ABSTRACT
Curve Number (CN) values estimating from rainfall-runoff data is an attractive topic in hydrology. However, CN values are lacking for Interlocking Concrete Pavement (ICP) material, mainly when seated over bare soil (not over a permeable pavement structure). Here, we compute CN values for the ICP seated over clayey soil using measured rainfall and infiltration capacity data. We estimated runoff () using 32 events of 24-hour rainfall depth () and an infiltration model, assuming a hortonian runoff process. To estimate the CN for each event, we used the rainfall-runoff incremental approach. Overall, we obtained CN values ranging from 52 to 63. The best CN values to estimate were equal to 52.2 ( = 9.09 mm and = 0.03) and 60.1 ( = 1.45 mm and = 0.97), considering natural- and rank-ordered - data, respectively. Our results indicate that it is more suitable to use the initial abstraction ratio () equal to 0.20 for the ICP material. The findings provide a better understanding of the rainfall-runoff process in ICP and help improve the design of stormwater drainage systems.
Keywords:
Paver; Low impact development systems; Stormwater Drainage System; Flooding
RESUMO
A estimativa de valores Curva Número (CN) a partir de dados chuva-vazão é um tópico atrativo em hidrologia. No entanto, há carência de valores de CN para o material Pavimento de Concreto Intertravado (PCI), particularmente quando assentado sobre o solo exposto (não sobre uma estrutura de pavimentos permeáveis). Aqui, nós calculamos valores de CN para o PCI assentado sobre solo argiloso e usando dados medidos de chuva e capacidade de infiltração. Nós estimamos o escoamento superficial () usando dados de altura de chuva com duração de 24 horas () junto com um modelo de infiltração, sob a hipótese do processo hortoniano de geração de . Para estimar o valor de CN para cada evento de chuva, nós adotamos a abordagem incremental do tipo chuva-vazão. Nós obtivemos valores de CN variando de 52 ( = 9,09 mm and = 0,03) a 63 ( = 1,45 mm and = 0,97). Resumidamente, os melhores valores de CN foram iguais a 52,2 e 60,1, considerando os dados-ordenados naturalmente e ranqueados, respectivamente. Nossos resultados indicam que é melhor usar um valor de taxa de abstração inicial () igual a 0,20 para o material PCI. As descobertas fornecem um melhor entendimento sobre o processo chuva-vazão no material PCI e ajudam a aprimorar projetos de sistemas de drenagem pluvial.
Palavras-chave:
Paver; Sistemas de baixo Impacto de Desenvolvimento; Sistemas de drenagem pluvial; Inundações
INTRODUCTION
Water resources engineers face the challenge of estimating stormwater runoff, primarily for applications in flood control design and early flood warning systems in urban areas and soil and water conservation practices in agricultural/natural land. Traditionally, engineers have dealt with the aforementioned applications in small and ungauged watersheds by transforming rainfall depth into runoff depth (Grimaldi et al., 2013Grimaldi, S., Petroselli, A., & Romano, N. (2013). Green-Ampt Curve-Number mixed procedure as an empirical tool for rainfall–runoff modelling in small and ungauged basins. Hydrological Processes, 27(8), 1253-1264. http://dx.doi.org/10.1002/HYP.9303.
http://dx.doi.org/10.1002/HYP.9303...
) using a rainfall-runoff model.
In the mid-1950s, the Soil Conservation Service’s Curve Number method (CN method) arose as a mathematically simple, low-cost, and versatile rainfall-runoff model. This method is catchy because only rainfall depth (variable input) and CN (parameter) are required to estimate runoff. Further, it is versatile because CN values are tabulated in the National Engineering Handbook, Section 4 (NEH4), of the US Department of Agriculture (United States Department of Agriculture, 2004United States Department of Agriculture – USDA. (2004). Hydrologic Soil- Cover Complexes. In United States Department of Agriculture – USDA. National Engineering Handbook: Part 630 Hydrology (pp. 20). USA: United States Department of Agriculture (USDA) and Natural Resources Conservation Service (NRCS).), for several land use and cover and soil types (Hydrologic Soil Groups, HSG).
The CN method was solely developed to assess the influence of land use and cover modification in runoff for small agricultural watersheds (Ponce & Hawkins, 1996Ponce, V. M., & Hawkins, R. H. (1996). Runoff curve number: has it reached maturity? Journal of Hydrologic Engineering, 1(1), 11-19. http://dx.doi.org/10.1061/(ASCE)1084-0699(1996)1:1(11).
http://dx.doi.org/10.1061/(ASCE)1084-069...
). Over time, practical engineers have extended the application of the CN method for designing stormwater drainage systems in urban watersheds (United States Department of Agriculture, 1986United States Department of Agriculture – USDA. (1986). Urban Hydrology for Small Watersheds.). The CN method is also applied in incremental rainfall amounts with an associated watershed unit-hydrograph to estimate runoff hydrographs (Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
). The CN method was not originally intended to be used in incremental rainfall amounts less than the duration of the 24-hour rainfall (Karpathy & Chin, 2019Karpathy, N. S., & Chin, D. A. (2019). Relationship between Curve Number and ϕ-Index. Journal of Irrigation and Drainage Engineering, 145(11), 06019009. http://dx.doi.org/10.1061/(asce)ir.1943-4774.0001426.
http://dx.doi.org/10.1061/(asce)ir.1943-...
). Here, we referred to this as the INCremental RAinfall-RUNoff (INCRARUN) approach.
The CN method’s limitations are widely reported (Ajmal et al., 2016Ajmal, M., Waseem, M., Ahn, J.-H., & Kim, T.-W. (2016). Runoff estimation using the NRCS slope-adjusted curve number in mountainous watersheds. Journal of Irrigation and Drainage Engineering, 142(4), 04016002. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0000998.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
; Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
; Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
, 2014Hawkins, R. H. (2014). Curve number method: time to think anew? Journal of Hydrologic Engineering, 19(6), 1059. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000954.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
; Jain et al., 2006Jain, M. K., Mishra, S. K., Babu, P. S., Venugopal, K., & Singh, V. P. (2006). Enhanced runoff curve number model incorporating storm duration and a nonlinear Ia-S Relation. Journal of Hydrologic Engineering, 11(6), 631-635. http://dx.doi.org/10.1061/(ASCE)1084-0699(2006)11:6(631).
http://dx.doi.org/10.1061/(ASCE)1084-069...
; Michel et al., 2005Michel, C., Andréassian, V., & Perrin, C. (2005). Soil Conservation Service Curve Number method: how to mend a wrong soil moisture accounting procedure? Water Resources Research, 41(2), 1-6. http://dx.doi.org/10.1029/2004WR003191.
http://dx.doi.org/10.1029/2004WR003191...
; Ponce & Hawkins, 1996Ponce, V. M., & Hawkins, R. H. (1996). Runoff curve number: has it reached maturity? Journal of Hydrologic Engineering, 1(1), 11-19. http://dx.doi.org/10.1061/(ASCE)1084-0699(1996)1:1(11).
http://dx.doi.org/10.1061/(ASCE)1084-069...
; Sahu et al., 2012Sahu, R. K., Mishra, S. K., & Eldho, T. I. (2012). Improved storm duration and antecedent moisture condition coupled SCS-CN Concept-Based Model. Journal of Hydrologic Engineering, 17(11), 1173-1179. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000443.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
; Shi et al., 2021Shi, W., Wang, N., Wang, M., & Li, D. (2021). Revised runoff curve number for runoff prediction in the Loess Plateau of China. Hydrological Processes, 35(10), e14390. http://dx.doi.org/10.1002/HYP.14390.
http://dx.doi.org/10.1002/HYP.14390...
; Verma et al., 2020Verma, S., Singh, P. K., Mishra, S. K., Singh, V. P., Singh, V., & Singh, A. (2020). Activation soil moisture accounting (ASMA) for runoff estimation using soil conservation service curve number (SCS-CN) method. Journal of Hydrology (Amsterdam), 589, 125114. http://dx.doi.org/10.1016/J.JHYDROL.2020.125114.
http://dx.doi.org/10.1016/J.JHYDROL.2020...
). Nevertheless, researchers still make efforts to soften these limitations by adjusting the CN method’s formulation or estimating CN values for specific site features. Applying the INCRARUN approach using the CN tabulated values invokes at least two limitations (Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
). First is the lack of consideration of variation in rainfall characteristics. Second, it does not constrain the infiltration rate to be less than or equal to the infiltration capacity of the watershed. To overcome these limitations, a few studies have combined an infiltration model with 24-hour hyetographs to estimate the CN parameter (e.g., Bertotto et al., 2021Bertotto, L. E., Lucas, M. C., Destro, C. A. M., Chin, D. A., Alves, W. S., & de Oliveira, P. T. S. (2021). Effects of infiltration conditions and rainfall characteristics on simulated curve numbers. Journal of Irrigation and Drainage Engineering, 147(10), 05021004. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001605.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
; Chin, 2017Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
).
Studies have focused on CN estimating for crops (Durán-Barroso et al., 2017Durán-Barroso, P., González, J., & Valdés, J. B. (2017). Sources of uncertainty in the NRCS CN model: recognition and solutions. Hydrological Processes, 31(22), 3898-3906. http://dx.doi.org/10.1002/HYP.11305.
http://dx.doi.org/10.1002/HYP.11305...
; Lal et al., 2017Lal, M., Mishra, S. K., Pandey, A., Pandey, R. P., Meena, P. K., Chaudhary, A., Jha, R. K., Shreevastava, A. K., & Kumar, Y. (2017). Evaluation de la méthode du numéro de courbe du Service de la Conservation des Sols à partir de données provenant de parcelles agricoles. Hydrogeology Journal, 25(1), 151-167. http://dx.doi.org/10.1007/S10040-016-1460-5/FIGURES/9.
http://dx.doi.org/10.1007/S10040-016-146...
), undisturbed vegetation (Oliveira et al., 2016Oliveira, P. T. S., Nearing, M. A., Hawkins, R. H., Stone, J. J., Rodrigues, D. B. B., Panachuki, E., & Wendland, E. (2016). Curve number estimation from Brazilian Cerrado rainfall and runoff data. Journal of Soil and Water Conservation, 71(5), 420-429. http://dx.doi.org/10.2489/JSWC.71.5.420.
http://dx.doi.org/10.2489/JSWC.71.5.420...
), and forests (Im et al., 2020Im, S., Lee, J., Kuraji, K., Lai, Y. J., Tuankrua, V., Tanaka, N., Gomyo, M., Inoue, H., & Tseng, C. W. (2020). Soil conservation service curve number determination for forest cover using rainfall and runoff data in experimental forests. Journal of Forest Research, 25(4), 204-213. https://doi.org/10.1080/13416979.2020.1785072.
https://doi.org/10.1080/13416979.2020.17...
). However, CN values are lacking for Interlocking Concrete Pavement (ICP) material. This is an imporante issue because ICP is commonly used as a wear layer of permeable pavements (i.e., Permeable Interlocking Concrete Paver, PICP) (Beecham et al., 2012Beecham, S., Pezzaniti, D., & Kandasamy, J. (2012). Stormwater treatment using permeable pavements. Proceedings of the Institution of Civil Engineers: Water Management, 165(3), 161-170. https://doi.org/10.1680/wama.2012.165.3.161.
https://doi.org/10.1680/wama.2012.165.3....
; Lucke et al., 2015Lucke, T., White, R., Nichols, P., & Borgwardt, S. (2015). A simple field test to evaluate the maintenance requirements of permeable interlocking concrete pavements. Water, 7(6), 2542-2554. https://dx.doi.org/10.3390/W7062542.
https://dx.doi.org/10.3390/W7062542...
) in sidewalks and parking lots. PICP is recognized as a SUstainable Drainage System (SUDS) because it can mitigate urban flooding significantly by reducing runoff peak and volumes (Collins et al., 2008Collins, K. A., Hunt, W. F., & Hathaway, J. M. (2008). Hydrologic comparison of four types of permeable pavement and standard asphalt in Eastern North Carolina. Journal of Hydrologic Engineering, 13(12), 1146-1157. http://dx.doi.org/10.1061/(ASCE)1084-0699(2008)13:12(1146).
http://dx.doi.org/10.1061/(ASCE)1084-069...
; Liu et al., 2020Liu, Y., Li, T., & Yu, L. (2020). Urban heat island mitigation and hydrology performance of innovative permeable pavement: a pilot-scale study. Journal of Cleaner Production, 244, 118938. http://dx.doi.org/10.1016/J.JCLEPRO.2019.118938.
http://dx.doi.org/10.1016/J.JCLEPRO.2019...
; Palla & Gnecco, 2015Palla, A., & Gnecco, I. (2015). Hydrologic modeling of Low Impact Development systems at the urban catchment scale. Journal of Hydrology (Amsterdam), 528, 361-368. http://dx.doi.org/10.1016/J.JHYDROL.2015.06.050.
http://dx.doi.org/10.1016/J.JHYDROL.2015...
; Winston et al., 2019Winston, R. J., Arend, K., Dorsey, J. D., Johnson, J. P., & Hunt, W. F. (2019). Hydrologic performance of a permeable pavement and stormwater harvesting treatment train stormwater control measure. Journal of Sustainable Water in the Built Environment, 6(1), 04019011. http://dx.doi.org/10.1061/JSWBAY.0000889.
http://dx.doi.org/10.1061/JSWBAY.0000889...
) and pollutant loading (Legret et al., 1999Legret, M., Nicollet, M., Miloda, P., Colandini, V., & Raimbault, G. (1999). Simulation of heavy metal pollution from stormwater infiltration through a porous pavement with reservoir structure. Water Science and Technology, 39(2), 119-125. http://dx.doi.org/10.1016/S0273-1223(99)00015-3.
http://dx.doi.org/10.1016/S0273-1223(99)...
; Pratt et al., 1999Pratt, C. J., Newman, A. P., & Bond, P. C. (1999). Mineral oil bio-degradation within a permeable pavement: long term observations. Water Science and Technology, 39(2), 103-109. http://dx.doi.org/10.1016/S0273-1223(99)00013-X.
http://dx.doi.org/10.1016/S0273-1223(99)...
), mimicking the pre-development hydrologic conditions (Woods-Ballard et al., 2015Woods-Ballard, B., Wilson, S., Udale-Clarke, H., Illman, S., Scott, T., Ashley, R., & Kellagher, R. (2015). The SuDS Manual. London: CIRIA.).
To our knowledge, few studies have reported the CN values for the PICP using measured rainfall and runoff data (e.g., Bean et al., 2007Bean, E. Z., Hunt, W. F., & Bidelspach, D. A. (2007). Field survey of permeable pavement surface infiltration rates. Journal of Irrigation and Drainage Engineering, 133(3), 249-255. http://dx.doi.org/10.1061/(ASCE)0733-9437(2007)133:3(249).
http://dx.doi.org/10.1061/(ASCE)0733-943...
). Schwartz (2010)Schwartz, S. S. (2010). Effective curve number and hydrologic design of pervious concrete storm-water systems. Journal of Hydrologic Engineering, 15(6), 465-474. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000140.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
adopted design rainfall and infiltration capacity of the subgrade soil to simulate runoff and the CN for permeable pavements. Martin & Kaye (2014)Martin, W. D., & Kaye, N. B. (2014). Hydrologic characterization of undrained porous pavements. Journal of Hydrologic Engineering, 19(6), 1069-1079. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000873.
https://doi.org/10.1061/(ASCE)HE.1943-55...
used design rainfall and the theoretical framework from Schwartz (2010)Schwartz, S. S. (2010). Effective curve number and hydrologic design of pervious concrete storm-water systems. Journal of Hydrologic Engineering, 15(6), 465-474. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000140.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
to present a generalized method for calculating the CN for permeable pavements. Damodaram et al. (2010)Damodaram, C., Giacomoni, M. H., Prakash Khedun, C., Holmes, H., Ryan, A., Saour, W., & Zechman, E. M. (2010). Simulation of combined best management practices and low impact development for sustainable stormwater management1. Journal of the American Water Resources Association, 46(5), 907-918. http://dx.doi.org/10.1111/J.1752-1688.2010.00462.X.
http://dx.doi.org/10.1111/J.1752-1688.20...
validated a CN estimating approach for permeable pavements using three rainfall-runoff datasets of the literature.
In Brazil, the decision-makers have commonly employed the ICP material over bare soil (not over a permeable pavement structure) to save financial costs. However, CN estimates from field data for this situation are even scarce. To fill this gap, we focus on estimating the CN parameter for interlocking concrete pavement seated over low-permeability clayey soil. We investigated the ICP surface under clogging and unclogging conditions. Our CN values account for intrarainfall variability and infiltration capacity data in the study area.
MATERIALS AND METHODS
Study area
This study was developed at the Federal University of Technology - Parana (UTFPR) in the municipality of Pato Branco, located southwest of Parana State, southern Brazil (26°19′ S, 52°69′ W) (Figure 1).
Location of the study area. The eight infiltration tests were performed at the Federal University of Technology - Parana (UTFPR) in the municipality of Pato Branco.
The Pato Branco city Hall has decreed the mandatory use of ICP in the sidewalks (3037 Law) since 2008, leading to extensive adoption of this material as a wear layer, mainly the downtown. This municipality Law aims to increase infiltration and reduce runoff in the urban area.
According to Köppen’s climate classification, the climate in the study area is the temperate oceanic climate (Cfb), humid subtropical with temperate summer and without a dry season (Alvares et al., 2013Alvares, C. A., Stape, J. L., Sentelhas, P. C., de Moraes Gonçalves, J. L., & Sparovek, G. (2013). Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift (Berlin), 22(6), 711-728. http://dx.doi.org/10.1127/0941-2948/2013/0507.
http://dx.doi.org/10.1127/0941-2948/2013...
). The annual average precipitation standard deviation is 1994 487.8 mm between 1965 and 2021. Tabalipa (2008)Tabalipa, N. L. (2008). Estudo da estabilidade de vertentes da bacia do rio Ligeiro, Pato Branco, Paraná [Tese de doutorado). Universidade Federal do Paraná, Curitiba. Retrieved in 2022, May 15, from https://acervodigital.ufpr.br/handle/1884/21252
https://acervodigital.ufpr.br/handle/188...
observed high clay (64.4%) and silt (29.3%) content in the soil samples (1.5 m of depth) around the UTFPR area. Hence, according to USDA (United States Department of Agriculture, 2004United States Department of Agriculture – USDA. (2004). Hydrologic Soil- Cover Complexes. In United States Department of Agriculture – USDA. National Engineering Handbook: Part 630 Hydrology (pp. 20). USA: United States Department of Agriculture (USDA) and Natural Resources Conservation Service (NRCS).), the HSG around the UTFPR is classified as type D.
Study delineation
To estimate runoff depth for the ICP material, we used the methodology proposed by Chin (2017)Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
. The study delineation is summarized in Figure 2.
Study delineation for Curve Number (CN) estimating in the Interlocking Concrete Pavement (ICP). The black arrows indicate the path of the main methodological steps: (a) The 24-hour hyetograph; (b) The Horton’s model fitted against infiltration capacity data; (c) The combined infiltration model and hyetograph to estimate runoff; and (d) The runoff estimation according to rainfall depth using different methods for CN adjusting (least-squares, median, mean, and asymtopic fit).
We first graphed the 32 hyetographs using 24-hour rainfall depth () data at 10-minutes time steps. Thus, measured rainfall was used here instead of design rainfall. Second, to adjust an infiltration curve model, we used field infiltration data of the ICP surface. Third, to estimate runoff for each event, we combined the infiltration model and hyetographs. Then, to adjust the best CN value using the CN method’s formulation, we related and runoff () datasets (- ).
24-hour hyetographs
The 24-hour rainfall depth () data came from the Center for Natural Disaster Monitoring and Alert (CEMADEN). The automatic tipping-bucket rain gauge (411850104A station) records rainfall depth every 10 minutes during the event and records zero value (absence of rainfall) every 1 hour. The CEMADEN does not perform a consistent analysis of rainfall data before it is available at Mapa Interativo (Brasil, 2022Brasil. Ministério da Ciência, Tecnologia, Inovações e Comunicações. Centro Nacional de Monitoramento e Alertas de Desastres Naturais. (2022). Mapa Interativo da Rede Observacional para Monitoramento de Risco de Desastres Naturais do Cemaden. Retrieved in 2022, May 15, from http://www2.cemaden.gov.br/mapainterativo
http://www2.cemaden.gov.br/mapainterativ...
).
We used 32 events to generate hyetographs at sequential 10-minute time intervals (Supplementary Material Table S1). The hyetographs of were transformed into rainfall intensity hyetographs, . We selected events randomly ranging from 0 to 150 mm over the 2014-2021 period. The range of rainfall depths was chosen to account for different rainfall characteristics (distribution, return period, and intensity) for the analysis of the - data.
Infiltration capacity
The infiltration capacity data came from Bazzo & Horn (2017)Bazzo, J. A., & Horn, P. L. (2017). Calibração do modelo matemático de infiltração de Horton em pavimento de concreto tipo blocos intertravados (Trabalho de Conclusão de Curso). Universidade Tecnológica Federal do Paraná, Pato Branco. Retrieved in 2022, May 15, from http://repositorio.utfpr.edu.br/jspui/handle/1/14558
http://repositorio.utfpr.edu.br/jspui/ha...
. Eight infiltration tests were conducted for ICP in situ using a single-ring infiltrometer at the sidewalks of the Federal University of Technology – Parana during August in 2017 year. The sidewalks are made of ICP material seated over bare soil. Bazzo & Horn (2017)Bazzo, J. A., & Horn, P. L. (2017). Calibração do modelo matemático de infiltração de Horton em pavimento de concreto tipo blocos intertravados (Trabalho de Conclusão de Curso). Universidade Tecnológica Federal do Paraná, Pato Branco. Retrieved in 2022, May 15, from http://repositorio.utfpr.edu.br/jspui/handle/1/14558
http://repositorio.utfpr.edu.br/jspui/ha...
performed infiltration tests under clogging and unclogging conditions on the ICP surface (four tests in each ICP condition). To perform infiltration tests, they adopted a modified version of the single-ring infiltration method for permeable pavement structures (American Society for Testing and Materials, 2013American Society for Testing and Materials – ASTM. (2013). C1781: Standard test method for surface infiltration rate of permeable unit pavement systems. West Conshohocken: ASTM International.), because the ICP is seated over bare soil.
A 0.30 m-diameter infiltrometer ring was placed over the ICP surface (sidewalks). Following Bean et al. (2007)Bean, E. Z., Hunt, W. F., & Bidelspach, D. A. (2007). Field survey of permeable pavement surface infiltration rates. Journal of Irrigation and Drainage Engineering, 133(3), 249-255. http://dx.doi.org/10.1061/(ASCE)0733-9437(2007)133:3(249).
http://dx.doi.org/10.1061/(ASCE)0733-943...
, Bazzo & Horn (2017)Bazzo, J. A., & Horn, P. L. (2017). Calibração do modelo matemático de infiltração de Horton em pavimento de concreto tipo blocos intertravados (Trabalho de Conclusão de Curso). Universidade Tecnológica Federal do Paraná, Pato Branco. Retrieved in 2022, May 15, from http://repositorio.utfpr.edu.br/jspui/handle/1/14558
http://repositorio.utfpr.edu.br/jspui/ha...
molded a thin ribbon of plumber’s putty along the ring’s bottom (Figure 3). To avoid leakage, the putty was depressed, forming a tight seal between the ICP surface and the ring.
After the ring was filled with freshwater, water level drops were measured over time (variable-head). When the water level dropped to 1/3 of its initial level, water volume was added until it rose to the initial level. The infiltration rate was calculated by dividing the flow rate by the cross-sectional area of the ring. The tests were finished three (equal) consecutive values of infiltration rate were achieved.
We fitted Horton’s infiltration model (Horton, 1933Horton, R. E. (1933). The Rôle of infiltration in the hydrologic cycle. Eos (Washington, D.C.), 14(1), 446-460. http://dx.doi.org/10.1029/TR014I001P00446.
http://dx.doi.org/10.1029/TR014I001P0044...
) against the infiltration capacity data using the Levenberg-Marquardt method (Levenberg, 1944Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2(2), 164-168. Retrieved in 2022, May 15, from http://www.jstor.org/stable/43633451
http://www.jstor.org/stable/43633451...
; Marquardt, 1963Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441. Retrieved in 2022, May 15, from http://www.jstor.org/stable/2098941
http://www.jstor.org/stable/2098941...
) for nonlinear least-squares problems. Because the water was ponded above the ICP surface, we assumed that the infiltration rate equals the infiltration capacity. The empirical Horton’s equation can be written as:
Where is the infiltration capacity () at time, (h), is the initial infiltration capacity (), is the asymptotic (steady) infiltration capacity (), and is the Horton’s decay parameter (). We measured and from infiltration tests, while and (Equation 1) were fitted using the Levenberg-Marquardt method in the MATLAB Curve Fitting Toolbox, version 2021a.
Hortonian runoff processes for runoff calculation
Background
Most studies have estimated the CN parameter using measured and data at the plot scale (e.g., Cao et al., 2011Cao, H., Willem Vervoort, R., & Dabney, S. M. (2011). Variation in curve numbers derived from plot runoff data for New South Wales (Australia). Hydrological Processes, 25(24), 3774-3789. https://doi.org/10.1002/hyp.8102.
https://doi.org/10.1002/hyp.8102...
; Lal et al., 2017Lal, M., Mishra, S. K., Pandey, A., Pandey, R. P., Meena, P. K., Chaudhary, A., Jha, R. K., Shreevastava, A. K., & Kumar, Y. (2017). Evaluation de la méthode du numéro de courbe du Service de la Conservation des Sols à partir de données provenant de parcelles agricoles. Hydrogeology Journal, 25(1), 151-167. http://dx.doi.org/10.1007/S10040-016-1460-5/FIGURES/9.
http://dx.doi.org/10.1007/S10040-016-146...
; Liu et al., 2018Liu, W., Chen, W., & Feng, Q. (2018). Field simulation of urban surfaces runoff and estimation of runoff with experimental curve numbers. Urban Water Journal, 15(5), 418-426. https://dx.doi.org/10.1080/1573062X.2018.1508597.
https://dx.doi.org/10.1080/1573062X.2018...
; Oliveira et al., 2016Oliveira, P. T. S., Nearing, M. A., Hawkins, R. H., Stone, J. J., Rodrigues, D. B. B., Panachuki, E., & Wendland, E. (2016). Curve number estimation from Brazilian Cerrado rainfall and runoff data. Journal of Soil and Water Conservation, 71(5), 420-429. http://dx.doi.org/10.2489/JSWC.71.5.420.
http://dx.doi.org/10.2489/JSWC.71.5.420...
) and at the watershed scale (e.g., Assaye et al., 2021Assaye, H., Nyssen, J., Poesen, J., Lemma, H., Meshesha, D. T., Wassie, A., Adgo, E., & Frankl, A. (2021). Curve number calibration for measuring impacts of land management in sub-humid Ethiopia. Journal of Hydrology: Regional Studies, 35, 100819. http://dx.doi.org/10.1016/J.EJRH.2021.100819.
http://dx.doi.org/10.1016/J.EJRH.2021.10...
; Galbetti et al., 2021Galbetti, M. V., Zuffo, A. C., Shinma, T. A., Boulomytis, V. T. G., & Imteaz, M. (2021). Evaluation of the tabulated, NEH4, least squares and asymptotic fitting methods for the CN estimation of urban watersheds. Urban Water Journal, 19(3), 244-255. https://doi.org/10.1080/1573062X.2021.1992639.
https://doi.org/10.1080/1573062X.2021.19...
). Due to the lack of measured data at the watershed scale, researchers have applied filtering techniques in observed streamflow data to separate baseflow and components for estimating (D’Asaro et al., 2014D’Asaro, F., Grillone, G., & Hawkins, R. H. (2014). Curve number: empirical evaluation and comparison with curve number handbook tables in sicily. Journal of Hydrologic Engineering, 19(12), 04014035. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000997.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
; Valle Junior et al., 2019).
In this paper, we used the alternative methodology presented by Chin (2017)Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
for estimating the parameter. We named this combined method generically as HORTOnian RUNoff (HORTORUN) method. The method does not differ in finding the best-fitted that matches versus relation. However, instead of using measured from a given event at plot or watershed scales, the values were estimated by combining the INCRARUN approach with Horton’s infiltration model.
In the HORTORUN approach, runoff occurs when rainfall intensity exceeds the surface infiltration capacity. Additionally, runoff can occur due to the water-table rise above the ground surface (Dingman, 2015Dingman, L. S. (2015). Physical hydrology (3rd ed). Illinois: Waveland Press, Inc.). This saturation from the below mechanism is usually called Dunne overland flow. Two assumptions underlay the HORTORUN method: i) Hortonian runoff process is mandatory, and ii) infiltration is the dominant process during initial abstraction and runoff until the end of the rainfall event, meaning that other abstraction processes such as interception, surface storage, and evaporation are not considered (Chin, 2017Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
).
One advantage of this method is that the CN parameter can be related to field-measurable parameters of the infiltration process (Chin, 2017Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
), whereas measured data are not required. Further, the HORTORUN method does not violate hydrologic principles when applied in incremental rainfall-runoff amounts. On the other hand, the typical application of the CN method in incremental time intervals results in infiltration that exceeds the watershed’s infiltration capacities (Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
). A detailed relationship between the infiltration model and the CN method is presented by Lal et al. (2017)Lal, M., Mishra, S. K., Pandey, A., Pandey, R. P., Meena, P. K., Chaudhary, A., Jha, R. K., Shreevastava, A. K., & Kumar, Y. (2017). Evaluation de la méthode du numéro de courbe du Service de la Conservation des Sols à partir de données provenant de parcelles agricoles. Hydrogeology Journal, 25(1), 151-167. http://dx.doi.org/10.1007/S10040-016-1460-5/FIGURES/9.
http://dx.doi.org/10.1007/S10040-016-146...
and Karpathy & Chin (2019)Karpathy, N. S., & Chin, D. A. (2019). Relationship between Curve Number and ϕ-Index. Journal of Irrigation and Drainage Engineering, 145(11), 06019009. http://dx.doi.org/10.1061/(asce)ir.1943-4774.0001426.
http://dx.doi.org/10.1061/(asce)ir.1943-...
.
Regardless the scale analysis, studies usually related - data in two ways: natural- and rank-ordered. The rationale for using rank-ordered data is that the CN method is used to predict values having the same exceedance probability as the corresponding value (Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
). While, the natural-ordered data consist of the actual observed - dataset. Becase there is no concensus to the usage of rank-ordered data among hydrologists (Moglen et al., 2022Moglen, G. E., Sadeq, H., Hughes, L. H., Meadows, M. E., Miller, J. J., Ramirez-Avila, J. J., & Tollner, E. W. (2022). NRCS curve number method: comparison of methods for estimating the curve number from Rainfall-Runoff Data. Journal of Hydrologic Engineering, 27(10), 4022023. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0002210.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
), we used both approaches here.
Calculation procedure
We calculated incremental runoff using Horton’s infiltration model and sequential 10-minutes time intervals for each rainfall-intensity hyetograph. We implemented the HORTORUN method in the Python programming language to optimize the calculation and decrease the chance of freehand miscalculation. We organized the HORTORUN method into six procedures keeping the original ideas presented by Chin (2017)Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
as follows:
Procedure 1 (the conversion of rainfall hyetographs units): The rainfall intensity hyetograph is calculated using a 24-hour rainfall depth hyetograph. If is the incremental rainfall during the th time interval, , then the average intensity during the th time interval is calculated as .
Procedure 2 (the incremental runoff calculation): Incremental runoff at the th time interval, , is determined only in the occurrence of ponding on the ground surface. In this case, a simple water balance equation is applied as , where is the incremental cumulative infiltration and represents the difference between the initial () and final () value at the th time interval; for instance, . Contrary, if all the rainfall during the infiltrates, then = 0.
The runoff, , is the sum of all incremental runoff values ( for a given event. To calculate , infiltration capacity is evaluated against rainfall intensity as described in Procedure 3.
Procedure 3: (the choice of infiltration equations): The infiltration capacity at the beginning of the th time interval, , is determined from the known value of under two conditions: i) continuous ponded ground surface and ii) noncontinuous ponded ground surface from the beginning of rainfall event.
The Horton’s infiltration model for (Equation 1) is valid under continuous ponding conditions, and is given by:
However, Horton’s infiltration model is not valid under noncontinuous ponding condition. Hence, infiltration capacity is a function of the cumulative infiltration given by (Chin, 2013Chin, D. A. (2013). Water-resources engineering (3rd ed). London: Pearson Education.):
Procedure 4 (the evaluation of infiltration condition): If during the th time interval, then it is assumed that all the rainfall during the infiltrates. Thus, = 0, and . It must be noted that is known, and consequently, Equation 3 can be solved as a function of .
If , then the rainfall infiltrates at the during the . In this case, if ponding is noncontinuous, the calculation of the is obtained based on the shifting of the noncontinuous to the continuous ponding condition. At first, if is the cumulative infiltration under noncontinuous ponding, then the reference time, , to infiltrate the same under continuous ponding condition is calculated by:
Horton’s equation for cumulative infiltration is implicit in (Equation 4), where is the unknown value. Next, the cumulative infiltration values are calculated based on the continuous ponding assumption. Thus, Equation 4 becomes Equation 5 to calculate and Equation 1 is used to obtain .
Particularly if this is the first that runoff occurs (i.e., ), then the cumulative infiltration up to the beginning of the time interval is equal to the initial abstraction, , hence .
Procedure 6 (the implementation in a programming language): The previous procedures are applied sequentially in each th time interval for all the 32 rainfall events.
Curve Number estimating
The CN method is semiempirical and relates rainfall depth to the corresponding runoff depth based on the water balance equation. The CN method formulation is given by (United States Department of Agriculture, 1986United States Department of Agriculture – USDA. (1986). Urban Hydrology for Small Watersheds.):
Where is the rainfall depth (mm), is the initial abstraction before runoff begins (mm), and is the cumulative infiltration after runoff begins (mm), is the potential maximum watershed storage (mm).
One assumption is that occurs before begins (Chin, 2021Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
), and it represents a fraction of the thought the relationship:
Where is the initial abstraction coefficient (dimensionless). Currently, this parameter is set as = 0.20 (United States Department of Agriculture, 1986United States Department of Agriculture – USDA. (1986). Urban Hydrology for Small Watersheds.). However, an update for the use of = 0.05 is in progress (United States Department of Agriculture, 2017United States Department of Agriculture – USDA. (2017). Estimation of direct runoff from storm rainfall (draft). In United States Department of Agriculture – USDA. National Engineering Handbook: Part 630 Hydrology (pp. 45). USA: United States Department of Agriculture (USDA) and Natural Resources Conservation Service (NRCS).), which is supported by some studies (Durán-Barroso et al., 2017Durán-Barroso, P., González, J., & Valdés, J. B. (2017). Sources of uncertainty in the NRCS CN model: recognition and solutions. Hydrological Processes, 31(22), 3898-3906. http://dx.doi.org/10.1002/HYP.11305.
http://dx.doi.org/10.1002/HYP.11305...
; Valle Junior et al., 2019; Woodward et al., 2003Woodward, D. E., Hawkins, R. H., Jiang, R., Hjelmfelt Junior, A. T., Van Mullem, J. A., & Quan, Q. D. (2003). Runoff curve number method: examination of the initial abstraction ratio. World Water & Environmental Resources Congress, 2003, 1-10. http://dx.doi.org/10.1061/40685(2003)308.
http://dx.doi.org/10.1061/40685(2003)308...
).
The potential maximum watershed storage in Equation 6 is scaled into a tabulated Curve Number, (dimensionless), which varies in the range . The transformation of into results in:
We estimated the CN value for each of the 32 rainfall events using the presented CN method formulation. First, was calculated for = 0.20 () as (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
):
Then, was calculated for = 0.05 () as (Valle Junior et al., 2019):
Next, CN was estimated via Equation 8. Last, we assessed a representative value of the CN using the well-accepted methods: asymptotic fit (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
), least-squares (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
), and central tendency (arithmetic mean, , and median, ). Hawkins (1993)Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
noticed three types of behavior using the asymptotic fit method: standard, complacent, and violent. The standard behavior occurs when the CN values decline with increasing rainfall depth until reaching an asymptotic CN value, (dimensionless). The standard asymptotic fit method is mathematically written as (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
):
Where is the CN as a function of and is the decay coefficient (mm-1). In Equation 11, both and are adjusting parameters.
The complacent behavior profile is a decline in CN with increasing rainfall depth but without reaching an asymptotic value. If complacent behavior is presented, the CN method is unsuitable for the study area (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
). The violent behavior depicted a decline in CN values until a threshold rainfall depth () and then increases suddenly with increasing rainfall depth (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
). The violent behavior is expressed as (D’Asaro et al., 2014D’Asaro, F., Grillone, G., & Hawkins, R. H. (2014). Curve number: empirical evaluation and comparison with curve number handbook tables in sicily. Journal of Hydrologic Engineering, 19(12), 04014035. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000997.
http://dx.doi.org/10.1061/(ASCE)HE.1943-...
):
Where is a coefficient (mm-1), and both and are adjusting parameters.
We performed the asymptotic fit method using the MATLAB Curve Fitting Toolbox, version 2021a. In addition, we also solved the least-squares method using MATLAB nonlinear least-squares algorithm. The performance of the CN estimating methods was evaluated by employing metrics of error and agreement. We chose the Root Mean Square Error () and determination coefficient () to quantify the average error and the goodness-of-fit, respectively.
RESULTS AND DISCUSSION
Infiltration curves and runoff calculation
Results show that and ranged from 258.00 to 96.00 mm.h-1 and from 46.80 to 19.20 mm.h-1, respectively, for clogged ICP (Figure 4). The Horton’s decay parameter varied from 13.05 to 3.17 h-1. (Figure 4). While for unclogged ICP, and varied between 927.60 and 68.40 mm.h-1 and between 104.40 and 27.00 mm.h-1, respectively, and varied from 7.32 to 2.38 h-1. Thus, we found that, on average, clogged ICP showed lower values of and than unclogged ICP. This is expected because clogged ICP has solid sediments (dust, mosses, and twigs) between the joints that decreases infiltration capacity. The results of for clogged ICP are, on average, closed to those reported for dry clayey soil (173.83 mm.h-1) by Bertotto et al. (2021)Bertotto, L. E., Lucas, M. C., Destro, C. A. M., Chin, D. A., Alves, W. S., & de Oliveira, P. T. S. (2021). Effects of infiltration conditions and rainfall characteristics on simulated curve numbers. Journal of Irrigation and Drainage Engineering, 147(10), 05021004. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001605.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
in the Pato Branco city. On the other hand, the results of for clogged ICP are much higher than those for clayey soil (9.93 mm.h-1) (i.e., Bertotto et al., 2021Bertotto, L. E., Lucas, M. C., Destro, C. A. M., Chin, D. A., Alves, W. S., & de Oliveira, P. T. S. (2021). Effects of infiltration conditions and rainfall characteristics on simulated curve numbers. Journal of Irrigation and Drainage Engineering, 147(10), 05021004. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001605.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
).
The fit between measured infiltration capacity and Horton’s model. Four infiltration tests (a); (b); (c); and (d) were performed for the ICP clogging condition. is the Root Mean Squared Error, is the coefficient of determination, is the infiltration capacity during the time,
We assessed the descriptive statistics of , , and for clogged and unclogged ICP. Because there were no outliers, we used the arithmetic mean of , , and to generate a single representative Horton’s model for each ICP surface condition. Hence, we calculated an average value of = 157.50 mm.h-1, = 29.25 mm.h-1, and = 7.38 h-1 for the ICP clogging condition, while for unclogged ICP, the average values were = 429.00 mm.h-1, = 64.20 mm.h-1, and = 4.96 h-1. These average values were used to calculate the runoff through the HORTORUN approach.
We presented the runoff and CN results solely for the ICP clogging condition because runoff was not generated ( = 0 mm) under the unclogged ICP. Results showed poor agreement and high scattered ( = 0.30) for natural-ordered - data (Figure 5a), whereas rank-ordered - data showed very good agreement and low scattered ( = 0.93) (Figure 5b).
The relationship between measured 24-hour rainfall () data and calculated runoff () for the ICP clogging condition: (a) Natural-ordered data; and (b) Rank-ordered data. Runoff was computed using the HORTORUN method. is the Root Mean Squared Error, is the coefficient of determination, and is the Pearson’s coefficient of correlation.
The poor agreement in natural-ordered data means that runoff depth did not increase as rainfall depth increased because similar events generated very different values (Figure 5a). For instance, two similar events of 111.6 and 113.5 mm generated values of 9.8 and 26.9 mm, respectively (Figure 5a). Further, we noted that the largest event (122.9 mm) lead to small value (0.40 mm), whereas the smallest event (47.6 mm) generated the largest value (30.2 mm) (Figure 5a). This occurs because the event of = 113.5 mm is less uniformly distributed and presents greater rainfall intensities exceeding infiltration capacities (Figure 6a) than the event of = 111.6 (Figure 6b), both within the 24-hour standardized duration.
Normalized hyetographs of rainfall intensity () and normalized infiltration capacity () curves over normalized time () for different 24-hour rainfall depths (): (a) = 113.5 mm; (b) = 111.6 mm; (c) = 47.6 mm; and (d) = 122.9 mm. The , , and are the maximum rainfall intensity, infiltration capacity and time of each event. All rainfall events have 24-hour duration.
Similarly, it is apparent that the event of = 47.6 mm is shortly distributed and has high intensity (Figure 6c), while the event of = 122.9 has long distribution and low intensity (Figure 6d). Thus, our results indicate that rainfall temporal distribution within the standard duration (24-hour) strongly affects runoff generation and, ultimately, the CN estimating. Hu et al. (2020)Hu, P., Tang, J., Fan, J., Shu, S., Hu, Z., & Zhu, B. (2020). Incorporating a rainfall intensity modification factor γ into the Ia-S Relationship in the NRCS-CN method. International Soil and Water Conservation Research, 8(3), 237-244. http://dx.doi.org/10.1016/J.ISWCR.2020.07.004.
http://dx.doi.org/10.1016/J.ISWCR.2020.0...
obtained similar results at the watershed scale and found that accounting for rainfall intensity in the CN method improved runoff calculations. Chin (2021)Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552.
http://dx.doi.org/10.1061/(ASCE)IR.1943-...
demonstrated that rainfall distribution is essential in determining the appropriate CN value across the United States of America territory. Our results also agree with the other study (Wang & Bi, 2020Wang, X., & Bi, H. (2020). The effects of rainfall intensities and duration on SCS-CN model parameters under simulated rainfall. Water, 12(6), 1595. https://doi.org/10.3390/W12061595.
https://doi.org/10.3390/W12061595...
) that used a rainfall simulator at a plot scale to demonstrate the effect of rainfall intensity and duration on , , CN, and .
Curve Number and initial abstraction estimates
Overall, we observed that CN values under clogged condition ranged slightly from 64.7 to 56.4 (with = 61.7 and = 62.2) for = 0.20 and from 48.5 to 30.8 (with = 40.2 and = 41.1) for = 0.05, considering the 32 - events (Table 1). We found the CN = 52.2 (natural-ordered data) and the CN = 60.1 (rank-ordered data), both for = 0.20, using the Least-squares method (Table 1). Further, for = 0.20 we found the CN = 36.5 (natural-ordered data) and the CN = 44.4 (rank-ordered data) using the Least-squares method. Bean et al. (2007)Bean, E. Z., Hunt, W. F., & Bidelspach, D. A. (2007). Field survey of permeable pavement surface infiltration rates. Journal of Irrigation and Drainage Engineering, 133(3), 249-255. http://dx.doi.org/10.1061/(ASCE)0733-9437(2007)133:3(249).
http://dx.doi.org/10.1061/(ASCE)0733-943...
reported CN values ranging from 37 to 50 (with = 44 and = 45) for PICP at plot scale. Thus, our results are consistent because CN values for the clogged ICP were higher than those for PICP.
The summary of Curve Number estimates for two initial abstraction ratios (λ = 0.20 and λ = 0.05) using natural and rank-ordered data. The CN is valid for the clogged ICP. The “–” indicates no CN value, and “*” means the asymptotic CN ().
Although results demonstrate that the did not explain the for natural ordered data (Figure 5a), we assessed the relationship between CN and for rank-ordered data using Asymptotic fit method (Hawkins, 1993Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334).
http://dx.doi.org/10.1061/(ASCE)0733-943...
).
Results showed a standard behavior for = 0.20 (Figure 7a) and violent behavior for = 0.05 (Figure 7a) using the asymptotic fit method. Hence, we found that CN behavior is strongly affected by the initial abstraction ratio for the clogged ICP material. The standard and violent behavior revealed a = 60.7 and = 42.3, respectively (Table 1). However, the goodness of fit was unsatisfactory for both standard ( = 0.26) and violent behavior ( = 0.30).
Asymptotic fit method using rank-ordered rainfall () and runoff () data for: (a) = 0.20 (standard behavior); and (b) = 0.05 (violent behavior). The threshold rainfall depth () is equal to 42.34 mm in violent behavior. The Curve Numbers are valid for the clogged ICP surface, is the Root Mean Squared Error, and is the coefficient of determination.
We compared the CN results of CN (Table 1) using the - relation using the CN method formulation. We found that the CN estimates fitted better to the - relation for = 0.20 (Figure 8a, c) than for = 0.05 (Figure 8b, c) regardless the CN estimating method (Least-squares, Median, Mean, or Asymptotic). Further, it is clear that the simulated runoff values were overestimated using = 0.05 (Figure 8b, d). Hence, the usage of = 0.05 was inappropriate to estimate runoff depth under the clogged ICP material.
The CN estimating methods (Least-squares, Median, Mean, and Asymptotic fit) for the relationship between rainfall () and runoff (): (a) Natural-ordered data ( = 0.20); (b) Natural-ordered data ( = 0.05); (c) Rank-ordered data ( = 0.20); and (d) Rank-ordered data ( = 0.05).
We also observed that the CN estimating methods did not differ significantly to fit the - relation (Figure 8). Nevertheless, the least-squares method presented performance ( = 0.97 and = 1.45 mm) using rank-ordered data to simulate runoff depth. Thus, in practice, the most suitable CN values for natural- and rank-ordered data ( = 0.20) are equal to 52.2 and 60.1, respectively, considering the intrarainfall application of the CN method.
CONCLUSION
We present the initial abstraction ratio () and Curve Number (CN) values for runoff estimating in interlocking concrete pavement (ICP) material. It is essential to mention that the ICP is seated over bare soil (not over a permeable pavement structure), and CN estimates are valid for the clogged ICP condition because the unclogged ICP did not generate runoff. Further, our CN values do not account for runoff from surrounding areas, that is, runoff generation occurs only from rainfall that falls directly over the ICP material. We concluded that the temporal distribution and intensity of 24-hour rainfall depth are essential characteristics to explain runoff generation under the incremental approach. We noted that = 0.20 is appropriate to estimate runoff for ICP material instead of the ongoing value of = 0.05. Finally, we demonstrated that representative CN values are equal to 52.2 (natural-ordered data) and 60.1 (rank-ordered data), respectively. Therefore, our findings can improve the accuracy of rainfall-runoff simulations and, consequently, stormwater drainage system design to mitigate urban flooding.
DATA AVAILABILITY STATEMENTS
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Supplementary Material
Supplementary material accompanies this paper.
Table S1 Summary of the 24-hour rainfall events.This material is available as part of the online article from https://doi.org/10.1590/2318-0331.272220220035
REFERENCES
- Ajmal, M., Waseem, M., Ahn, J.-H., & Kim, T.-W. (2016). Runoff estimation using the NRCS slope-adjusted curve number in mountainous watersheds. Journal of Irrigation and Drainage Engineering, 142(4), 04016002. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0000998
» http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0000998 - Alvares, C. A., Stape, J. L., Sentelhas, P. C., de Moraes Gonçalves, J. L., & Sparovek, G. (2013). Köppen’s climate classification map for Brazil. Meteorologische Zeitschrift (Berlin), 22(6), 711-728. http://dx.doi.org/10.1127/0941-2948/2013/0507
» http://dx.doi.org/10.1127/0941-2948/2013/0507 - American Society for Testing and Materials – ASTM. (2013). C1781: Standard test method for surface infiltration rate of permeable unit pavement systems. West Conshohocken: ASTM International.
- Assaye, H., Nyssen, J., Poesen, J., Lemma, H., Meshesha, D. T., Wassie, A., Adgo, E., & Frankl, A. (2021). Curve number calibration for measuring impacts of land management in sub-humid Ethiopia. Journal of Hydrology: Regional Studies, 35, 100819. http://dx.doi.org/10.1016/J.EJRH.2021.100819
» http://dx.doi.org/10.1016/J.EJRH.2021.100819 - Bazzo, J. A., & Horn, P. L. (2017). Calibração do modelo matemático de infiltração de Horton em pavimento de concreto tipo blocos intertravados (Trabalho de Conclusão de Curso). Universidade Tecnológica Federal do Paraná, Pato Branco. Retrieved in 2022, May 15, from http://repositorio.utfpr.edu.br/jspui/handle/1/14558
» http://repositorio.utfpr.edu.br/jspui/handle/1/14558 - Bean, E. Z., Hunt, W. F., & Bidelspach, D. A. (2007). Field survey of permeable pavement surface infiltration rates. Journal of Irrigation and Drainage Engineering, 133(3), 249-255. http://dx.doi.org/10.1061/(ASCE)0733-9437(2007)133:3(249)
» http://dx.doi.org/10.1061/(ASCE)0733-9437(2007)133:3(249) - Beecham, S., Pezzaniti, D., & Kandasamy, J. (2012). Stormwater treatment using permeable pavements. Proceedings of the Institution of Civil Engineers: Water Management, 165(3), 161-170. https://doi.org/10.1680/wama.2012.165.3.161
» https://doi.org/10.1680/wama.2012.165.3.161 - Bertotto, L. E., Lucas, M. C., Destro, C. A. M., Chin, D. A., Alves, W. S., & de Oliveira, P. T. S. (2021). Effects of infiltration conditions and rainfall characteristics on simulated curve numbers. Journal of Irrigation and Drainage Engineering, 147(10), 05021004. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001605
» http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001605 - Brasil. Ministério da Ciência, Tecnologia, Inovações e Comunicações. Centro Nacional de Monitoramento e Alertas de Desastres Naturais. (2022). Mapa Interativo da Rede Observacional para Monitoramento de Risco de Desastres Naturais do Cemaden. Retrieved in 2022, May 15, from http://www2.cemaden.gov.br/mapainterativo
» http://www2.cemaden.gov.br/mapainterativo - Cao, H., Willem Vervoort, R., & Dabney, S. M. (2011). Variation in curve numbers derived from plot runoff data for New South Wales (Australia). Hydrological Processes, 25(24), 3774-3789. https://doi.org/10.1002/hyp.8102
» https://doi.org/10.1002/hyp.8102 - Chin, D. A. (2013). Water-resources engineering (3rd ed). London: Pearson Education.
- Chin, D. A. (2017). Estimating the parameters of the curve number model. Journal of Hydrologic Engineering, 22(6), 06017001. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0001495 - Chin, D. A. (2021). Deficiencies in the curve number method. Journal of Irrigation and Drainage Engineering, 147(5), 04021008. http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552
» http://dx.doi.org/10.1061/(ASCE)IR.1943-4774.0001552 - Collins, K. A., Hunt, W. F., & Hathaway, J. M. (2008). Hydrologic comparison of four types of permeable pavement and standard asphalt in Eastern North Carolina. Journal of Hydrologic Engineering, 13(12), 1146-1157. http://dx.doi.org/10.1061/(ASCE)1084-0699(2008)13:12(1146)
» http://dx.doi.org/10.1061/(ASCE)1084-0699(2008)13:12(1146) - D’Asaro, F., Grillone, G., & Hawkins, R. H. (2014). Curve number: empirical evaluation and comparison with curve number handbook tables in sicily. Journal of Hydrologic Engineering, 19(12), 04014035. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000997
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000997 - Damodaram, C., Giacomoni, M. H., Prakash Khedun, C., Holmes, H., Ryan, A., Saour, W., & Zechman, E. M. (2010). Simulation of combined best management practices and low impact development for sustainable stormwater management1. Journal of the American Water Resources Association, 46(5), 907-918. http://dx.doi.org/10.1111/J.1752-1688.2010.00462.X
» http://dx.doi.org/10.1111/J.1752-1688.2010.00462.X - Dingman, L. S. (2015). Physical hydrology (3rd ed). Illinois: Waveland Press, Inc.
- Durán-Barroso, P., González, J., & Valdés, J. B. (2017). Sources of uncertainty in the NRCS CN model: recognition and solutions. Hydrological Processes, 31(22), 3898-3906. http://dx.doi.org/10.1002/HYP.11305
» http://dx.doi.org/10.1002/HYP.11305 - Galbetti, M. V., Zuffo, A. C., Shinma, T. A., Boulomytis, V. T. G., & Imteaz, M. (2021). Evaluation of the tabulated, NEH4, least squares and asymptotic fitting methods for the CN estimation of urban watersheds. Urban Water Journal, 19(3), 244-255. https://doi.org/10.1080/1573062X.2021.1992639
» https://doi.org/10.1080/1573062X.2021.1992639 - Grimaldi, S., Petroselli, A., & Romano, N. (2013). Green-Ampt Curve-Number mixed procedure as an empirical tool for rainfall–runoff modelling in small and ungauged basins. Hydrological Processes, 27(8), 1253-1264. http://dx.doi.org/10.1002/HYP.9303
» http://dx.doi.org/10.1002/HYP.9303 - Hawkins, R. H. (1993). Asymptotic determination of runoff curve numbers from data. Journal of Irrigation and Drainage Engineering, 119(2), 334-345. http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334)
» http://dx.doi.org/10.1061/(ASCE)0733-9437(1993)119:2(334) - Hawkins, R. H. (2014). Curve number method: time to think anew? Journal of Hydrologic Engineering, 19(6), 1059. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000954
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000954 - Horton, R. E. (1933). The Rôle of infiltration in the hydrologic cycle. Eos (Washington, D.C.), 14(1), 446-460. http://dx.doi.org/10.1029/TR014I001P00446
» http://dx.doi.org/10.1029/TR014I001P00446 - Hu, P., Tang, J., Fan, J., Shu, S., Hu, Z., & Zhu, B. (2020). Incorporating a rainfall intensity modification factor γ into the Ia-S Relationship in the NRCS-CN method. International Soil and Water Conservation Research, 8(3), 237-244. http://dx.doi.org/10.1016/J.ISWCR.2020.07.004
» http://dx.doi.org/10.1016/J.ISWCR.2020.07.004 - Im, S., Lee, J., Kuraji, K., Lai, Y. J., Tuankrua, V., Tanaka, N., Gomyo, M., Inoue, H., & Tseng, C. W. (2020). Soil conservation service curve number determination for forest cover using rainfall and runoff data in experimental forests. Journal of Forest Research, 25(4), 204-213. https://doi.org/10.1080/13416979.2020.1785072
» https://doi.org/10.1080/13416979.2020.1785072 - Jain, M. K., Mishra, S. K., Babu, P. S., Venugopal, K., & Singh, V. P. (2006). Enhanced runoff curve number model incorporating storm duration and a nonlinear Ia-S Relation. Journal of Hydrologic Engineering, 11(6), 631-635. http://dx.doi.org/10.1061/(ASCE)1084-0699(2006)11:6(631)
» http://dx.doi.org/10.1061/(ASCE)1084-0699(2006)11:6(631) - Karpathy, N. S., & Chin, D. A. (2019). Relationship between Curve Number and ϕ-Index. Journal of Irrigation and Drainage Engineering, 145(11), 06019009. http://dx.doi.org/10.1061/(asce)ir.1943-4774.0001426
» http://dx.doi.org/10.1061/(asce)ir.1943-4774.0001426 - Lal, M., Mishra, S. K., Pandey, A., Pandey, R. P., Meena, P. K., Chaudhary, A., Jha, R. K., Shreevastava, A. K., & Kumar, Y. (2017). Evaluation de la méthode du numéro de courbe du Service de la Conservation des Sols à partir de données provenant de parcelles agricoles. Hydrogeology Journal, 25(1), 151-167. http://dx.doi.org/10.1007/S10040-016-1460-5/FIGURES/9
» http://dx.doi.org/10.1007/S10040-016-1460-5/FIGURES/9 - Legret, M., Nicollet, M., Miloda, P., Colandini, V., & Raimbault, G. (1999). Simulation of heavy metal pollution from stormwater infiltration through a porous pavement with reservoir structure. Water Science and Technology, 39(2), 119-125. http://dx.doi.org/10.1016/S0273-1223(99)00015-3
» http://dx.doi.org/10.1016/S0273-1223(99)00015-3 - Levenberg, K. (1944). A method for the solution of certain non-linear problems in least squares. Quarterly of Applied Mathematics, 2(2), 164-168. Retrieved in 2022, May 15, from http://www.jstor.org/stable/43633451
» http://www.jstor.org/stable/43633451 - Liu, W., Chen, W., & Feng, Q. (2018). Field simulation of urban surfaces runoff and estimation of runoff with experimental curve numbers. Urban Water Journal, 15(5), 418-426. https://dx.doi.org/10.1080/1573062X.2018.1508597
» https://dx.doi.org/10.1080/1573062X.2018.1508597 - Liu, Y., Li, T., & Yu, L. (2020). Urban heat island mitigation and hydrology performance of innovative permeable pavement: a pilot-scale study. Journal of Cleaner Production, 244, 118938. http://dx.doi.org/10.1016/J.JCLEPRO.2019.118938
» http://dx.doi.org/10.1016/J.JCLEPRO.2019.118938 - Lucke, T., White, R., Nichols, P., & Borgwardt, S. (2015). A simple field test to evaluate the maintenance requirements of permeable interlocking concrete pavements. Water, 7(6), 2542-2554. https://dx.doi.org/10.3390/W7062542
» https://dx.doi.org/10.3390/W7062542 - Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431-441. Retrieved in 2022, May 15, from http://www.jstor.org/stable/2098941
» http://www.jstor.org/stable/2098941 - Martin, W. D., & Kaye, N. B. (2014). Hydrologic characterization of undrained porous pavements. Journal of Hydrologic Engineering, 19(6), 1069-1079. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000873
» https://doi.org/10.1061/(ASCE)HE.1943-5584.0000873 - Michel, C., Andréassian, V., & Perrin, C. (2005). Soil Conservation Service Curve Number method: how to mend a wrong soil moisture accounting procedure? Water Resources Research, 41(2), 1-6. http://dx.doi.org/10.1029/2004WR003191
» http://dx.doi.org/10.1029/2004WR003191 - Moglen, G. E., Sadeq, H., Hughes, L. H., Meadows, M. E., Miller, J. J., Ramirez-Avila, J. J., & Tollner, E. W. (2022). NRCS curve number method: comparison of methods for estimating the curve number from Rainfall-Runoff Data. Journal of Hydrologic Engineering, 27(10), 4022023. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0002210
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0002210 - Oliveira, P. T. S., Nearing, M. A., Hawkins, R. H., Stone, J. J., Rodrigues, D. B. B., Panachuki, E., & Wendland, E. (2016). Curve number estimation from Brazilian Cerrado rainfall and runoff data. Journal of Soil and Water Conservation, 71(5), 420-429. http://dx.doi.org/10.2489/JSWC.71.5.420
» http://dx.doi.org/10.2489/JSWC.71.5.420 - Palla, A., & Gnecco, I. (2015). Hydrologic modeling of Low Impact Development systems at the urban catchment scale. Journal of Hydrology (Amsterdam), 528, 361-368. http://dx.doi.org/10.1016/J.JHYDROL.2015.06.050
» http://dx.doi.org/10.1016/J.JHYDROL.2015.06.050 - Ponce, V. M., & Hawkins, R. H. (1996). Runoff curve number: has it reached maturity? Journal of Hydrologic Engineering, 1(1), 11-19. http://dx.doi.org/10.1061/(ASCE)1084-0699(1996)1:1(11)
» http://dx.doi.org/10.1061/(ASCE)1084-0699(1996)1:1(11) - Pratt, C. J., Newman, A. P., & Bond, P. C. (1999). Mineral oil bio-degradation within a permeable pavement: long term observations. Water Science and Technology, 39(2), 103-109. http://dx.doi.org/10.1016/S0273-1223(99)00013-X
» http://dx.doi.org/10.1016/S0273-1223(99)00013-X - Sahu, R. K., Mishra, S. K., & Eldho, T. I. (2012). Improved storm duration and antecedent moisture condition coupled SCS-CN Concept-Based Model. Journal of Hydrologic Engineering, 17(11), 1173-1179. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000443
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000443 - Schwartz, S. S. (2010). Effective curve number and hydrologic design of pervious concrete storm-water systems. Journal of Hydrologic Engineering, 15(6), 465-474. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000140
» http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000140 - Shi, W., Wang, N., Wang, M., & Li, D. (2021). Revised runoff curve number for runoff prediction in the Loess Plateau of China. Hydrological Processes, 35(10), e14390. http://dx.doi.org/10.1002/HYP.14390
» http://dx.doi.org/10.1002/HYP.14390 - Tabalipa, N. L. (2008). Estudo da estabilidade de vertentes da bacia do rio Ligeiro, Pato Branco, Paraná [Tese de doutorado). Universidade Federal do Paraná, Curitiba. Retrieved in 2022, May 15, from https://acervodigital.ufpr.br/handle/1884/21252
» https://acervodigital.ufpr.br/handle/1884/21252 - United States Department of Agriculture – USDA. (1986). Urban Hydrology for Small Watersheds.
- United States Department of Agriculture – USDA. (2004). Hydrologic Soil- Cover Complexes. In United States Department of Agriculture – USDA. National Engineering Handbook: Part 630 Hydrology (pp. 20). USA: United States Department of Agriculture (USDA) and Natural Resources Conservation Service (NRCS).
- United States Department of Agriculture – USDA. (2017). Estimation of direct runoff from storm rainfall (draft). In United States Department of Agriculture – USDA. National Engineering Handbook: Part 630 Hydrology (pp. 45). USA: United States Department of Agriculture (USDA) and Natural Resources Conservation Service (NRCS).
- Valle Junior, L. C. G., Rodrigues, D. B. B., & de Oliveira, P. T. S. (2019). Initial abstraction ratio and Curve Number estimation using rainfall and runoff data from a tropical watershed. Revista Brasileira de Recursos Hidricos, 24, http://dx.doi.org/10.1590/2318-0331.241920170199
» http://dx.doi.org/10.1590/2318-0331.241920170199 - Verma, S., Singh, P. K., Mishra, S. K., Singh, V. P., Singh, V., & Singh, A. (2020). Activation soil moisture accounting (ASMA) for runoff estimation using soil conservation service curve number (SCS-CN) method. Journal of Hydrology (Amsterdam), 589, 125114. http://dx.doi.org/10.1016/J.JHYDROL.2020.125114
» http://dx.doi.org/10.1016/J.JHYDROL.2020.125114 - Wang, X., & Bi, H. (2020). The effects of rainfall intensities and duration on SCS-CN model parameters under simulated rainfall. Water, 12(6), 1595. https://doi.org/10.3390/W12061595
» https://doi.org/10.3390/W12061595 - Winston, R. J., Arend, K., Dorsey, J. D., Johnson, J. P., & Hunt, W. F. (2019). Hydrologic performance of a permeable pavement and stormwater harvesting treatment train stormwater control measure. Journal of Sustainable Water in the Built Environment, 6(1), 04019011. http://dx.doi.org/10.1061/JSWBAY.0000889
» http://dx.doi.org/10.1061/JSWBAY.0000889 - Woods-Ballard, B., Wilson, S., Udale-Clarke, H., Illman, S., Scott, T., Ashley, R., & Kellagher, R. (2015). The SuDS Manual London: CIRIA.
- Woodward, D. E., Hawkins, R. H., Jiang, R., Hjelmfelt Junior, A. T., Van Mullem, J. A., & Quan, Q. D. (2003). Runoff curve number method: examination of the initial abstraction ratio. World Water & Environmental Resources Congress, 2003, 1-10. http://dx.doi.org/10.1061/40685(2003)308
» http://dx.doi.org/10.1061/40685(2003)308
Edited by
Publication Dates
-
Publication in this collection
28 Nov 2022 -
Date of issue
2022
History
-
Received
04 May 2022 -
Reviewed
29 Oct 2022 -
Accepted
30 Oct 2022