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Curve Number Estimation for a Small Urban Catchment from Recorded Rainfall-Runoff Events

Curve Number Estimation for a Small Urban Catchment from Recorded Rainfall-Runoff Events Runoff estimation is a key component in various hydrological considerations. Estimation of storm runoff is especially important for the effective design of hydraulic and road structures, for the flood flow management, as well as for the analysis of land use changes, i.e. urbanization or low impact development of urban areas. The curve number (CN) method, developed by Soil Conservation Service (SCS) of the U.S. Department of Agriculture for predicting the flood runoff depth from ungauged catchments, has been in continuous use for ca. 60 years. This method has not been extensively tested in Poland, especially in small urban catchments, because of lack of data. In this study, 39 rainfall-runoff events, collected during four years (2009­2012) in a small (A=28.7 km2), urban catchment of Sluew Creek in southwest part of Warsaw were used, with the aim of determining the CNs and to check its applicability to ungauged urban areas. The parameters CN, estimated empirically, vary from 65.1 to 95.0, decreasing with rainfall size and, when sorted rainfall and runoff separately, reaching the value from 67 to 74 for large rainfall events. INTRODUCTION Estimation of direct runoff, which is also called the effective rainfall, as response to heavy rainfall is often required for both: agricultural and urban catchment flood management [2, 10, 11]. Among many ways of its estimation for ungauged catchments a great reputation enjoys a curve number method proposed in the 1950s by the USDA Soil Conservation Service ­ USDA-SCS [23, 27, 37]. The Natural Resources Conservation Service curve number (NRCS-CN) method, earlier called the SCS-CN method, represents an event-based lumped conceptual approach and is often used due to its simplicity and practical design. Utilizations of the method for small catchments in Poland have been carried on for more than 30 years [6, 19, 20, 25]. Nevertheless, a number of studies, which consider recorded rainfall-runoff events from gauged catchments, is still very limited [6, 8, 9]. In this work, 39 rainfall-runoff events, collected during four years (2009­2012) in a small (A=28.7 km2) urban catchment of Sluew Creek, located in southwest part of Warsaw, were used with the aim of determining the CNs and comparing them with the CN-table value. RESEARCH METHODOLOGY Description of the NRCS-CN method The original equation for runoff estimation was developed applying the basic water budget for rainfall event, i.e. on the assumption that rainfall (P) is distributed for two components, i.e. runoff (H) and losses (L), all in depth units [16]. Then maximum potential retention of the catchment (S) was defined as upper limit of losses (L), when rainfall (P) is reaching infinity, and finally equality between H/P and L/S was assumed. As a result, after substituting the losses (L) by difference of rainfall and runoff (P-H), the following equation for storm runoff was found: H = P P+S (1) where H is runoff (mm), P is rainfall (mm) and S is maximum potential retention of the catchment (mm). After introducing initial abstraction and assuming its amount as 0.2S, the commonly used equation was presented in the form: ( P - 0 .2 S ) (P + 0 .8 S ) 0 for P > 0 . 2 S for P 0 . 2 S H = (2) The maximum potential retention (S) has been arbitrary related to the catchment curve number (CN) [16], which in metric units, forms the equation: S = 25 . 4 1 000 - 10 CN (3) where CN is curve number, i.e. nondimensional quantity varying in the range (0,100>, and for ungauged catchment it is estimated on the basis of land use and soil type as constant factors, and of land moisture and hydrological conditions as variable ones. Tables and charts for CN as a function of land use and soil types were given in NEH-4 for agricultural areas and in TR-55 for urban catchments. The NRCS-CN method has gained general acceptance in engineering practice due to its simplicity in estimating storm water runoff depth from rainfall depth [7, 11, 12, 16, 18, 21, 31, 40]. For design, the CN value is selected for ungauged catchments representing an acceptable level of risk. Historically, the method for determining the design CN value has been used to select it from tabulated values in published handbooks such as the SCS National Engineering Handbook Section 4: Hydrology (NEH-4) or Technical Release 55 (TR-55) based on watershed characteristics including the hydrologic soil group (HSG), land use, surface condition, and antecedent runoff condition (ARC) [4, 36­38]. Estimation of the CN from rainfall-runoff data Solving Eq. (2) for S as a function of rainfall depth (P) and runoff depth (H) [15] gives: S = 5 (P + 2 H - (4 H + 5 P H ) ) (4) where S is maximum potential retention of the catchment, P is the storm rainfall depth and H is the storm runoff depth, all in mm. The curve number for each event can be calculated from the converted Eq. (3) to the form: CN = 25 400 S + 254 (5) When equations 4 and 5 are used to calculate values of CN from observed rainfall depth and runoff depth, a strong secondary relationship between CN and P often develops. The CN method is often used as a transformation of design rainfall depth to design runoff depth for a given return period. Frequency matching or rank ordering rainfall and runoff data separately to approximate the same frequency (ordered pairs) is a useful approach for determining a CN value from data [15, 17]. Such approach, i.e. estimating the CNs for pairs of rainfall and runoff depths, ordered separately in descending way, used in some earlier researches [9, 26, 32, 34, 35], has been also applied in the presented investigation for small urban catchment located in Warsaw. Study area and data used The catchment of Sluew Creek, located in the southwest part of Warsaw, is a research area of the Department of Water Engineering, in which rainfall-runoff and water quality issues have been investigated for over 25 years [1, 5, 22, 29, 30]. The stream passes through the following districts of Warsaw: Wlochy, Okcie, Grabów, Ursynów and Wilanów. The investigation, conducted for the upper part of the catchment, upstream of the gauge at Wycigi Pond, is shown in Fig. 1. Fig. 1. Sluew Creek catchment upstream of the Wycigi gauge Its area is 28.7 km2 and the impervious factor of the catchment is about 22% [3, 13, 28]. The catchment is heterogeneous in terms of land development. The northern part can be characterized by stronger urbanization, as it is encircled by housing estates and the Okcie airport. Further south, there are single-family houses, fields, wastelands and woodlands. From this area, the water reaches the Sluew Creek flowing through a network of artificial canals, and the watercourses pass through several small detention ponds. The catchment area is flat, there are no hills or depressions. The land slopes are inconsiderable. The analyzed catchment, upstream of Wycigi Pond, is located on moraine upland. It is composed mostly of boulder clay and fluvioglacial sands. Undeveloped areas are covered with vegetation typical for such urban green areas, e.g. weeds, ruderal species accompanying allotments [14]. The average annual precipitation for that part of Warsaw is estimated for 510­530 mm [13, 24]. The table curve number value for the catchment, treated as ungauged one, was estimated as CNtabl=75.8 [13, 28], based on topographic and soil maps. The rainfall data, for this study, was derived from six rain gauges located within the area, and outside the catchment (Fig. 1). Five of them were installed and operated by the Division of River Engineering of Warsaw University of Life Sciences ­ SGGW, and one of them, marked as 1 in Fig 1, was operated by Okcie Airport. The rainfall depth was recorded in 10-minute intervals. The average areal rainfall for the analyzed part of catchment was determined by means of the Thiessen polygon method. Water level at Wycigi gauge, which is located just upstream of the Wycigi Pond, was recorded with use of a digital limnigraph, also in 10-minute intervals. Water level records were verified by staff gauge readings, which were conducted two or three times a week. Based on the rating curve, estimated with use of hydrometric measurements and hydraulic relationship, the water levels were converted to stream flow. Monitoring of the precipitation and stream flow was carried out from May 2009 to November 2012. For further analysis, we selected events for which the peak flow was at least four times greater than the average long period discharge. Winter floods, i.e. caused by snowmelt, were excluded from the investigations. The characteristic of 39 rainfall-runoff events selected for the analysis, with the computed CNs according the Eqs 4 and 5, are presented in Table 1. Table 1. Characteristics of the 39 recorded rainfall ­ runoff events Category 1 Rainfall depth ­ P (avg. in the catchment) Rainfall depth ­ P (at Okcie gauge) Runoff depth ­ H Peak discharge ­ Qmax Curve Number Unit 2 mm mm mm m /s Value for the events average 3 24.3 20.8 2.49 1.76 82.2 range 4 8.0­56.9 5.8­75.2 0.6­17.8 0.89­5.74 65.1­95.0 RESULTS AND DISCUSSION The purpose of this study was: (i) to estimate the values of CNemp (empirical) for each of the recorded rainfall-runoff events, (ii) to estimate the catchment (design) CNdesign, which can be assumed as representative for computing design runoff from design rainfall, (iii) to compare the last one (CNdesign) with the table CN, i.e. with CNtabl, estimated in the earlier analysis, as CNtabl = 75.8 [3, 13, 28], from the land use and soil maps. The CNs were computed from recorded rainfall depths H, and runoff depths P, according to Eqs 4 and 5 for each of the 39 events, and the relationship H vs. P are shown in Figure 2 (as dots), with the relationship H vs P estimated for CNtabl=75.8, from equation 2 and 3 (shown as line). In Figure 3 the empirical CN values, which range from 65.1 to 95.0, are related to rainfall depth of the events. The distribution of the dots in Figure 3 indicates a strong secondary relationship between curve number vs. rainfall depth, i.e. the CNs are decreasing with the increase of rainfall depths. Hawkins [15] proposed to use asymptotic functions for approximation of the relationship CN vs. P values, after applying a sorting technique to the measured data. H [mm] P [mm] Fig. 2. Relationship of runoff depth (H) vs. rainfall depth (P) for the 39 recorded events (dots) and for the CNtabl=75.8 (line) CNemp [-] P [mm] Fig. 3. Curve Number of recorded events versus rainfall depth This technique is based on the frequency matching concept, i.e. the rainfall depths and runoff depths are sorted separately, and then realigned on the rank-order basis to form P:H pairs of equal return periods. As Hawkins indicated [15], CNs calculated from the recorded data for the matched pairs, according to equation 4 and 5, approach a constant value with increasing rainfall. A standard asymptote occurs if there is a tendency for CN to decline and then approach a constant value with increasing P according to formula: (6) where CN is a constant approached as P; and b is a fitted constant. The 39 pairs P vs CN are plotted in Fig. 4. Table Curve 2D software [33], "Automated curve fitting and equation discovery" of SYSTAT has been used to find parameters of the formula 5. The flowing relationship was found: (7) with r2 (coefficient of determination) = 0.925 and SE (standard error of estimation) of CN = 1.78. Relatively high coefficient of determination of the equation 6, confirms the standard behavior of the catchment, i.e. declining of CN with increasing storm size and then approaching a near constant value with increasingly larger storms, what happens in about 70% of all watersheds evaluated [15, 39]. However, the CN = 67.3 seems to be significantly lower than the tabulated CNtabl = 75.8 estimated on the basis of land use and soil types. So, using CN = 67.3 as design value for estimating response of the catchment to 100-year rainfall would led to significant underestimation of design flood. Also computing CN(P) according equation 7 for P=70 mm and 80 mm, what accounts for rainstorm of 100-year return period of duration 8 and 20 hours [3], one receives CN=69.8 and CN-69.0, what still seems to be too big difference with comparison to CNtabl. Fig. 4. CNs estimated on the based on rainfall and runoff data ranged separately (dots), with approximation relationship 6 (CN vs. P) As the CNs, computed for 39 pairs of P-H, earlier ordered separately, indicate systematic decrease with P (Figure 4), in search for better agreement the CN of large rainfall depth with the CNtabl, two other relationships of CN versus rainfall depth are presented, one from a group of kinetic functions and the other from a group of peak functions. To estimate the parameters of the set of functions of two groups of functions, the above mentioned TableCurve 2D software [33] was used. The following functions were selected as the best approximations: from the set of kinetic equations, the variable order decay function (DecayN): (8) where: CNL is curve number for large P, b is amplitude, c and d ­ are fitted constants, from the set of symmetric peak functions the best approximation was reached for complementary error function peak (Erfc Peak) in the form: (9) where CN is a constant approached as P; b is amplitude, c ­ location parameter (mode), d ­ scaling parameter, i.e. parameter related to full width at half-maximum of amplitude (FWHM is 1.381d). The values of the constants of equations 8 and 9, as well as measure of approximation functions 7­9, i.e. determination coefficients and standard errors of estimation, are presented in Table 2. The relationships 8 and 9 are also presented in the Figure 5. Table 2. Characteristics of the various statistical relationships of CN vs. rainfall depth Relationship 1 Standard asymptotic function Variable order decay function (DecayN) Equation number 2 7 Values of parameters 3 CN= 67.3 b = 27.3 CNL = 74.2 b = 23.8 c = 0.552 d = 0.103 CN = 74.1 b = 20.3 c = -3.31 d = 31.8 Determination coefficient ­ r2 4 0.925 Standard error of estimation 5 1.78 Complementary error function peak (Erfc Peak) CN, CNL, b, c, d ­ estimated parameters of the Eqs (7)­(9) Fig. 5. CNs estimated on the based on rainfall and runoff data ranged separately (dots), with approximation relationship 8 (upper graph) and 9 (lower graph) The value CN(P) = CNL in equation 8 is reached when the value of the expression in brackets is not larger than zero, which after rearranging assumes the form: (10) where b, c and d are fitted constants of eq. 8. After inserting the constants as given in Table 2, one receives P34.7 mm, for which CN(P) = CNL = 74.2. Analyzing the equation 9 with the fitted parameters as in Table 2, one can find out that for P45 mm the values of erfc(x2) is close to zero, so one can replace CN by CNL, and consequently would receive CN(P) = CNL 74.1. In both cases the values CNL equal to 74.2 and 74.1 are relatively close to the table value CNtabl = 75.8, which should be assumed as confirmation of the curve number method as reliable procedure for estimating runoff depth as urban catchment response to design rainfall. The table CNtabl is 1.7 and 1.6 above that of CNL, estimated on the basis of empirical data according to the equations 8 and 9. This will cause also slight difference in flood prediction, i.e. overestimation when using CNtabl in comparison with the application of CNL. As the difference in CN is quite small, and application of FFA (flood frequency analysis) for verification is not possible, as continuous land use changes take place in the catchment, the recommendation for further study are: in respect of this catchment; to carry out a similar investigation, however with splitting the investigating area for two sub-catchments to be able to consider the differences in land use between them and for estimating more reliable rainfall, assumed as lumped values, of the events, to collect additional set of rainfall-runoff data to confirm these findings, in respect of other natural or agricultural small catchments, with long rainfall-runoff records, where land use changes are insignificant ­ to compare results of presented procedure with the results of flood frequency analysis. CONCLUSIONS The following conclusions can be drown from the investigation: the values of curve number estimated from the recorded rainfall-runoff events characterize large variation, since 65.1 to 95.0 with the mean value equals 82.2. As there is tendency for CN decreasing with increase of rainfall depth, application of mean CN for design flood estimation is not allowed. Table CN, estimated for the investigated catchment as for ungauged are, on the basis of land use and soil types was CNtabl = 75.8. applying the frequency matching concept, i.e. after sorted the rainfall depths and runoff depths separately, and estimating CNs for rank-order P:H pairs of equal return periods, we confirmed that standard asymptotic relation occurs, with a tendency for CN to decline and then approach a constant value with increasing P, as suggested in many contributions of Hawkins and others. However the approached constant, as well as CN(P) for design P, were significantly lower than CNtabl, what would produce underestimation in flood runoff when applied for designing. the value of CNs, estimated with the frequency matching concept, are well approximated with rainfall depths by the following equations: (i) the variable order decay function (DecayN), and (ii) complementary error function peak (Erfc Peak). In both cases CNL for large rainfall (i.e. for P34.7 mm, and P45 mm, for the first and the other case) was 74.2 and 74.1, for the first and the other function, respectively. Good agreement, i.e. very small differences between the CNL and CNtabl, allow to accept the curve number procedure for applying it in designing flood runoff from urban catchments, further investigations would be specially required in natural or agricultural small catchments, with long rainfall-runoff records, where land use changes are insignificant ­ to compare results of application of the curve number procedure with results of flood frequency analysis. ACKNOWLEDGMENTS The investigation described in this paper has been carried out within research project no. N N305 396238 founded by National Center of Science (NCN). The support provided by the organization is gratefully acknowledged. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Environmental Protection de Gruyter

Curve Number Estimation for a Small Urban Catchment from Recorded Rainfall-Runoff Events

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Abstract

Runoff estimation is a key component in various hydrological considerations. Estimation of storm runoff is especially important for the effective design of hydraulic and road structures, for the flood flow management, as well as for the analysis of land use changes, i.e. urbanization or low impact development of urban areas. The curve number (CN) method, developed by Soil Conservation Service (SCS) of the U.S. Department of Agriculture for predicting the flood runoff depth from ungauged catchments, has been in continuous use for ca. 60 years. This method has not been extensively tested in Poland, especially in small urban catchments, because of lack of data. In this study, 39 rainfall-runoff events, collected during four years (2009­2012) in a small (A=28.7 km2), urban catchment of Sluew Creek in southwest part of Warsaw were used, with the aim of determining the CNs and to check its applicability to ungauged urban areas. The parameters CN, estimated empirically, vary from 65.1 to 95.0, decreasing with rainfall size and, when sorted rainfall and runoff separately, reaching the value from 67 to 74 for large rainfall events. INTRODUCTION Estimation of direct runoff, which is also called the effective rainfall, as response to heavy rainfall is often required for both: agricultural and urban catchment flood management [2, 10, 11]. Among many ways of its estimation for ungauged catchments a great reputation enjoys a curve number method proposed in the 1950s by the USDA Soil Conservation Service ­ USDA-SCS [23, 27, 37]. The Natural Resources Conservation Service curve number (NRCS-CN) method, earlier called the SCS-CN method, represents an event-based lumped conceptual approach and is often used due to its simplicity and practical design. Utilizations of the method for small catchments in Poland have been carried on for more than 30 years [6, 19, 20, 25]. Nevertheless, a number of studies, which consider recorded rainfall-runoff events from gauged catchments, is still very limited [6, 8, 9]. In this work, 39 rainfall-runoff events, collected during four years (2009­2012) in a small (A=28.7 km2) urban catchment of Sluew Creek, located in southwest part of Warsaw, were used with the aim of determining the CNs and comparing them with the CN-table value. RESEARCH METHODOLOGY Description of the NRCS-CN method The original equation for runoff estimation was developed applying the basic water budget for rainfall event, i.e. on the assumption that rainfall (P) is distributed for two components, i.e. runoff (H) and losses (L), all in depth units [16]. Then maximum potential retention of the catchment (S) was defined as upper limit of losses (L), when rainfall (P) is reaching infinity, and finally equality between H/P and L/S was assumed. As a result, after substituting the losses (L) by difference of rainfall and runoff (P-H), the following equation for storm runoff was found: H = P P+S (1) where H is runoff (mm), P is rainfall (mm) and S is maximum potential retention of the catchment (mm). After introducing initial abstraction and assuming its amount as 0.2S, the commonly used equation was presented in the form: ( P - 0 .2 S ) (P + 0 .8 S ) 0 for P > 0 . 2 S for P 0 . 2 S H = (2) The maximum potential retention (S) has been arbitrary related to the catchment curve number (CN) [16], which in metric units, forms the equation: S = 25 . 4 1 000 - 10 CN (3) where CN is curve number, i.e. nondimensional quantity varying in the range (0,100>, and for ungauged catchment it is estimated on the basis of land use and soil type as constant factors, and of land moisture and hydrological conditions as variable ones. Tables and charts for CN as a function of land use and soil types were given in NEH-4 for agricultural areas and in TR-55 for urban catchments. The NRCS-CN method has gained general acceptance in engineering practice due to its simplicity in estimating storm water runoff depth from rainfall depth [7, 11, 12, 16, 18, 21, 31, 40]. For design, the CN value is selected for ungauged catchments representing an acceptable level of risk. Historically, the method for determining the design CN value has been used to select it from tabulated values in published handbooks such as the SCS National Engineering Handbook Section 4: Hydrology (NEH-4) or Technical Release 55 (TR-55) based on watershed characteristics including the hydrologic soil group (HSG), land use, surface condition, and antecedent runoff condition (ARC) [4, 36­38]. Estimation of the CN from rainfall-runoff data Solving Eq. (2) for S as a function of rainfall depth (P) and runoff depth (H) [15] gives: S = 5 (P + 2 H - (4 H + 5 P H ) ) (4) where S is maximum potential retention of the catchment, P is the storm rainfall depth and H is the storm runoff depth, all in mm. The curve number for each event can be calculated from the converted Eq. (3) to the form: CN = 25 400 S + 254 (5) When equations 4 and 5 are used to calculate values of CN from observed rainfall depth and runoff depth, a strong secondary relationship between CN and P often develops. The CN method is often used as a transformation of design rainfall depth to design runoff depth for a given return period. Frequency matching or rank ordering rainfall and runoff data separately to approximate the same frequency (ordered pairs) is a useful approach for determining a CN value from data [15, 17]. Such approach, i.e. estimating the CNs for pairs of rainfall and runoff depths, ordered separately in descending way, used in some earlier researches [9, 26, 32, 34, 35], has been also applied in the presented investigation for small urban catchment located in Warsaw. Study area and data used The catchment of Sluew Creek, located in the southwest part of Warsaw, is a research area of the Department of Water Engineering, in which rainfall-runoff and water quality issues have been investigated for over 25 years [1, 5, 22, 29, 30]. The stream passes through the following districts of Warsaw: Wlochy, Okcie, Grabów, Ursynów and Wilanów. The investigation, conducted for the upper part of the catchment, upstream of the gauge at Wycigi Pond, is shown in Fig. 1. Fig. 1. Sluew Creek catchment upstream of the Wycigi gauge Its area is 28.7 km2 and the impervious factor of the catchment is about 22% [3, 13, 28]. The catchment is heterogeneous in terms of land development. The northern part can be characterized by stronger urbanization, as it is encircled by housing estates and the Okcie airport. Further south, there are single-family houses, fields, wastelands and woodlands. From this area, the water reaches the Sluew Creek flowing through a network of artificial canals, and the watercourses pass through several small detention ponds. The catchment area is flat, there are no hills or depressions. The land slopes are inconsiderable. The analyzed catchment, upstream of Wycigi Pond, is located on moraine upland. It is composed mostly of boulder clay and fluvioglacial sands. Undeveloped areas are covered with vegetation typical for such urban green areas, e.g. weeds, ruderal species accompanying allotments [14]. The average annual precipitation for that part of Warsaw is estimated for 510­530 mm [13, 24]. The table curve number value for the catchment, treated as ungauged one, was estimated as CNtabl=75.8 [13, 28], based on topographic and soil maps. The rainfall data, for this study, was derived from six rain gauges located within the area, and outside the catchment (Fig. 1). Five of them were installed and operated by the Division of River Engineering of Warsaw University of Life Sciences ­ SGGW, and one of them, marked as 1 in Fig 1, was operated by Okcie Airport. The rainfall depth was recorded in 10-minute intervals. The average areal rainfall for the analyzed part of catchment was determined by means of the Thiessen polygon method. Water level at Wycigi gauge, which is located just upstream of the Wycigi Pond, was recorded with use of a digital limnigraph, also in 10-minute intervals. Water level records were verified by staff gauge readings, which were conducted two or three times a week. Based on the rating curve, estimated with use of hydrometric measurements and hydraulic relationship, the water levels were converted to stream flow. Monitoring of the precipitation and stream flow was carried out from May 2009 to November 2012. For further analysis, we selected events for which the peak flow was at least four times greater than the average long period discharge. Winter floods, i.e. caused by snowmelt, were excluded from the investigations. The characteristic of 39 rainfall-runoff events selected for the analysis, with the computed CNs according the Eqs 4 and 5, are presented in Table 1. Table 1. Characteristics of the 39 recorded rainfall ­ runoff events Category 1 Rainfall depth ­ P (avg. in the catchment) Rainfall depth ­ P (at Okcie gauge) Runoff depth ­ H Peak discharge ­ Qmax Curve Number Unit 2 mm mm mm m /s Value for the events average 3 24.3 20.8 2.49 1.76 82.2 range 4 8.0­56.9 5.8­75.2 0.6­17.8 0.89­5.74 65.1­95.0 RESULTS AND DISCUSSION The purpose of this study was: (i) to estimate the values of CNemp (empirical) for each of the recorded rainfall-runoff events, (ii) to estimate the catchment (design) CNdesign, which can be assumed as representative for computing design runoff from design rainfall, (iii) to compare the last one (CNdesign) with the table CN, i.e. with CNtabl, estimated in the earlier analysis, as CNtabl = 75.8 [3, 13, 28], from the land use and soil maps. The CNs were computed from recorded rainfall depths H, and runoff depths P, according to Eqs 4 and 5 for each of the 39 events, and the relationship H vs. P are shown in Figure 2 (as dots), with the relationship H vs P estimated for CNtabl=75.8, from equation 2 and 3 (shown as line). In Figure 3 the empirical CN values, which range from 65.1 to 95.0, are related to rainfall depth of the events. The distribution of the dots in Figure 3 indicates a strong secondary relationship between curve number vs. rainfall depth, i.e. the CNs are decreasing with the increase of rainfall depths. Hawkins [15] proposed to use asymptotic functions for approximation of the relationship CN vs. P values, after applying a sorting technique to the measured data. H [mm] P [mm] Fig. 2. Relationship of runoff depth (H) vs. rainfall depth (P) for the 39 recorded events (dots) and for the CNtabl=75.8 (line) CNemp [-] P [mm] Fig. 3. Curve Number of recorded events versus rainfall depth This technique is based on the frequency matching concept, i.e. the rainfall depths and runoff depths are sorted separately, and then realigned on the rank-order basis to form P:H pairs of equal return periods. As Hawkins indicated [15], CNs calculated from the recorded data for the matched pairs, according to equation 4 and 5, approach a constant value with increasing rainfall. A standard asymptote occurs if there is a tendency for CN to decline and then approach a constant value with increasing P according to formula: (6) where CN is a constant approached as P; and b is a fitted constant. The 39 pairs P vs CN are plotted in Fig. 4. Table Curve 2D software [33], "Automated curve fitting and equation discovery" of SYSTAT has been used to find parameters of the formula 5. The flowing relationship was found: (7) with r2 (coefficient of determination) = 0.925 and SE (standard error of estimation) of CN = 1.78. Relatively high coefficient of determination of the equation 6, confirms the standard behavior of the catchment, i.e. declining of CN with increasing storm size and then approaching a near constant value with increasingly larger storms, what happens in about 70% of all watersheds evaluated [15, 39]. However, the CN = 67.3 seems to be significantly lower than the tabulated CNtabl = 75.8 estimated on the basis of land use and soil types. So, using CN = 67.3 as design value for estimating response of the catchment to 100-year rainfall would led to significant underestimation of design flood. Also computing CN(P) according equation 7 for P=70 mm and 80 mm, what accounts for rainstorm of 100-year return period of duration 8 and 20 hours [3], one receives CN=69.8 and CN-69.0, what still seems to be too big difference with comparison to CNtabl. Fig. 4. CNs estimated on the based on rainfall and runoff data ranged separately (dots), with approximation relationship 6 (CN vs. P) As the CNs, computed for 39 pairs of P-H, earlier ordered separately, indicate systematic decrease with P (Figure 4), in search for better agreement the CN of large rainfall depth with the CNtabl, two other relationships of CN versus rainfall depth are presented, one from a group of kinetic functions and the other from a group of peak functions. To estimate the parameters of the set of functions of two groups of functions, the above mentioned TableCurve 2D software [33] was used. The following functions were selected as the best approximations: from the set of kinetic equations, the variable order decay function (DecayN): (8) where: CNL is curve number for large P, b is amplitude, c and d ­ are fitted constants, from the set of symmetric peak functions the best approximation was reached for complementary error function peak (Erfc Peak) in the form: (9) where CN is a constant approached as P; b is amplitude, c ­ location parameter (mode), d ­ scaling parameter, i.e. parameter related to full width at half-maximum of amplitude (FWHM is 1.381d). The values of the constants of equations 8 and 9, as well as measure of approximation functions 7­9, i.e. determination coefficients and standard errors of estimation, are presented in Table 2. The relationships 8 and 9 are also presented in the Figure 5. Table 2. Characteristics of the various statistical relationships of CN vs. rainfall depth Relationship 1 Standard asymptotic function Variable order decay function (DecayN) Equation number 2 7 Values of parameters 3 CN= 67.3 b = 27.3 CNL = 74.2 b = 23.8 c = 0.552 d = 0.103 CN = 74.1 b = 20.3 c = -3.31 d = 31.8 Determination coefficient ­ r2 4 0.925 Standard error of estimation 5 1.78 Complementary error function peak (Erfc Peak) CN, CNL, b, c, d ­ estimated parameters of the Eqs (7)­(9) Fig. 5. CNs estimated on the based on rainfall and runoff data ranged separately (dots), with approximation relationship 8 (upper graph) and 9 (lower graph) The value CN(P) = CNL in equation 8 is reached when the value of the expression in brackets is not larger than zero, which after rearranging assumes the form: (10) where b, c and d are fitted constants of eq. 8. After inserting the constants as given in Table 2, one receives P34.7 mm, for which CN(P) = CNL = 74.2. Analyzing the equation 9 with the fitted parameters as in Table 2, one can find out that for P45 mm the values of erfc(x2) is close to zero, so one can replace CN by CNL, and consequently would receive CN(P) = CNL 74.1. In both cases the values CNL equal to 74.2 and 74.1 are relatively close to the table value CNtabl = 75.8, which should be assumed as confirmation of the curve number method as reliable procedure for estimating runoff depth as urban catchment response to design rainfall. The table CNtabl is 1.7 and 1.6 above that of CNL, estimated on the basis of empirical data according to the equations 8 and 9. This will cause also slight difference in flood prediction, i.e. overestimation when using CNtabl in comparison with the application of CNL. As the difference in CN is quite small, and application of FFA (flood frequency analysis) for verification is not possible, as continuous land use changes take place in the catchment, the recommendation for further study are: in respect of this catchment; to carry out a similar investigation, however with splitting the investigating area for two sub-catchments to be able to consider the differences in land use between them and for estimating more reliable rainfall, assumed as lumped values, of the events, to collect additional set of rainfall-runoff data to confirm these findings, in respect of other natural or agricultural small catchments, with long rainfall-runoff records, where land use changes are insignificant ­ to compare results of presented procedure with the results of flood frequency analysis. CONCLUSIONS The following conclusions can be drown from the investigation: the values of curve number estimated from the recorded rainfall-runoff events characterize large variation, since 65.1 to 95.0 with the mean value equals 82.2. As there is tendency for CN decreasing with increase of rainfall depth, application of mean CN for design flood estimation is not allowed. Table CN, estimated for the investigated catchment as for ungauged are, on the basis of land use and soil types was CNtabl = 75.8. applying the frequency matching concept, i.e. after sorted the rainfall depths and runoff depths separately, and estimating CNs for rank-order P:H pairs of equal return periods, we confirmed that standard asymptotic relation occurs, with a tendency for CN to decline and then approach a constant value with increasing P, as suggested in many contributions of Hawkins and others. However the approached constant, as well as CN(P) for design P, were significantly lower than CNtabl, what would produce underestimation in flood runoff when applied for designing. the value of CNs, estimated with the frequency matching concept, are well approximated with rainfall depths by the following equations: (i) the variable order decay function (DecayN), and (ii) complementary error function peak (Erfc Peak). In both cases CNL for large rainfall (i.e. for P34.7 mm, and P45 mm, for the first and the other case) was 74.2 and 74.1, for the first and the other function, respectively. Good agreement, i.e. very small differences between the CNL and CNtabl, allow to accept the curve number procedure for applying it in designing flood runoff from urban catchments, further investigations would be specially required in natural or agricultural small catchments, with long rainfall-runoff records, where land use changes are insignificant ­ to compare results of application of the curve number procedure with results of flood frequency analysis. ACKNOWLEDGMENTS The investigation described in this paper has been carried out within research project no. N N305 396238 founded by National Center of Science (NCN). The support provided by the organization is gratefully acknowledged.

Journal

Archives of Environmental Protection – de Gruyter

Published: Dec 11, 2014

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