, J.R., EPIC - Erosion/Productivity Impuct Calculator: I. Model documentation, 2. User’s guide, USDA Technical Bulletin No. 1768, 1990. Shkinkis, Ts.N., Problems of drainage fydrologv (in Russian), Gidrometeoizdat, Leningrad, 1974. Skaggs, R.W., DRAINMOD, Reference Report, USDA - SCS, South National Technical Center, Fort Worth, TX, USA, 1980. Smedema, L.K. and Rycrofi, D.W., Land drainage, Batsford, London, 1983. van Schilfgaardc. J. led.). Druinqe_for apricuhre. Agronomy series No. ‘is, zun.%uc. kgron.,IGl&irson,“~~~, ‘f?Vt.
Pergamon
PII:
S1464-1909(01)00059-4
Hydrology of Tile Drainage Runoff F. Dolezal’, Z. Kulhavy’, M. Soukup’ and R. Kodesova2 ‘Research
Institute
for Soil and Water Conservation,
Zabovreska
250, 156 27 Praha 5 - Zbraslav,
Czech Republic
2Proutena 423, 149 00 Praha 4, Czech Republic
Abstract. The paper is focused on the statistical analysis of drainage runoff. The probability-of-exceedance (POE) curves of drainage runoff typically consist of three parts. The first part, a low-discharge domain, reflects the local hydrogeology of the drained land, provided that the drains are in contact with a permanent aquifer; otherwise the discharges in this part are zero. The second part comprises the cases when the soil profile itself is being drained, while in the third part the discharges are limited from above by the hydraulic capacity of the drainage system. The mechanisms behind the shape of the POE-curve are analysed. In the range of medium discharges, the rate of decline of the discharge depends on the discharge itself in an approximately linear manner and can be physically interpreted. An approximation of the middle part of the POE-curve, using the logarithmic Gumbel distribution, is proposed. Empirical POE-curves have been derived from the data measured on three different sites. Their shapes, as well as the shapes of synthetic POE-curves obtained from DRAINMOD simulation with a generated loo-year weather input, are in qualitative accordance with the stated hypotheses. The maximum observed discharges are near to their physical limits. The specific drainage runoff from a drained ploughed land is considerably higher than the total specific runoff from an undrained forested area. 0 2001 Elsevier Science Ltd. All rights reserved
1 Introduction The drainage runoff is a specific, directly measurable component of the catchment water balance. Its role and significance varies considerably, depending on the local climate, soils, hydrogeology and orography. This paper deals with the hydrological role of underground (tile or plastic pipe) drainage systems on agricultural lands in foothill zones of Central Europe and is mainly focused on
the stochastic aspect of drainage runoff. The main practical focus is on flood problems (cf. Fidler and Soukup, 1998).
2 Theory 2.1 Stochastic analysis of drainage runoff The drainage runoff probability-of-exceedance curves (referred to below as POE-curves) are often presented in terms of instantaneous or average daily runoff rates, rather than of peak flows (cf. Shkinkis, 1974, p. 285). The PoEcurves are most advantageously plotted as flow rates (vertical axis, linear scale) vs. probabilities of exceedance (horizontal axis, logarithmic scale). All statements about the shape of the POE-curves below refer to this way of plotting. The POE-curves of instantaneous of average daily discharges are typically composed of three parts. At low or zero discharges, the hydrogeology of the drained land is a decisive factor. The drainage system may drain a perennial aquifer, in which case the drainage runoff is almost uniform in time and virtually never ceases. If no such aquifer is around, the drainage runoff is ephemeral. In the former case, there is a certain non-zero discharge of which the POE is unity and the POE-curve in the domain of low discharges is concave downwards or approximately linear. In the latter case, the zero discharge has a certain non-zero probability of non-exceedance, i.e., a part of the POE-curve coincides with the x-axis. The second parts of POE-curves comprise medium discharges which result from abstraction of water from the soil profile itself. This parts of the POE-curves are usually concave upwards and can be approximated with a suitable theoretical distribution, e.g, with the logarithmic Gumbel (Cunnane, 1989). Finally, the third part of the POE-curve, the one which accounts for the highest discharges, is
624
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
Table 1. Basic characteristicsof experimental catchments Name of catchment: Average latitude:
Cerhovicky potok 490 51’E
Cemici 49’ 37’ N
Krepelka 50” 29’ N
Average longitude: Altitude (m):
13’ 50’ E 390 - 572
WWE 460 - 561
360 - 410
7.31 18%
1.42
2.0
65 %
7.5%
% forest:
22%3 61 %
14% 19%
20 % 5%
Average annual precipitation (mm):*)
617, Holoubkov 1901-50
Average annual air temperature(“C): *)
7.5, Jince 1901-50 S7 - 40.5 ha S8 - 23.5 ha
722, Cechtice 1961-95 7.5, Cechtice 1961-95
742, Hronov 1901-50 7.3, Broumov 1901-50
Sl - 0.605 ha S2-1.815ha
0.80 ha
Area (km*): % arable land: % grassland:
Drainage systems studied:
1992 - 2000 weatheredparagneiss
1986 - 2000 weatheredschist Parent rock: ‘) Including the set-asideland. *) According to the weather station and period indicated Measurementperiod:
influenced by the hydraulic capacity of the drainage system. It is usually concave downwards and its slope approaches zero. When the data are available for a longer period, it is possible to estimate a POE-curve for annual maxima, for peak-over-threshold flows or even for monthly maxima, even though the latter are not strictly stationary. The PoEcurves of monthly, annual or other maxima are composed of the same three parts as above but larger parts of them belong to the domains of high and medium discharges, while the domain of low discharges is less pronounced or is completely lacking.
2.2 Drainage hydraulics The hydrological analysis of a drainage system requires that the drainage hydraulics is understood. Suitable equations are those derived by Kirkham et al., namely, for a steady flow of groundwater towards the drains (cf. van Schilfgaarde, 1974, p. 204): q = K h,,, F(L,r, D)
16’ 14’ E
(1)
where q (m.d-‘) is the specific drainage runoff, K (m.d-‘) is the hydraulic conductivity of the soil, h,,, (m) is the groundwater table elevation above the level of drains taken in the mid-distance between the drains and F (mm’)is a geometrical factor which depends on the drain spacing L (m), the effective drain radius r (m) and the effective depth D (m) of an impermeable bedrock below the level of drains. It follows from (1) that the drainage runoff depends linearly on the groundwater table elevation. An analogous equation for unsteady drainage after a rain event (cf. van Schilfgaarde, 1974, p. 256) is:
where h,,,,, (m) is h,,, at t = 0, t (d) is the time elapsed since the rain cessation, f (m3.m”) is the drainable porosity of the
1965 - 1982 loess loam over sandstone
soil and G (m-l) is another geometrical factor. If the relation between q and h,,, can be approximated as (l), the rate of the drainage runoff decline will be: dq dt=
-- KG
(3)
f4
In other words, the slope of the plot of dq/dt vs. q or dQ/dt vs. Q, where Q (m3.s-‘) is the drain discharge, gives the ratio KG/J also referred to as the drainage intensity factor. At very high discharges, the flow regime in the critical point of the system can be regarded as a full-profile pipe flow. Smedema and Rycroft (1983, p. 158) give approximate formulae for the quasi-steady discharge Q (m3.s-‘) in smooth pipes: Q =89d2,7’ie,s7 (4) and in corrugated plastic pipes: Q = 38d2,67iO,sO (5) where d(m) is the inner diameter of the drain and i (m.m-‘) is the drain slope. The drainage flow hydraulics is, in our context, regarded as a tool which helps us to explain the POE curves. An attempt in this direction was made, e.g., by Fidler (cf. Benetin et al., 1987, pp. 206-209).
3 Experimental
sites and methodology
The characteristics of experimental sites are given in Table 1. The instantaneous as well as the average daily runoff rates are available for the Cerhovicky potok and the Cemici catchments while only the instantaneous rates sampled once per day are available for the Krepelka catchment. Synthetic POE-curves were produced by DRAINMOD (cf. Skaggs, 1980), a simulation model of soil water flow in which the processes in the unsaturated part of the soil are treated as sequences of steady states. The input parameters corresponded approximately to the Cemici catchment but
625
E Dolezal et al.: Hydrology of Tile Drainage Runoff
.-
2.5
_..__._,,.,___
-
.._-,_
-_-
.._. -
..___ -
..-...-
-
..-.-........- __
Q“.ma 3 2.0 2 i
!
g
j
6
I I,0 / / ;
il.5
1
'
ci 0.5 ; I
03
0.0 1
0 0,001
0.01
O,l Probabilityof excaedanca
0.ooo1
1
caG&aU.
Th
WC&W
inpur 10 IXMXMUB
0.01
0.1
1
Probabilityof exceadance
Fig.1. Empirical probability-of-exceedance curves for the instantaneous (Q) rtnh ti average &aiIy {QJ &r& &&harges ia he Cemici catch* draima_e system%1~t’Mtt*n~r.
wert nti
0,001
Fig.2. Empirical probability-of-exceedancecurves for the sampled daily (Qj, tfte maximum monthly (C&&J and tie maximum annual (QY.& $cllir~~ha~J~~.~~~~~i~,~~,~!
was
loo-year daily data series generated by WXGEN (cf. Sharpley and Williams, 1990), a stochastic weather generator in which the sequence of wet and dry days is simulated as a first-order Markovian process, while the daiIy precipitation sums on wet days and daily tenperamres, solar radiation sums, air humidities and wind speeds on all days are generated as autocorrelated random prescribed These processes with characteristics. characteristics were derived from observed weather stati& in adjacent weather stations. a
4 Results and discussion 4.1 Empirical POE-curves The POE-curves of instantaneous and average daily drainage discharges for the Cemici-Sl site are presented in Fig. 1. Similar POE-curves were obtained for the other sites. The average daily discharges are, at the same probability of exceedance, perceptibly lower than the instantaneous discharges. In general, the shape of the POE-curves follows the trends outlined in the theoretical part above. The zigzagbenavrour o? tie ‘ms~raneous tir&arge curve ‘mFtg. 1 is an artifact caused by physical insufficiency of the Vnotch flowmeter used. The POE-curve for sampled daily discharges in the Krepelka catchment is compared with the curves far monully anct annua1 maxima iaF&.ZAuI%ree curves entire1~ belong to tie domam of me&mu &ss&rges as discussed above. The high-discharge domain is not cl&~ indicated, exe+, perhaps, for the e.uNe of daily discharges.
0.caJ1
0,001
0.01
O,l
1
PMabiJ@nta,.CS&W
Fig.3. Empirical probability-of-exceedancecurves for the sampled daily (Krepelka) or the average daily (all other sites) specific drainage runoff rates - comparisonof different sites.
0.10 O,W 0.08 0.07 f =
0.06
=
0.05
3
w‘l 0.03 cm! 0.01 o,w 0.1
Probability of exceedance
1
Fig.4. Empirical probability-of-exceedancecurves for the sampled daily (K1qA9.a~ M ti Wage daily (at%tier sties) specific drainage runoff rams - compsr&on of di&renr sites. This is a blown-up porrion of- Fig. 3 showing the domain of low discharges.
626
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
% r: P -
I 1 a”- 0,8 ci &
2
___.
1.8
-.
,
1.8 1.4 1.2
ti
L E’ 0.8 0.4
E ‘@
l 0.8
”
0.8
=
0,4
0.2 0 o.oow1
o.ow1
0,001
0,Ol
O,l
1
0
0.1
0.3
0.2
0.4
0.5
0.8
qd,stream (Us/ha)
Probability of exceedance
Fig.5. Synthetic probability-of-exceedance curves for the average daily (QJ, the maximum monthly (Q,,,,,,,& and the maximum annual (QY.,,& drain discharges. The curves were obtained from a DRAMMOD simulation with the input parameters approximating the Cernici-Sl site and a loo-year daily weather data seriesgeneratedby WXGEN.
Fig.6. A comparison of the average daily specific drainage runoff rate (Cerhovicky potok, drainage system S7, 40.5 ha) with the average daily specific stream runoff rate (profile B I, 3 I5 ha) upstreamof the S7 outlet. The straight line indicatesa hypotheticalequality of the two runoff rates.
Comparisons between different sites are only possible in terms of the specific runoff rate, i.e., the discharge divided by the contributing area, which is taken as the nominal area of the drained land. The resulting POE-curves for daily (average or sampled) specific drainage runoff rates are displayed in Fig. 3. A blown-up portion of the same figure for lowest discharges is presented in Fig. 4. At first glance, all curves in Fig. 3 are similar to each other, but the Krepelka site, on which the underlying rock is permeable sandstone, undergoes periods without any drainage runoff, while the CerniciS2 site, which drains a permanent spring, has always non-zero discharges (see Fig. 4). The latter is the only site which reveals a clearly pronounced non-zero low-discharge domain of the POE curve (up to about 0.8 l/s/ha). The medium-discharge domain of the CemiciS2 curve has a considerably larger slope than the lowdischarge domain which indicates that the mechanisms of drainage are different. These processes may be analysed using (2) and (3) above. The uppermost part of the CerniciS2 curve may already be regarded as belonging to the highdischarge domain.
empirical curves in Fig. 3 are qualitatively similar to the synthetic curves in Fig. 5. The upper limit of simulated discharges (1.45 1.i’) is considerably lower than the upper limit of measured discharges in Cemici-Sl (4.17 1.~~‘,see Fig. 1 and Table 2). Table 2 presents an approximate calculation of the possible upper limits of the drainage runoff based on the formulae given above. The results are only rough approximations because the soil and drain pipe properties are not accurately known and the assumed hydraulic scenarios may not be
‘4.2 Model calculations Synthetic POE-curves are presented in Fig. 5. They are far from fitting the measured data, because the DRAINMOD model has not been calibrated, but are deemed to be qualitatively correct because the physical processes simulated by DRAINMOD correspond more or less to the processes which really occur in the field. The synthetic POE-curves reveal well-developed high-discharge domains as discussed above. These domains are lacking or uncertain in most empirical POE-curves, because the latter are usually based on only few years of measured data. Otherwise, the
Table 2 Estimation of upper limits of the drain discharge (Q) and the specific runoff rate (q) Site: Area (ha):
Cemici Sl
Cemici S2
0.605
I.815
Cerhovicky potok 40.5
a) Limitation by drain pipe hydraulics: Pipe material:
plastic
Drain diameter d(m):
0.09 m
plastic 0.065 m
smooth 0.2 m
Drain slope i: Q (1,s’) =
0.025 9.70
0.0452 5.47
0.043 188.91
q (I.$-‘.ha”) =
16.03
3.01
4.66
b) Limitation by groundwaterhydraulics: Drain spacingL (m): Hydraulic conductivityK(m.d-‘): Groundwatertable elevation h, (m):
I3
I3
11
0.7
0.8
0.4
I.0
1.0
1.0
Eff. drain radius r(m): Geom. factor F (m-l): Q (1,s”) = q (I.s”.ha-‘) =
0.02 0.04532 2.22 367
0.02 0.04532 762 4.20
0.02 0.05529 103.67 2.56
c) Actually observedinstantaneousmaxima: Q (Is“) = 4.17 4.17
112.68
q (I.s“.ha-‘) =
2.78
6.90
2.30
F. Dolezal et al.: Hydrology of Tile Drainage Runoff
exactly the same as in reality. Nonetheless, these results suggest that the observed maximum discharges from the drainage systems studied are near to their physical limits.
621
paper is probably the first attempt to identify different parts of the POE curves and to analyse the mechanisms behind them. The analysis presented above suggests that this approach is correct and should be pursued further.
4.3 Comparison with stream runoff Fig. 06 coqpares tie averape b6ly sped% hr&mage mnc% (Cerhovicky potok, S7) with the average daily specific runoff in the stream (the Cerhovicky potok itself) at a profile (Bl) upstream of the S7 outlet. Bl is fed by the uppemnodg. un&tim& an& -mutiny -&r&e& pzrh. ti %fe catchment. Fig. 6 suggests that the specific drainage runoff from ploughed land is higher than the total specific runoff from an undrained and forested area. However, the actual contributing area of the drainage system may be much larger than its nominal area\ extent and is very ti%icuIrt to delineate.
5 Conclusions The tile drainage runoff is an important part of hydrological balance but is difficult to quantify, especially in foothill regions where the local conditions vary on an extremely short spatial scale. The quantification of the role which the drainage runoff plays during floods and droughts requires, amorg, otier aspecti_, SAaS&e pro&aMJ?y of exceedance curvces jtie POE-curves) 0Etie brainage rrrnopEIue &Aieh. While this approach as such is not completely new, this
Acknowledgement. The research was partly financed by the National Aqxq +& %z&ss!!~.~~Qx.~~x.assh as aqrx+&w. V&T!! Ep QQ@USS&
and 6y the Grant Agency or-tie Gecri RepubrSi: as a pro~&cf no. 103/99/1470. Technical assistance of A. Eichler, K. Mimrova, E. Pilna, P. Hospodka, P. Prazak and others is greatly acknowledged.
References Benetin, J., Dvorak, J., Fidler, J., and Kabina, P., Drainage (in Czech and Slovak), Prlroda, Bratislava, 1987. Cumxxke, C., Stattstical dtstrihutians far flood Jiie~uency analysis,
Operational Hydrology Report No. 33, WMO, Geneva, IY89. Fidler, J. and Soukup, M., The share of runoff from drainages in the size of flood discharge (in Czech), Rostlinna vyroba, h&237-241, 1998. Sharpley, A.N., and Williams, J.R., EPIC - Erosion/Productivity Impuct Calculator: I. Model documentation, 2. User’s guide, USDA Technical Bulletin No. 1768, 1990. Shkinkis, Ts.N., Problems of drainage fydrologv (in Russian), Gidrometeoizdat, Leningrad, 1974. Skaggs, R.W., DRAINMOD, Reference Report, USDA - SCS, South National Technical Center, Fort Worth, TX, USA, 1980. Smedema, L.K. and Rycrofi, D.W., Land drainage, Batsford, London, 1983. van Schilfgaardc. J. led.). Druinqe_for apricuhre. Agronomy series No. ‘is, zun.%uc. kgron.,IGl&irson,“~~~, ‘f?Vt.