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WATER RESOURCES RESEARCH, VOL. 46, W04501, doi:10.1029/2009WR007803, 2010
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Parsimonious modeling of hydrologic responses in engineered watersheds: Structural heterogeneity versus functional homogeneity Nandita B. Basu,1,2 P. S. C. Rao,1,3 H. Edwin Winzeler,3,4 Sanjiv Kumar,1 Phillip Owens,3 and Venkatesh Merwade1 Received 30 January 2009; revised 22 July 2009; accepted 7 October 2009; published 2 April 2010.
[1] The central premise of this paper is that extensive modifications of land use and hydrology, coupled with intensive management of watersheds in the Midwestern United States over the past century, have increased the predictability of hydrologic responses, allowing for the use of simpler, minimum‐calibration models. In these engineered watersheds, extensive tile‐and‐ditch networks have increased the effective drainage density and have created bypass flow hydrologic systems that generate “flashy” and “predictable” hydrographs. We propose a simple, threshold‐based model, the Threshold‐ Exceedance‐Lagrangian Model (TELM), for predicting event hydrographs. TELM was evaluated by comparing predicted hydrographs with those measured over a 4 year period at the outlet of a mesoscale watershed (Cedar Creek, ∼700 km2) in northeastern Indiana. Application of the Soil‐Land Inference Model (SoLIM) indicated that, despite structural heterogeneities (e.g., spatial variability in soil taxonomic mapping units), about 80% of the area of the watershed could be assigned a single value of available soil water storage, which was the primary soil parameter that defined hydrograph response. Hydrograph recession curves for multiple events were described well using an exponential function, with the mean arrival time (tr) estimated on the basis of the contributing drainage area (A) and the mean occurrence time (th) of the event hyetograph. Also, functional responses (event hydrographs) at the subwatershed scale could be grouped into just two categories on the basis of only spatial variability in rainfall patterns. TELM, with no parameter calibration, matched the observed hydrographs as well as the widely used SWAT model predictions with calibration. Advantages and limitations of the proposed modeling approach were identified, and needed improvements were discussed. Citation: Basu, N. B., P. S. C. Rao, H. E. Winzeler, S. Kumar, P. Owens, and V. Merwade (2010), Parsimonious modeling of hydrologic responses in engineered watersheds: Structural heterogeneity versus functional homogeneity, Water Resour. Res., 46, W04501, doi:10.1029/2009WR007803.
1. Introduction [2] Description of hydrologic processes occurring over a range of spatial scales presents numerous challenges [Beven and Binley, 1992; Bloschl and Sivapalan, 1995; Bonell, 1998; Beven, 2001; Cerdan et al., 2004]. First, the spatial attribute databases are available at incompatible spatial resolution and reliability [Hopmans and Schoups, 2005; Harter and Hopmans, 2004; Rogowski and Wolf, 1994], requiring interpolation or extrapolation. Examples include maps, at various scales of resolution, of soils, geology, 1
School of Civil Engineering, Purdue University, West Lafayette, Indiana, USA. 2 Now at Civil and Environmental Engineering Department, University of Iowa, Iowa City, Iowa, USA. 3 Agronomy Department, Purdue University, West Lafayette, Indiana, USA. 4 Now at Materials Matter, Inc., Gettysburg, Pennsylvania, USA. Copyright 2010 by the American Geophysical Union. 0043‐1397/10/2009WR007803
topography, land use cover, etc. Second, some of the essential landscape/terrain attributes may need to be estimated through empirical regression approaches [Beven and Binley, 1992; Beven, 2001], thus yielding indirect estimates with varying levels of uncertainty (e.g., pedotransfer functions) [Hoosebeck et al., 1999; Balland et al., 2008; Jana et al., 2008; Wessolek et al., 2008]. As a result, generating overlays of such spatial data to produce thematic maps of presumed homogeneous subdomains, as needed for watershed modeling, is fraught with uncertainty problems [Ogden et al., 2001]. [3] Watershed characterization efforts can be focused on understanding the spatial structure (as in most geospatial mapping) or on a description of the functional responses (as in most monitoring projects) to temporal perturbations in forcing functions, with the distributed‐parameter hydrologic models attempting to link the two. Thus, the key questions in watershed modeling are as follows. (1) What are the dominant forcing functions and their filters within the system that moderate the observed hydrologic responses (e.g., hydrographs, chemographs, and soil water storage dynamics)
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and emergent patterns? (2) What is the level of spatial discretization or complexity of representation (e.g., size of the representative elementary watershed) required to capture the hydrologic functions of the dominant filters within the landscape? (3) How heterogeneous are landscapes, both structurally (soil, land use patterns, etc.) and functionally (scaled hydrographs at subwatershed level)? [4] Existing watershed models, including detailed, process‐based models and lumped‐parameter conceptual/ empirical models, cover the gamut of options in addressing these questions (e.g., TOPMODEL [Beven, 1995], MIKE‐ SHE [Abbott et al., 1986; Refsgaard and Storm, 1995], DSHVM [Wigmosta et al., 1994], RHESSys [Band et al., 1991], VIC [Liang et al., 1994], TOPLATS [Famiglietti and Wood, 1994], J2K [Krause, 2002; Fink et al., 2007], IBIS‐HYDRA [Donner and Kucharik, 2008], SWAT [Arnold et al., 1998], and SWIM [Krysanova et al., 1998, 2005; Rinaldo et al., 2006a, 2006b]). Process‐based models describe processes at high spatial and temporal resolution, but are constrained by the absence of the requisite input data for all the model parameters [Todini, 2007]. In contrast, lumped‐parameter conceptual/empirical models (for example) have the problem of generating effective, spatially averaged estimates for the fewer parameters [e.g., Ogden et al., 2001; Breuer et al., 2009]. [5] One common feature of the distributed‐parameter hydrologic models is the need for calibration using “training” data sets gathered over a restricted timeline, cross validation using other data sets, and then generating model forecasts for much longer periods. While numerous, creative ways of calibration and optimization have been developed [e.g., Gupta et al., 1998; Madsen, 2003; Arabi et al., 2006; Marcé et al., 2008], this approach has two basic limitations: (1) equifinality or nonuniqueness, where multiple combinations of model parameters might produce the same model outcome [Beven and Binley, 1992; Grayson et al., 1992a, 1992b; Beven, 2001; Bloschl, 2001; Wagener et al., 2003; Vache and McDonnell, 2006; Savenije, 2008], and (2) lack of model validation at spatial scales smaller than at which the model was calibrated [Dehotin and Braud, 2008; Stisen et al., 2008]. Both problems are significant for multiple types of intended uses of model predictions (i.e., model utility). [6] In contrast to the model calibration approach, a few studies have recognized the value in studying patterns with an attempt to classify catchments and identify the dominant drivers and filters of hydrologic responses for each catchment class [e.g., Atkinson et al., 2002; Wagener et al., 2007; Zhang et al., 2008; Merz and Bloschl, 2009]. Merz and Bloschl [2009] analyzed event runoff coefficients from 64,000 events in 459 Austrian catchments (5–10,000 km2), and observed that the runoff coefficients were strongly correlated with climatic indicators (e.g., mean annual precipitation P and evapotranspiration) and only weakly related to land use, soil types and geology. The “top‐down” approach proposed by Klemeš [1983] was adapted by Atkinson et al. [2002, 2003] and Farmer et al. [2003] to explore climate, soil and vegetation controls on streamflow generation at varying time scales. A systematic study of multiple catchments in Australia and New Zealand indicated that the required model complexity increased with decreasing time scales, and with increasing catchment dryness index [Atkinson et al., 2002, 2003; Farmer et al., 2003]. Zhang et al. [2008], in a similar study based on the Budyko
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framework, examined 265 catchments in Australia spanning a range of climatic regimes. Their study indicated that at mean annual time scales the index of dryness (ratio of precipitation to evapotranspiration) was adequate to describe the water balance, while at monthly time scales, additional factors, such as catchment storage capacity, were important. It is important to note that the dominant processes vary with scale; while local‐scale soil characteristics may be important at the plot scale, geomorphology and climate may be the dominant controls on runoff response at the larger scales [Atkinson et al., 2002, 2003; Farmer et al., 2003; Zhang et al., 2008; Merz and Bloschl, 2009]. Identifying and understanding dominant processes helps in development of parsimonious predictive models that introduce complexity only when necessary, thus reducing the burden on calibration and parameter estimation [Atkinson et al., 2002, 2003; Sivapalan, 2003, 2005; Wagener et al., 2007]. [7] Our overall goal here is to develop a parsimonious approach for modeling hydrologic responses of watersheds (about 100–1,000 km2) in the Midwestern United States, specifically in the corn‐soybean belt covering northern regions of Indiana, Illinois, and Iowa. This geographic region, which at first glance would appear to be characterized by highly complex spatial patterns of geology, soils, and climate, land use, and crop management practices. To accommodate such complexity, detailed distributed‐parameter models, such as SWAT [Arnold et al., 1998], have been used to represent hydrologic processes in these watersheds. [8] In the modified Midwestern United States watersheds, intensive management requiring applications of large amounts of fertilizers, pesticides, and animal manures (both as crop nutrient supplements and for waste disposal) has contributed to widespread, adverse water quality impacts (nitrogen, phosphorus, pesticides, pharmaceuticals, hormones, pathogens, etc.) at both the local scale (streams, lakes), and as far away as the Gulf of Mexico (e.g., coastal hypoxia) [Committee on Environment and Natural Resources, 2000; Scavia et al., 2003; Scavia and Donnelly, 2007]. Models attempting to predict water quality impacts from the scale of a single tile (∼0.1 km2) to the scale of the Mississippi River Basin (∼3 million km2) often become computation‐intensive and calibration‐dependent. This paper is focused only on generation of event hydrographs; however, as will be discussed later, the essential attributes of the hydrograph that need to be reproduced are defined by water quality prediction goals (i.e., chemographs and loads). [9] Despite the complexity evident in these watersheds, there is a notable emergence of scale invariance (or “functional homogeneity”) and temporal persistence to observed hydrologic responses, enabling the use of much simpler models to reproduce the essential features of the hydrograph responses. The model we propose is called the Threshold Exceedance Lagrangian Model (TELM) to describe its principal components. We examine the utility of this simplified modeling approach using monitoring data collected over a 4 year period in a mesoscale, engineered watershed (∼700 km2), dominated by croplands, in northern Indiana. Our specific objectives are as follows. [10] 1. Evaluate the structural heterogeneity of soils and land use, and functional homogeneity of hydrologic response using existing modeling data for a typical, engineered watershed in Midwestern United States.
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Figure 1. Map showing geographic region of interest (ROI) in red. ROI extends between 35.5°N and 47.5°N latitude and 81.8°W and 99.1°W longitude. [11] 2. Develop a parsimonious model for generating hydrographs measured at the watershed outlet, and compare the predictive ability of the model with that of a widely used, distributed‐parameter model, SWAT [Arnold et al., 1998]. [12] We first present the rationale for adopting the parsimonious approach (section 2), then present an illustrative case study and describe the TELM model (sections 3 and 4) and illustrate its use for prediction of hydrographs, outline its limitations and suggest improvements (section 5). Using this case study, we then discuss the general features of the simplified watershed modeling approach proposed here (section 6).
2. Rationale for Parsimonious Modeling [13] The Midwestern U.S. landscapes represent an interesting scenario for watershed modeling, and for the reasons discussed below offer a good test case for parsimonious modeling approaches. This region has (1) similar geologic history, where soils were derived from similar glacial parent material (loess/till) undergoing similar pedogenic processes, and (2) shares a similar cultural history, in that over the past century of settlement, the landscape has undergone extensive modifications in being converted from erstwhile wetlands‐lowlands (forests and prairies) to highly productive croplands that are now intensely managed. Vast tracts of land (∼75%) in this region are planted to corn‐soybean rotation, and the soil/crop management (conservation) practices tend to be quite uniform to achieve maximum grain yields, and to minimize soil losses through sediment runoff [National Resources Conservation Service, 2006]. Thus, natural variations in soils may have been evened out enough that these soils tend to be functionally more homogenous than is commonly acknowledged or perceived from examining typical U.S. Department of Agriculture National Resources Conservation Service (USDA NRCS)
Soil Survey maps (1:24,000 scale) depicting numerous mapping units delineated on a soil taxonomic basis. [14] Hydrology of these landscapes has also been extensively modified to promote rapid drainage of low‐ permeability soils necessary for intensive crop production. Presence of extensive networks of artificial (tile drains, ditches) and natural (cracks, root holes, biochannels) preferential/bypass flow paths, has significantly altered the hydrologic responses [Evans and Fausey, 1999; Quisenberry and Phillips, 1976; Radcliff and Rasmussen, 2000; Kladivko et al., 2001; Haws et al., 2004; Schilling and Helmers, 2008; Cooke et al., 2001; Skaggs et al., 1995; Stillman et al., 2006]. Most event hydrographs and chemographs show quick response (time to peak) and rapid recession (few hours to days), at most spatial scales of interest; these are manifestations of engineered, bypass flow hydrologic systems with a high effective permeability. [15] For the foregoing reasons, our overall hypothesis is that in these engineered (modified and managed) Midwestern U.S. landscapes north of the Wisconsin and Illinois glaciation boundary, the watersheds are “functionally homogeneous” in spite of their obvious “structural heterogeneities,” and that predictions of event hydrographs and chemographs can be achieved using simpler and more robust models than are currently used. The necessary level of complexity of such a model would be a function of the spatial and temporal scales at which information is required. We recognize that with a decrease in spatial scale, greater detail may be needed to accurately assess the interaction of soils, land use and topographical controls on water movement and contaminant transport.
3. Illustrative Case Study [16] The proposed approach is specific to watersheds located in the targeted geographic area shown in Figure 1 (red area in map, covering ∼500,000 km2). Surficial materials in
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Figure 2. Location of the St. Joseph River basin (SJRB) (MI, Michigan; IN, Indiana; OH, Ohio) and the Cedar Creek watershed (IN, Indiana). SJRB extends between 41.1°N and 41.9°N latitude and 84.4°W and 85.3°W longitude.
this region include glacial deposits of till, outwash, and lacustrine sediments from Wisconsin, Illinois, and older glacial periods with a mantle of loess of variable thickness across the region in all areas except floodplains. Most of this area is underlain by Silurian and Devonian limestone and dolostone. Middle Devonian to Early Mississippian black shale and Early to Middle Mississippian siltstone and shale are in some areas of the northern part of the region. 3.1. Watershed Description [17] We examined a cropland‐dominated watershed (Cedar Creek), which is a part of the St. Joseph River Basin in northeastern Indiana (Figure 2). St. Joseph River supplies drinking water for a population of ∼250,000 (St. Joseph River Watershed Initiative, 2009, http://www.sjrwi.org/ watershed.htm) in Fort Wayne, Indiana. Cedar Creek watershed (CCW) covers an area of ∼707 km2 and drains two 11‐ digit subwatersheds the Upper Cedar (HUC 04100003080) and the Lower Cedar (HUC 04100003090). The landscape is predominantly flat, with a maximum elevation of 326 m AMSL, and an average land surface slope of 3%. About 76% of the basin is agricultural land, 21% forested lands, and 3% urban [Larose et al., 2007] (see also St. Joseph River Watershed Initiative, http://www.sjrwi.org/watershed.htm). The cropland is equally split between corn and soybean, and the “urban” areas are mostly small townships. Approximately 65% of CCW was represented by rainfall measured at the Garrett station, and the remaining 35% by the rainfall monitored at the Waterloo Station [National Climatic Data Center, 2004]. Cedar Creek has one USGS gauging station at the outlet (station 0418000), and one NAWQA water quality sampling station colocated with the streamflow gauging station.
3.2. Soil Landscape Modeling [18] Maps of CCW showing soil polygon delineations of mapping units according to soil taxonomic differences exhibit a high degree of spatial heterogeneity (Figure 3a), with each of these polygons assigned soil properties “typical” to that unit. Such maps suggest the need for detailed, spatially explicit hydrologic models for description of water flow. [19] We used an innovative soil mapping technique, Soil‐ Land Inference Model (SoLIM), that recognizes the oversimplification introduced in depicting soils as discrete polygons [Mark and Csillag, 1989; Zhu et al., 1996] and uses landscape attributes (e.g., digital elevation models (DEM)) and relationships between soil and landscape properties to derive spatially continuous soil maps from published soil survey data. Relationships between landscapes and soils are examined using the digital elevation model, patterns are extracted, and knowledge is consolidated and reapplied to landscapes using the landscape‐soil relationships [Qi and Zhu, 2003]. [20] Developed by researchers at the University of Wisconsin‐Madison and in conjunction with the USDA NRCS, SoLIM integrates knowledge of soil scientists with geographic information systems (GIS) techniques using fuzzy membership logic, artificial intelligence, and information representation theory. SoLIM estimates the soil property value (Dij) at a pixel on the land surface location using the representative value for the kth soil (Dk), and the fuzzy membership value (Sijk) for the kth soil at that location (Dij = n n P P Sijk Dk/ Sijk, n is the number of soil classes in the area). k¼1
k¼1
The Sijk value is obtained by creating frequency distributions of the soil property related to terrain attributes (or other
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Figure 3. (a) Soil taxonomic map, (b) SOLIM‐based map of available water storage (AWS), and (c) cumulative frequency distribution of AWS over CCW and subbasins within CCW (numbers refer to subbasins). landscape properties) on the basis of the quantified relationships between soils and landscape quantities. 3.3. SWAT Modeling of CCW Watershed [21] The Soil and Water Assessment Tool (SWAT) is a spatially distributed, physically based hydrologic model that predicts the impact of land management practices on water, sediment, and agricultural chemical yields in large, complex watersheds with varying soils, land use, and management conditions over long periods of time [Arnold et al., 1998; Gassman et al., 2007; Krysanova and Arnold, 2008]. In SWAT, a watershed is divided into multiple subwatersheds, which are further subdivided into hydrologic response units (HRUs) that comprise homogeneous land use, management and soil characteristics. The physical processes associated with water movement, sediment transport, crop growth, nutrient cycling, etc., are modeled at the HRU scale. The location and spatial distribution of these HRUs within the subwatersheds are, however, not taken into account; thus, the HRUs are hypothetical spatial units. Here, we use the SWAT model simulations of the hydrographs at the outlet of the Cedar Creek watershed that was recently reported by Kumar and Merwade [2009].
4. Hydrologic Modeling Framework: TELM [22] Any hydrologic model is driven by a set of forcing functions (weather, land use, management, etc.) that vary both spatially and temporally. These input signals are modified (filtered) as water travels through the network of pores, tiles, ditches, and streams, whose geometry is determined by the landscape attributes (soil and land use) that
vary spatially, to produce responses (hydrographs and chemographs) observed at the watershed outlet. [23] Prediction of hydrographs requires two essential steps: estimating the amount and timing of effective rainfall (J(t)) that contributes to stream flow and then routing the estimated J(t) through the hillslope and channel network. Following the simple linear reservoir model most commonly used in hydrological literature [cf. Atkinson et al., 2003; Farmer et al., 2003], the streamflow at the outlet is expressed as a convolution integral: Zt Qðt Þ ¼
J ðt Þ f ðt t 0 Þdt 0 ;
ð1Þ
0
where J(t) is the “effective” rainfall input that contributes to stream flow and f represents the instantaneous unit hydrograph (IUH). 4.1. Estimation of Effective Rainfall [24] The effective rainfall time series is estimated from the total rainfall time series by assuming that streamflow generation (by either surface or subsurface pathway) is a threshold‐driven process; the threshold here being the profile‐averaged “field capacity” water content, representing the soil water storage capacity. “Excess” rainfall (rainfall minus actual evapotranspiration (AET) [L/T] is routed to the stream network, only after the domain attains “field capacity.” This requires an implicit assumption that infiltration and redistribution occurs fast enough to restore deficits (D) [L/T] prior to initiation of overland or subsurface flow. Here, soil water storage deficit is defined as the difference between the values of antecedent and “field capacity” soil
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water contents. Note that explicit accounting of the pathways/ mechanisms generating flow is not considered in this approach. This assumption is valid in these watersheds because of the presence of an extensive tile drain network that acts as a bypass flow system which routes the water in excess of field capacity through the landscape to the streams. [25] The following simple soil water storage balance model was used to estimate the effective rainfall, J(t), as a function of the precipitation, P(t), the actual evapotranspiration, AET(t), the soil water storage deficit, D(t), and the fraction, g, contributing to groundwater recharge. Note that the streamflow Q(t) estimated using equations (1) and (3) is the streamflow (SF) minus the base flow (BF). The “excess rainfall” T(t) is given by T ðt Þ ¼ Pðt Þ AET ðtÞ Dðt 1Þ:
ð2Þ
The effective rainfall contributing to streamflow and the soil water storage deficit is given as J ðt Þ ¼
8 < ð1 g ÞT ðt Þ f or T ðt Þ > 0 :
0
D ðt Þ ¼
ð3Þ
otherwise 8 0
T ðt Þ otherwise:
ð4Þ
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bution [e.g., Schilling and Helmers, 2008; Kladivko et al., 2001]. Thus, we adopted an exponential function, f ðtÞ ¼ ð1=tr Þ expðt=tr Þ;
ð5Þ
where tr is mean travel time (days) to route the water through the landscape. The mean travel time, tr can be estimated as a function of the watershed area (A, km2) [Alexander et al., 2000] and the first moment of the hyetograph, th: tr ¼ th þ 0:0065 þ 0:2642 * A1=3 :
ð6Þ
The travel time formulation provided by Alexander et al. [2000] refers only to residence time in the channel states. Here, we extend its use to include residence times both in the hillslope and the river network. This assumption is valid in these systems because extensive tile drains and ditches that effectively function as a high‐density drainage network for short circuit links of the hillslopes to the stream networks. The effective rainfall J(t) estimated in section 4.1 is routed through the network using the exponential function in equation (5). The mean travel time tr is estimated independently from the zeroth moment of the hydrograph and the area of the basin. Thus, estimation of the hydrograph using TELM required no calibration.
5. Results
[26] An average recharge fraction g ∼ 0.4 was estimated using the filter program [Arnold and Allen, 1999] for base flow (BF) separation and the 10 year streamflow data at Cedar Creek outlet. The FAO approach [Allen et al., 2005] was used to estimate daily AET values from the potential evapotranspiration (PET) values that were estimated from meteorological data using the Priestley‐Taylor equation [e.g., Dingman, 1994]. The FAO approach uses information on the available soil water storage (AWS), crop planting date, crop growth stages, and maximum rooting depth to estimate daily AET values. The model also includes a correction factor to account for crop physiologic stress resulting from soil water deficits; the PET is corrected to reduce in a linear fashion whenever soil water content is below a certain threshold (50% of field capacity). We modified the FAO model to add a root growth term that mimics the crop growth term, to account for less water extraction from the soil during the early growth stages. These details are provided in Appendix A. Crop planting dates and growth stages used in the FAO model were obtained from the National Agricultural Statistics Service database [National Agricultural Statistics Service (NASS), 2004]. [27] The landscape was divided into multiple homogeneous response units (HRUs) using information from SoLIM modeling, hydrograph analysis and land use data (sections 5.2 and 5.3). Within each HRU equations (2)–(4) were used along with the AET model (see Appendix A) to do water balance at daily time steps to estimate the effective rainfall, J(t) as a function of the input rainfall P(t). 4.2. Routing Through the Landscape [28] Hydrograph recession curves for tile‐drained landscapes have been observed to follow an exponential distri-
5.1. Soil Landscape Modeling of CCW Watershed [29] The Cedar Creek Watershed was mapped by NRCS, with over 14,000 discrete soil polygons, and more than 80 soil series (Figure 3a). The available soil water (AWS) storage maps created using SoLIM were significantly less variable (Figure 3b) than that suggested by soil taxonomic classifications. In fact, greater than 80% of CCW area had AWS values between 80 mm and 120 mm (Figure 3c), with higher AWS values (∼300 mm) restricted to soils located along the riparian zones, primarily as a result of greater depth to the confining clay/dense till layer. Subwatersheds (area ∼10–20 km2) within CCW had very similar spatial distribution patterns of AWS, suggesting homogeneity at that scale (Figure 3c). These results support the representation of the entire watershed as a single, effectively homogeneous hydrologic unit. As will be shown in later (section 5.5), consideration of the spatial domain as two distinct regions (hillslopes and riparian zones) may be required under specific “extreme” hydrologic conditions. 5.2. Functional Homogeneity [30] Further evidence for functional homogeneity in CCW comes from examining the subwatershed hydrographs, simulated by Kumar and Merwade [2009] using SWAT model [Arnold et al., 1998; Gassman et al., 2007]. Using a 1.5% critical source area (CSA) for stream generation, 5% threshold each for land use and soil types (STATSGO), 45 subwatersheds, and 310 hydrologic response units (HRUs) were delineated within CCW [Kumar and Merwade, 2009]. Normalized hydrographs (flow normalized by subwatershed or HRU area) from subwatersheds within CCW could be grouped into just two categories across the watershed (Figure 4) only on the basis of the spatial differences in the temporal forcing function (i.e., rainfall patterns), supporting
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Figure 4. Functional homogeneity of hydrograph responses over CCW (SWAT simulations from Kumar and Merwade [2009]). our argument for functional homogeneity. Within a subwatershed, multiple HRUs with same land use, but different soil types had similar hydrograph responses, once again pointing toward functional homogeneity (or scale invariance) even at the scale of a single HRU. Hydrologic monitoring data at the subwatershed scale, however, are not available to validate this pattern observed in SWAT model outcomes; thus, this assertion remains to be tested experimentally. [31] Is this apparent homogeneity of hydrologic response we observed a model artifact, or is it an accurate representation of process dynamics? If the latter is true, is it necessary to use such complex models in these landscapes? Our analysis suggests that weather variability (precipitation and evapotranspiration, driven by land use and climate) are the primary drivers of hydrologic response in CCW, and that the landscape is functionally homogeneous, at least at the scale of 10–20 km2 subwatersheds. This is similar to the observations made by Merz and Bloschl [2009] and Zhang et al. [2008] for catchments in Austria and Australia, respectively. Cho and Olivera [2009] reported that for three small watersheds, hydrographs modeled using SWAT were similar whether or not the spatial variations in land use, soils, and precipitation were explicitly accounted for in delineation of hydrologic response units (HRUs). 5.3. Dominant Flow Paths [32] We plotted recession curves from several hydrographs measured at CCW outlet (Figure 5). Note that in Figure 5, discharge (Q) is scaled to peak discharge (Q0), while time (t) is scaled to tr (equation (6)). For CCW, with A ∼707 km2, the third term in equation (6) is ∼1.8 days, whereas the th varied from 0.5 days (for the smallest event) to 2 days (for the larger, multiday storm events). A single, exponential, travel time distribution, with a mean travel time between 2 to 3 days, was sufficient to describe all hydrographs at the watershed outlet for all four simulation years. The expo-
nential approximation fits the data for the first 90% of the hydrograph recession (0.1 < Q/Q0 < 1) (Figure 5). The longer travel times (>3 days), associated with about 10% of the observed discharge (0 < Q/Q0 < 0.1), is represented in the tails of the recession curves, and is explained by an exponential function with much smaller slope (Figure 5). Faster recession during the first phase is the result of macropore flow, while the much slower and extended recession is attributed to drainage from the soil matrix with much smaller hydraulic conductivity [Kladivko et al., 2001]. These observations suggest that (1) a single dominant transport pathway was active for most events, (2) a significant portion of the hydrograph recession is “flashy,” with short travel times, and (3) rainfall is a strong driver of the hydrograph response. 5.4. Hydrograph Modeling [33] We evaluated TELM to predict hydrographs at the outlet of CCW. On the basis of the observations regarding homogeneity of effective hydrologic properties (e.g.,
Figure 5. Selected measured hydrograph recession curves for the years 2000–2003 and fits of exponential functions.
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Figure 6. Comparison of measured hydrographs and predictions (TELM and SWAT) for four years. Note that P is the annual precipitation (mm), SF is streamflow (mm), and BF is base flow (mm). AWS; see section 5.1) and resulting hydrologic response (sections 5.2 and 5.3), entire CCW was treated as a single, homogeneous unit in terms of soil properties (AWS), and then subdivided into two zones based on rainfall patterns, and four land use classes (corn, soybean, forest, urban)
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within each zone. Thus, CCW was subdivided in to just 8 HRUs, in contrast with 310 HRUs delineated in SWAT modeling of CCW, as conducted by Kumar and Merwade [2009]. Hydrographs were simulated for four consecutive years (2000–2003) at the CCW outlet (Figure 6). Of these, the year 2002 was a drier year (mean annual rainfall of 808 mm, compared to 1,009 mm, 1,063 mm and 1,035 mm for 2000, 2001, and 2003, respectively), while there was an extreme event (∼10 cm rainfall in 1 day) in year 2000. The other 2 years were representative of “typical” scenarios. Thus, the modeling approach was tested over a range of forcing functions. Simulations were done only for a 5 month period (May to September) during the crop growing season, during which significant fraction of the contaminant loads (e.g., pesticides) are transported to the streams [see Kladivko et al., 2001]. [34] The coefficient of determination (R2) between observed and TELM‐simulated daily flows varied between 0.4 and 0.6, except for the year 2002 when TELM did not predict any hydrograph events. We did not evaluate the Nash‐Sutcliffe (N–S) efficiency as both the N–S efficiency and R2 are single‐valued indices that are sensitive to a number of factors, including sample size, outliers, magnitude bias, and time offset bias [McCuen et al., 2006]. Alternatively, model performance can also be evaluated using distributed metrics that cover a wide range of dependent variables [Jain and Sudheer, 2008]. There is controversy regarding the “right” metrics for ascertaining the predictive power of a model [e.g., Son and Sivapalan, 2007; Krause et al., 2005a, 2005b; McCuen et al., 2006]. [35] We used the following approaches to evaluate model performance at three time scales of predictions, generally following the strategy employed by Atkinson et al. [2003]: (1) compare differences (EOP) between observed and predicted discharge values, for performance assessment at the daily time scale (Figure 7); (2) compare flow duration curves (FDC) of observed and predicted discharge (Figure 8), which provides a measure of performance of discharge statistics; and (3) cumulative discharge over the crop growing season, both on an event‐by‐event basis and on an annual basis to examine model performance at longer time scales (Figure 9). [36] For the point by point comparison, on the average (except for the year 2002, and a single event in the year 2000), the TELM (with no calibration) matched the observed hydrograph data at least as well as the calibrated (14 calibrated parameters) SWAT predictions (see Figure 7) generated by Kumar and Merwade [2009]. The year 2002 was a “dry year” when TELM failed to predict any hydrograph events, while SWAT was calibrated to predict several of these events. The only large event that TELM severely overpredicted was an extreme rainfall event (10 cm rainfall in a day, at ∼250 days) in the year 2000. [37] An FDC analysis is useful to help in evaluating the predictive ability of the model in different flow regimes, rather than metrics like the Nash‐Sutcliffe efficiency that are single valued and may provide limited insight. Further, the choice of the appropriate metric should be based on the purpose for which the model was developed. In the engineered Midwestern watersheds of our study, large contaminant loads are generally generated during high‐flow events [see Kladivko et al., 2001], and since the purpose of our model is to capture such high‐flow and high‐load
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Figure 7. Differences (EOP) between observed and predicted (TELM and SWAT) hydrographs.
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Figure 8. Comparison of measured and predicted (SWAT and TELM) flow duration curves for 2000–2003.
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(Figure 9c). The zeroth moments (M0) plotted in the Figures 9a and 9b are the integrals of the hydrographs (representing the total volume of runoff during the event) generated for each event, while Figure 9c represents the total volume of runoff during the season. On an event‐by‐event basis, performances of TELM and SWAT were comparable, except for some low‐flow events that TELM failed to capture. As expected, predictions were more robust on a cumulative basis, with deviations occurring in the “wet” (year 2003) and “dry” (year 2002) years.
Figure 9. Comparison of measured and predicted (SWAT and TELM) zeroth moments (M0) for multiple hydrograph events during 2000–2003 under (a) “uniform deficit” assumption, (b) “riparian zone” assumption, and (c) cumulative seasonal discharge. events, an FDC analysis seemed more appropriate for model performance rather than single‐valued indices. For the same reason, the FDC analysis was done only for flows greater than 0.1 mm. The FDC analysis indicated that TELM underpredicted low‐flow events (less than 0.5 to 1 mm), but performed at least as well as SWAT for high‐flow events (Figure 8), and captured certain high‐flow events more effectively than SWAT (Figure 6). Since our overall goal was to predict high‐flow events essential for estimating contaminant load events, the performance of TELM was considered to be satisfactory for this purpose. [38] The cumulative discharge over the crop growing season was evaluated both on a event‐by‐event basis (Figures 9a and 9b) and was based on seasonal totals
5.5. Model Limitations and Suggested Refinements [39] Following the “top‐down” approach, first proposed by Klemeš [1983] and subsequently applied to Australian catchments by Atkinson et al. [2002, 2003] and Farmer et al. [2003], we start with the simplest model possible, and systematically increase model complexity to overcome deficiencies in model prediction. The above results (section 5.4) suggest that the simplified representation in TELM failed to capture the extreme events (especially the low‐flow events), and this was illustrated by the use of both FDCs and point‐by‐ point hydrograph comparisons. This is consistent with the observation of Atkinson et al. [2003] of decreasing predictive ability of simple models with increasing catchment dryness index. Instead of adopting the familiar route of calibrating the model to improve predictions, we attempted first to identify the possible reasons contributing to model deviations. [40] 1. We assumed that entire CCW can be represented as a single store (linear reactor) with spatially uniform soil water storage deficit. However, SoLIM modeling had shown that the riparian zones, representing ∼20% of the watershed area, would have larger soil water storage deficit (see section 5.1), and are likely to have less frequent soil water storage deficits resulting from replenishment by run‐on from the other hillslope areas. This being the case, more of the smaller rainfall events could generate hydrograph responses even when the rainfall depth is, as assumed, smaller than the mean soil water storage deficit over the entire domain. The effect of this modification is explored in this section. [41] 2. In formulating TELM, we did not include depression storage (possibly predictable from the topographic wetness index or other similar indicators) and evaporation/drainage from such surface stores. These processes would become important especially for infrequent, very large rainfall events, like the one event occurring in 2000. Since this was a single event, and on the average TELM captured the high‐flow events reasonably well, we decided not to explore these effects in this paper. [42] 3. TELM simulations were sensitive to the crop planting date (corn or soybean) used in the crop model to convert PET to AET. The agricultural databases [NASS, 2004] for northern Indiana indicated that planting dates varied over a window of one month. In our modeling exercises, we used the median value as the single planting date for the entire watershed. Incorporation of the distribution of planting dates across the watershed could improve the performance of TELM, but such planting patterns are likely to be different each year, and data gathering would be difficult. [43] In order to simulate the effect of the first item on the above list, we assumed the riparian zones to be always at field capacity soil water content, i.e., rainfall over that domain contributes directly to runoff and recharge. Thus,
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by referring to the analyses done by Kumar and Merwade [2009] for the St. Joseph Watershed (2,800 km2) of which the Cedar Creek is a subwatershed. They observed that calibrated parameters at the Cedar Creek scale were adequate to describe responses at the larger scale of the St. Joseph watershed (2,800 km2), again indicating the possibility of functional homogeneity at the larger scale. [45] In order to extend this analysis further we need to understand the unique features of the Cedar Creek watershed that enabled such approximations. Our longer‐term goal is to define a class of watersheds that share common functional attributes, such that they are amenable to the simplifications adopted by TELM. Such watershed classification would be based on patterns noted in watershed monitoring data, and would be based on the following attributes: (1) complexity, (2) functional homogeneity, (3) thresholds, and (4) dominance. Guided by these attributes, we offer some generalizations and generate hypotheses regarding the limits of applicability of this modeling approach, which need to be tested in later work.
Figure 10. Comparison of measured hydrograph with predictions using SWAT and TELM with riparian zone assumption for years 2002 and 2003. 20% of the rainfall contributed directly to each runoff event. With this assumption, TELM generated the smaller hydrographs, even those during the dry year 2000, but resulted in overprediction of the amount of runoff for the bigger events (Figure 10). The FDC (Figure 8) and the zeroth moment (Figures 9a, 9b, and 9c) analysis also indicate that TELM modification resulted in capturing the low‐flow events much better (years 2002 and 2003), but overpredicted high‐flow events (years 2000 and 2001). These results suggest that better description of the interaction between the “hillslopes” and the “riparian” areas would need to be represented in TELM to predict the low‐flow events. Further improvements of TELM would involve modifications based on the items listed above.
6.1. Complex Versus Engineered Systems [46] Natural ecosystems behave as complex systems, defined by their highly interconnected subsystems and processes, nonequilibrium dynamics, nonlinear filtering, adaptive cycles, self organization, emergent processes, pervasive uncertainties in prediction of system responses, and “surprises” with unexpected and unintended consequences from management efforts [e.g., Holling, 1973; Liu et al., 2007; Gordon et al., 2008]. Responses of complex systems are difficult to predict because of dynamic, adaptive characteristics of its components (that are not always well understood), creating emergent patterns that cannot be explained entirely by the sum of its parts. Landscape modifications (i.e., extensive tile drainage or intensive soil/crop management) of cropped watersheds in the Midwestern United States have created a fast‐flow hydrologic system that bypasses the complex subsurface and leads to a more predictable watershed hydrologic response typical of an engineered system rather than a complex system. On the basis of an analysis of entropy decrease in flows monitored over a 131 year period, Li and Zhang [2008] suggested that complexity of the Mississippi River system had declined since the 1940s. Such decrease in entropy (or loss of complexity) is the result, in part, because of significant changes in land uses across the basin, and also the changes (loss of wetlands, construction of numerous dams, channelization of rivers, etc) made to the river network itself [Pinter et al., 2006]. Thus, the TELM approach may be useful for hydrologic predictions in tile‐drained, intensively managed, mesoscale watersheds in the Midwestern United States. Similar engineered watersheds occur in Europe (e.g., Sweden and Germany), and parsimonious modeling approaches may be useful for hydrologic predictions.
6. Criteria for Using Simplified Models [44] The foregoing analysis indicates that a simple, threshold‐based model is able to predict hydrographs at the outlet of a 700 km2, agriculture‐dominated, extensively tile drained, and intensively managed (i.e., engineered) watershed in the Midwestern United States. What is the spatial scale and geographic domain of validity of such a simple model? The spatial scale question can be partially addressed
6.2. Structural Heterogeneity Versus Functional Homogeneity [47] Here, structural heterogeneity refers to the spatial patterns of specific landscape attributes (e.g., soils and land use), while functional homogeneity refers to the similarity of hydrologic responses that arise despite the structural differences [Sivapalan, 2003; McDonnell et al., 2007]. We
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recognize that landscapes are structurally heterogeneous at all scales of observation; however, a definition of functional heterogeneity needs to consider the specific response (e.g., hydrographs and chemographs), and the spatial scale of observation. Most hydrologic models use traditional soil maps (e.g., 1:250,000 scale STATSGO databases and 1:24,000 scale SSURGO database produced by the USDA NRCS) as their source for spatial data. These detailed maps (e.g., SSURGO soil maps) exhibit a high degree of spatial heterogeneity, yet the key attributes affecting hydrologic response (e.g., AWS and saturated hydraulic conductivity Ks) may be similar, resulting in similar hydrologic response despite structural variations at the soil taxonomic level. Thus, (spatial) structural heterogeneity does not necessarily translate to functional heterogeneity. For CCW, SoLIM analysis showed that despite the presence of 80 soil series and 14,000 soil mapping units, >80% of CCW could be assigned a single AWS value. Such functional homogeneity is expected in other Midwestern U.S. watersheds that share similar geologic and management history; SoLIM and TELM modeling will be required to test this assertion. We also identified a representative scale of 10–20 km2 at which hydrologic responses were functionally homogeneous; whether this scale is unique to CCW or if it can be applied to other watersheds in the region also needs to be examined. 6.3. Thresholds for Hydrologic Response [48] Antecedent conditions of the landscape play a major role in the hydrologic response for a given rainfall event; that is, how the rainfall is to be partitioned, how the soil water storage in various compartments is changed, and how much “excess” water is shed from the landscape. The notion of a crossing a threshold before initiating runoff is not new. A recent review [Zehe and Sivapalan, 2009] provides an excellent summary of various examples of threshold phenomenon in hydrologic systems. Here, the concept of threshold‐controlled hydrologic response simply means that there will be no “runoff” event as long as the soil water content is below a threshold, which defined as the product of the mean field capacity water content and the depth to the confining unit. Thus, for any given rainfall event, the “excess” precipitation is estimated as that above the set threshold soil water storage. 6.4. Dominant and Persistent Flow Paths [49] Water is transported off the landscape into the stream network through three pathways: (1) overland flow, (2) fast subsurface flow, and (3) groundwater flow. The response time scales of these pathways are generally very different, with overland flow occurring during certain storm events, fast subsurface flow continuing for a few days after the storm, and groundwater flow contributing to base flow with time scales in the order of months to years. Observations at various spatial scales in the Midwestern U.S. watersheds suggest that hydrologic responses are flashy (e.g., small Richards path length [Gustafson et al., 2004; Kumar et al., 2007; Kumar and Merwade, 2009]), and characteristic of a single, dominant and rapid flow pathway by which the “excess” water is delivered to the ditch/stream networks. Highly developed and interconnected macropore network within the vadose zone, dense combined with dense, irreg-
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ular network of tile drains and ditches, and highly evolved networks of streams all contribute to the observed rapid bypass flow response at all spatial scales in these Midwestern U.S. watersheds [e.g., Algoazany, 2006; Kalita et al., 2007]. Local overland flow generated may reenter the tile system via run‐on and transport through the extensive macropore network that develops around an installed tile [Akay and Fox, 2007]. Schilling and Helmers [2008] compared paired watersheds (with and without tile drains) in Iowa and concluded that the recession curves of tile‐ drained systems could be described by a single exponential function, while recession curves of the other watersheds were more complex. Both overland and tile flow pathway have “fast” response time that are stronger functions of the storm characteristics, rather than local soil properties. [50] Analysis of measured hydrographs in CCW indicated that recession curves measured for multiple events can be described by a single exponential function, representing a highly skewed travel time distribution; thus, a single model parameter (mean, tr) suffices to describe the hydrograph recession. Further, the mean travel time (tr), represented by the first temporal moment of the hydrograph, is dominantly determined by the first temporal moment of the hyetograph. Thus, the transport pathways (tile ditch drainage) persist from event to event. This too is a manifestation of the response of a highly engineered hydrologic system. Presence of a single, dominant, and persistent flow pathway enabled the simplifications in TELM, and the hypothesis is that this approach would be valid in similar tile‐drained watersheds.
7. Concluding Remarks [51] We have adopted here a “top‐down” hydrologic modeling approach [e.g., Sivapalan, 2005; Savenije, 2008] in developing TELM. Structural and functional homogeneities of hillslopes observed in spatial data or patterns in outputs of more complex hydrologic models were used to develop simpler models for hydrograph predictions. TELM was tested using monitoring data from a mesoscale watershed in northern Indiana to examine its shortcomings and evaluate “necessary” improvements. The validity of the approach needs to be further established by comparing with hydrograph data from other watersheds within the geographic region. [52] Hydrograph prediction without calibration was possible because of the unique attributes of the intensely managed, engineered landscapes we examined here. The dominance and persistence of short‐circuiting flow paths (tile flow and overland flow) enabled us to use a single exponential travel time distribution for predicting of hydrographs. This suggests that distinction between surface and subsurface flow paths was not essential, at least at the spatial scales examined in this study. SoLIM modeling indicated 10–20 km2 as the representative scale at which subwatersheds are homogeneous in terms of AWS; however, whether this is valid for other watersheds in the region of interest here needs to be established. The spatial homogeneity assumption made may not be apparent at smaller spatial scales as the local‐scale variations dominate. Failure to predict hydrographs for “extreme” events arises from inaccurate estimation of soil water storage deficit (both the
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capacity (fc) and wilting point (wp), and the average soil water deficit (Dr) over the rooting depth: Ks ¼
TAW Dr ; TAW RAW
TAW ¼ fc wp Zr ;
ðA3Þ
RAW ¼ p TAW ;
ðA4Þ
Dr ¼ D * Zr =depth to limiting layer ð¼ 76 cmÞ;
Figure A1. Basal crop coefficient function for 2003. mean value and spatial patterns), and thus the “excess water” delivered to the streams. Future work will involve modification of the TELM approach to incorporate additional processes/pathways, when necessary to account for these effects.
Appendix A: Modeling PET and AET [53] The actual evapotranspiration (AET) is estimated from the potential evapotranspiration (PET) using the following equation: ET ¼ ðKcb Ks þ Ke ÞPET ;
ðA1Þ
where Kcb is basal crop coefficient, Ks is soil water stress factor, and Ke is evaporation factor from bare soil. The PET is estimated using the Priestley‐Taylor equation. Estimation of the remaining terms in equation (A1) is described in sections A1–A3. The land comprises 72% agricultural (50– 50 corn‐soybean split), 10% residential, 14% forests, and 4% open water. The ET of residential area is assumed to be equal to zero, while that of open water is assumed to be equal to PET. Forests are assumed to transpire at the same rate as corn.
A1. Estimation of Basal Crop Coefficient [54] The basal crop coefficient is a function dependent on the crop growth stage. It increases from 0.15 during the initial growth stage to 1.15 during silking (for corn) or podding (for soybean) and decreases to 0.6 post maturity. The planting dates, silking and maturity times vary from year to year as a function of climatic variables. We use the NASS database to estimate the approximate dates relevant to our study area. An example growth curve for corn and soybean for the year 2003 is given in Figure A1.
ðA2Þ
ðA5Þ
where D is the total deficit over the limiting layer thickness. Here, TAW is defined as the total available water, RAW as the readily available water, and p is the fraction of TAW that can be depleted from the root zone before moisture stress occurs. This is assumed to be equal to 0.55 for corn and 0.5 for soybean [Allen et al., 2005]. The water contents at field capacity and wilting points were assumed to be equal to 0.36 and 0.2, respectively, on the basis of SOLIM modeling. Since the rooting depth is a function of the growth stage of the plant, the depth function Zr is assumed to mimic the crop coefficient Kcb, with a minimum depth of 10 cm for corn and 5 cm for soybean, and a maximum depth of 76 cm for corn (defined by the depth of the limiting layer as estimated from SOLIM) and 50 cm for soybean. The difference between the root function and the crop coefficient is that unlike Kcb that declines post maturity, the root growth function reaches the maximum value and remains constant till harvest.
A3. Estimation of Evaporation Factor [56] The bare soil evaporation factor is defined as a function of the fractional vegetation coverage fc, the soil evaporation reduction coefficient due to water deficit in the top few mm Kr and the maximum value of Kc following rain Kcmax(=1.2): Ke ¼ MINðKr ðKc max Kcb Þ; ð1 fc ÞKc max Þ:
ðA6Þ
The evaporation reduction coefficient Kr is a function of the total evaporable water, TEW, the readily evaporable water REW, depth of soil surface subject to evaporation Ze, and the cumulative depth of evaporation over Ze, De. For REW < De < TEW, Kr ¼
TEW De ; TEW REW
ðA7Þ
for the energy limiting stage Kr ¼ 1 f or De < REW ;
ðA8Þ
and with no evaporation component, Kr ¼ 0 f or De > TEW ;
ðA9Þ
TEW ¼ fc 0:5 * wp Ze ;
ðA10Þ
where
A2. Estimation of Soil Water Stress Factor [55] The soil water stress factor, Ks, is a function of the rooting depth, Zr, average water contents of the soil at field
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where TEW = total evaporable water, Ze = 100 mm, and REW = readily evaporable water = 8 mm: fc ¼
Kcb Kc min Kc max Kc min
1þ0:5h ðA11Þ
where Kcmax = 1.15, Kcmin = 0.15, and h = mean plant height in m = 1.5 m for corn and 0.5 m for soybean. De = D * Ze/depth to limiting layer (=760 mm), where D is the total deficit over the limiting layer thickness.
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