Streamflow Predictions in a Small Urban–Rural Watershed

atmosphere

Article Streamflow Predictions in a Small Urban–Rural Watershed: The Effects of Radar Rainfall Resolution and Urban Rainfall–Runoff Dynamics

Lauren E. Grimley 1,* , Felipe Quintero 2 and Witold F. Krajewski 2

1 Department of Geological Sciences, University of North Carolina at Chapel Hill, Chapel Hill, NC 27514, USA 2 IIHR—Hydroscience and Engineering, University of Iowa, Iowa City, IA 52242, USA; [email protected] (F.Q.); [email protected] (W.F.K.) * Correspondence: [email protected]

Received: 27 May 2020; Accepted: 21 July 2020; Published: 23 July 2020

Abstract: The authors predicted streamflow in an urban–rural watershed using a nested regional–local modeling approach for the community of Manchester, Iowa, which is downstream of a largely rural watershed. The nested model coupled the hillslope-link model (HLM), used to simulate the upstream rural basins, and XPSWMM, which was used to simulate the more complex rainfall–runoff dynamics and surface and subsurface drainage in the urban areas, making it capable of producing flood maps at the street level. By integrating these models built for different purposes, we enabled fast and accurate simulation of hydrological processes in the rural basins while also modeling the flows in an urban environment. Using the model, we investigated how the spatial and temporal resolution of radar rainfall inputs can affect the modeled streamflow. We used a combination of three radar rainfall products to capture the uncertainty of rainfall estimation in the model results. Our nested model was able to simulate the hydrographs and timing and duration above the threshold known to result in nuisance flooding in Manchester. The spatiotemporal resolution the radar rainfall input to the model impacted the streamflow outputs of the regional, local, and nested models differently depending on the storm event.

Keywords: hydrologic modeling; radar-rainfall; streamﬂow predictions; urban hydrology

1. Introduction In Iowa, the dominant contributor to streamflow is the runoff generated from regional watersheds, which are characterized by more natural terrain, but the urban areas primarily experience the negative effects of fluvial and pluvial flooding [1,2]. Hydrological and hydraulic models are commonly used as tools to understand past, present, and future flood risk profiles at various scales. [1,3–5]. Integrating regional- and local-scale hydrological models is difficult because of the varying heterogenous spatial and temporal scales and dimensionality within the watershed [6–8]. These kinds of challenges are not unique to Iowa. In this study, the authors simulated historical peak streamflow and urban flood extents using a nested regional–local model with three radar rainfall products as inputs. In the context of this paper, “nested” refers to one-way coupling of a coarse resolution model to a model with a finer resolution. We use “local” to refer to an urban area of interest that is within a “regional” watershed where rural landscapes and natural terrain are dominant. We used a nested model to study flooding in a small town, Manchester, IA in the regional Maquoketa River basin (Figure1). This area was suitable for a case study because we were able to use radar rainfall products, streamflow measurements, rain gauge data, and the statewide forecasting model managed by the Iowa Flood Center (IFC). Our objective

Atmosphere 2020, 11, 774; doi:10.3390/atmos11080774 www.mdpi.com/journal/atmosphere Atmosphere 2020,, 11,, x 774 FOR PEER REVIEW 2 2of of 22 21 was to gain an improved understanding of the impacts of the spatial and temporal resolution of radar was to gain an improved understanding of the impacts of the spatial and temporal resolution of radar rainfall at the regional and local scales for extreme rainfall events, and to identify the benefits of using rainfall at the regional and local scales for extreme rainfall events, and to identify the benefits of using a nested modeling approach for streamflow prediction and local flood modeling. a nested modeling approach for streamflow prediction and local flood modeling.

(a) (b)

FigureFigure 1. 1. (a()a )The The extent extent of ofthe the regional regional model model was was 725 725km2km of rural2 of rural land landin the in upper the upper Maquoketa Maquoketa River watershed,River watershed, located located in northeast in northeast Iowa. Iowa. The Themajo majorr tributaries tributaries are areCoffins Coﬃ nsCreek Creek and and Honey Honey Creek, Creek, which drain into thethe MaquoketaMaquoketa RiverRiver at at the the north north end end of of the the city city limits limits of of Manchester. Manchester.(b )(b The) The extent extentof ofthe the local local model model included included Manchester Manchester city limits,city limit whichs, which are divided are divided by the by Maquoketa the Maquoketa River. TheRiver. Eastern The EasternTributary Tributary drains into drains the Maquoketainto the Maquoketa River near River the United near the State United Geological State Ge Surveyological USGS Survey streamﬂow USGS streamflowgauge and NWSgauge Coop and NWS rain gauge Coop locatedrain gauge at the located model at outlet. the model outlet.

AA hydrological hydrological and and hydraulic hydraulic model model developed at the the regional regional scale is is typically typically used used to to generate generate streamflowstreamflow estimates estimates along along a a major major stream stream network, network, and and the the dominant dominant rainfall–runoff rainfall–runoff andand routing processes can can be be described described at at a coarser a coarser scale scale (i.e., (i.e., datasets datasets at a at resolution a resolution of 50 of m 50 or mgreater) or greater) and with and simplificationswith simplifications (such (such as channel as channel geometry) geometry) [1,9–11]. [1,9– Local11]. Local hydrodynamic hydrodynamic models models are aredeveloped developed on anon “as an “asneeded” needed” basis basis for a for specific a specific purpose, purpose, with witha desired a desired set of set output of output variables variables and accuracy and accuracy such assuch floodplain as floodplain mapping mapping or evaluating or evaluating changes changes in the water in the level water from level a proposed from a proposed engineering engineering project [12,13].project [In12 these,13]. In cases, these a cases,fine-resolution a fine-resolution model is model often is necessary often necessary for simulating for simulating pluvial pluvial flooding flooding in an urbanin an urban landscape, landscape, because because the dominant the dominant hydrologic hydrologic processes processes vary vary spatially spatially and and temporally temporally due due to to increasinglyincreasingly complexcomplex drainagedrainage networks networks with with subsurface subsurface (e.g., (e.g., storm storm sewers) sewers) and surface and surface (e.g., streets, (e.g., streets,buildings) buildings) routing. routing. To get an To accurate get an depiction accurateof depiction water movement of water through movement urban through morphologies, urban morphologies,hydrological models hydrological should models account should for these accoun flowt interchanges for these flow and interchanges the resulting and impact the resulting on water impactsurface on elevations. water surface [14–16 elevations.]. By using [14–16]. a nested By modeling using a nested approach, modeling we were approach, able to one-way we were couple able to a one-waycoarse-resolution couple a model, coarse-resolution suitable for model, characterizing suitable regional for characterizing rainfall–runo regionalff, to a fine-resolution rainfall–runoff, model to a fine-resolutionrequired for local model flood required information for local [17, 18flood]. information [17,18]. AnAn important important source source of of uncertainty uncertainty in in hydrological hydrological models models is isthe the spatiotemporal spatiotemporal resolution resolution of theof therainfall rainfall input input (see Villarini (see Villarini and Krajewski and Krajewski [19] for [a19 review] for aof review radar rainfall of radar uncertainty rainfall uncertaintymodeling), becausemodeling), it heavily because influences it heavily influencesthe rainfall–runof the rainfall–runof processesff processes simulated simulated in the model in the [20–22]. model [ 20Many–22]. researchersMany researchers seek to accurately seek to accurately capture the capture non-linear, the non-linear,spatiotemporal spatiotemporal patterns of rainfall patterns and of how rainfall this variabilityand how this will variability change the will accura changecy of the flood accuracy models of and flood their models predictions and their [20,22–28]. predictions Furthermore, [20,22–28]. radarFurthermore, and satellite radar rainfall and satellite datasets rainfall can be datasetsresolved canand beused resolved as input and to usedlocal scale as input or urban to local models scale [20,22,25,27,29].or urban models By [20 using,22,25 ,27multiple,29]. By rainfall using multipleinputs, we rainfall produced inputs, an we ensemble produced of an hydrological ensemble of predictions that implicitly accounted for the uncertainty in the equations and parameters that were

Atmosphere 2020, 11, 774 3 of 21 Atmosphere 2020, 11, x FOR PEER REVIEW 3 of 22 hydrologicalused to describe predictions the physical that implicitly system accounted[30]. In this for paper, the uncertainty the authors in thedescribe equations the andstudy parameters area and thathistorical were usedflood to events, describe the the data physical and systemmodeling [30 ].framework, In this paper, and the the authors model’s describe performance the study when area andpredicting historical streamflow flood events, and theurban data flood and extents. modeling La framework,stly, we discuss and thesome model’s general performance observations when and predictingconclusions streamflow drawn from and this urban study flood that will extents. inform Lastly, modelers we discuss on the somebenefits general and limitations observations of using and conclusionsa nested regional–local drawn from model this study and thatmultiple will inform radar rainfall modelers inputs on the for benefits predicting and streamflow. limitations of using a nested regional–local model and multiple radar rainfall inputs for predicting streamflow. 2. Study Area 2. Study Area The city of Manchester covers an area of approximately 12.2 km2 and is located along the MaquoketaThe city River of Manchester in the northeastern covers an arearegion of approximatelyof Iowa (Figure 12.2 1). kmThe2 andwatershed is located upstream along the of MaquoketaManchester River is 712 in km the2 northeasternof agricultural region land, of and Iowa the (Figure eastern1). Thebank watershed of the Maquoketa upstream River of Manchester draining isthrough 712 km Manchester2 of agricultural is approximately land, and 15 the m eastern lower than bank the of west the bank, Maquoketa which is River adjacent draining to downtown. through ManchesterThe city experienced is approximately costly flooding 15 m lower nine than times the between west bank, 2002 which and is2017 adjacent when tothe downtown. river exceeded The citythe experiencedNational Weather costly Service flooding (NWS) nine timesModerate between Flood 2002 Stage and of 2017 5.2 m. when In addition the river to exceeded riverine theflooding, National the Weathereastern Serviceneighborhoods (NWS) Moderateexperience Flood nuisance Stage offlood 5.2 m.ing In after addition an toextreme riverine st flooding,orm occurs the easternlocally, neighborhoodsoverwhelming experiencethe drainage nuisance network. flooding The risk after incr aneases extreme when storm local occurs flooding locally, occurs overwhelming coincident with the drainagea high tailwater network. level The in risk the increases Maquoketa when River. local flooding occurs coincident with a high tailwater level in theOne Maquoketa of the more River. memorable fluvial flooding events occurred after a regional extreme storm passedOne over of the northeast more memorable Iowa in fluvialJuly 2010, flooding resultin eventsg in occurred the highest after recorded a regional stage extreme of storm7.5 m passedon the overMaquoketa northeast River Iowa at inManchester July 2010, resulting(Figure 2a). in theThe highest July 2010 recorded flood stagehad an of annual 7.5 m on flood the Maquoketaprobability Riverrange atofManchester 0.2–1%, which (Figure is a 2recurrencea). The July interval 2010 flood of 50 had0 to an100 annual years. floodThe flood probability waters rangeremained of 0.2–1%, above whichthe NWS is a “major recurrence flood” interval stage of for 500 over to 100 37 years.h, result Theing flood in over waters $850,000 remained of recorded above the project NWS costs “major in flood”Delaware stage County for over [31]. 37 h,In resultingSeptember in over2016, $850,000 the local of area recorded experienced project high costs rainfall in Delaware intensities County over [31 ].a Inshort September period 2016,of time the in local the arealower experienced portion of high the rainfallbasin (Figure intensities 2b). over Local a shortofficials period recall of timethis inevent the lowerbecause portion of the of quick the basin hydrological (Figure2 b).response Local o offfi thecials watershed recall this compared event because to previous of the quick historical hydrological floods. response of the watershed compared to previous historical floods.

(a)

Figure 2. Cont.

Atmosphere 2020, 11, x FOR PEER REVIEW 4 of 22 Atmosphere 2020, 11, 774 4 of 21

(b)

Figure 2.2. ((aa)) TheThe observedobserved discharge discharge in in units units of of m 3ms3⋅1s−(black1 (black dots) dots) at at the the USGS USGS streamflow streamflow gauge gauge on theon · − Maquoketathe Maquoketa River River at Manchester at Manchester during during the July the 2010 July flood, 2010 withflood, hourly with Stagehourly IV Stage radar IV rainfall radar intensity rainfall timeintensity series time in mm seriesh 1 (blackin mm vertical⋅h−1 (black bars) vertical and the threebars) NWSand floodthe three stage NWS categories flood (horizontal stage categories colored · − lines)(horizontal (b) the colored September lines) 2016 (b) the flood. September 2016 flood.

3. Data and Methods We developed a a simulation simulation framework framework to to invest investigateigate how how the the scale scale of hydrological of hydrological models models and andthe resolution the resolution of their of theirinputs, inputs, specifically specifically rainfa rainfall,ll, can improve can improve streamflow streamflow predictions predictions with a withnested a nestedmodeling modeling approach. approach. We modeled We modeled the local the area local in area XPSWMM, in XPSWMM, which which is a one-dimensional is a one-dimensional and two- and two-dimensionaldimensional (1D/2D) (1D/ 2D)spatially spatially distributed distributed model model used used for for simulating simulating hydrological hydrological and and hydraulic processesprocesses [[32].32]. In the regional area, wewe usedused thethe hillslope-linkhillslope-link modelmodel (HLM),(HLM), which is aa distributeddistributed model developeddeveloped at theat IFCthe toIFC be robust,to be requiringrobust, requir significantlying significantly less computer less eff ortcomputer than hydrodynamic effort than modelshydrodynamic because models it has lower because demands it has lower on the demands representation on the representation and accuracy ofand the accuracy flow dynamics of the flow [1]. Thedynamics two physics-based [1]. The two models physics-based used in this models study used differ in theirthis approachstudy differ to hydrological in their approach modeling, to but,hydrological by using modeling, a nested modeling but, by using approach, a nested we modeling were able approach, to investigate we were how able coupling to investigate these models how builtcoupling with these different models scales built (i.e., with regional different and local) scales could (i.e., add regional value toand our local) understanding could add ofvalue streamflow to our predictionsunderstanding in watersheds of streamflow with predictions urban and ruralin watershe landscapes.ds with Additional urban and information rural landscapes. on the modelsAdditional and theinformation data used on is the provided models in and the followingthe data used sections. is prov Forided both in thethe localfollowing and the sect regionalions. For model, both the we usedlocal aand calibration-free the regional approach,model, we i.e., used a common a calibration-free configuration approach, of parameters i.e., a determined common configuration a priori applied of forparameters all the model determined inputs, a and priori no applied adjustments for all were the model made inputs, for specific and basinsno adjustments [1]. We considered were made that for calibratingspecific basins would [1]. obscure We considered our understanding that calib ofrating the hydrological would obscure system, our and understanding that model calibration of the compensateshydrological forsystem, the errors and that in the model model calibration inputs and compensates modeling processes.for the errors in the model inputs and modeling processes. 3.1. Regional Model 3.1. RegionalThe regional Model area was modeled using the HLM, a distributed model that decomposes the landscape into hillslopesThe regional and channels.area was Themodeled HLM solvesusing thethe mass HLM, conservation a distributed equations model within that thedecomposes four hillslope the layerslandscape and into between hillslopes the channels and cha andnnels. hillslopes The HLM using solves ordinary the mass diff conservationerential equations. equations The within portion the of rainfallfour hillslope that becomes layers and runo betweenff is determined the channels by the and near-surface hillslopes using soil saturation ordinary anddifferential the hydraulic equations. soil properties.The portion The of rainfall complex that drainage becomes and runoff landcover is determined patterns inby urban the near-surface areas are not soil necessarily saturation captured and the byhydraulic the HLM’s soil simplifiedproperties. infiltrationThe complex process drainage at the and land landcover surface. patterns To route in flow urban through areas the are river not network,necessarily HLM captured uses a by power the HLM’s law wherein simplified the water infiltra velocitytion process is related at the to theland discharge surface. andTo route upstream flow drainagethrough the area. river HLM network, does consider HLM uses the variability a power law of flow wherein across the the water stream velocity network, is butrelated it does to notthe accountdischarge for and reservoirs upstream or includedrainage local area. hydraulic HLM does considerations. consider the Itvariability considers of variability flow across of flowthe stream in the network, but it does not account for reservoirs or include local hydraulic considerations. It considers

Atmosphere 2020, 11, 774 5 of 21 different channels of the network, but it does not include local hydraulic considerations or backwater effects from reservoirs. Additional information on the HLM can be found in References [5] and [33]. The performance of the HLM has been extensively evaluated using seven years of radar rainfall data. Model simulations of streamflow have been compared to observed values at approximately 140 USGS streamflow gauges in Iowa, showing skillful performance, especially for eastern Iowa basins [4].

3.2. Local Model The urban area was modeled in XPSWMM, where we used area-average radar rainfall estimates as inputs. We derived land use, soil type, and other hydrological parameters from national datasets, but did not use calibration to correct the local model’s behavior. With an unclear understanding of the soil and landcover in the area, there was a risk of over-calibrating the model to fit the solution. For this study, we did not calibrate because we considered the average (or typical) values to be suitable for accurately modeling the runoff and flow paths in the local model. Soil data were retrieved from the National Soil Survey Geographic (SSURGO) database and we determined that the prominent soil types in the local model consisted of loam and sand [34]. We modeled losses due to infiltration using the Green–Ampt equation [32]. The soil types and parameters, specifically saturated hydraulic conductivities, covered a wide range of values because soils are redistributed and compacted at varying levels throughout the watershed [35]. The infiltration parameters are often difficult to estimate without in situ measurements, so the average values used in the local model were derived from the typical values listed in References [32] and [36]. We derived the land surface properties from geospatial datasets, including impervious cover and land use from high-resolution landcover for Delaware County in 2009 [37]. The Manning’s n values (roughness) vary significantly in space and are difficult to estimate, particularly in floodplains [38], so we used the typical range of roughness values for the different land types as specified by the Natural Resources Conservation Service [39]. Representing buildings in a hydrodynamic model can be done by manipulating the terrain to include them in the topography or by imposing an additional head loss to the model grid [40–44]. We modeled the buildings as a landcover type with varying vertical roughness to account for storage. We manually digitized the layout of the subsurface and surface drainage network and the corresponding hydraulic parameters (i.e., geometry, elevation data, and conveyance information) using engineering drawings, surveys, and local knowledge. We incorporated multiple sets of river cross-sectional data and routing information directly into XPSWMM from models built using the Hydrologic Engineering Center River Analysis System (HEC-RAS) by the U.S. Army Corps of Engineers (USACE) and the Iowa Department of Natural Resources (IDNR). The final XPSWMM model had 862 nodes that represented common features in the storm-sewer network, including outfalls, culverts, intakes, and manholes. The nodes were connected with over 20.1 km of links that represented the storm sewers in the network (see Figure3b). We modeled the storm sewers as pipe flow, the natural channels as open channel flow, and bridge and inline structures were modeled in 1D. The 1D drainage network was connected to the 2D domain at nodes (intakes and outfalls) and polyline interfaces (the river or channel banks). Hydrodynamic models are commonly used for urban flood modeling [45–47], where the minimum grid resolution is determined by the width of the streets or the size of the buildings [48,49]. We used a 1.5 m digital terrain model (DTM) derived from 1 m LiDAR topography from the 2007–2010 Iowa LiDAR Project [37] to extract terrain information that was used by grids applied in XPSWMM. The 2D domain was 7.5 km2 and we used a 4.6 and 9.1 m (15 and 30 ft) grid-cell size to balance accuracy and computational efficiency. Atmosphere 2020, 11, 774 6 of 21 Atmosphere 2020, 11, x FOR PEER REVIEW 6 of 22

(a)

(b)

Figure 3. ((a) The The flow flow diagram diagram of of the the nested nested regional–local regional–local model approach used to test the sensitivity of thethe streamflowstreamflow predictions predictions to to various various radar radar rainfall rainfall products products and and urban urban hydrodynamics. hydrodynamics. (b) The (b) local The XPSWMMlocal XPSWMM model (XP—C2)model (XP—C2) included included the green the rainfall–runo green rainfall–runoffff subcatchments, subcatchments, and their connections and their toconnections the 2D domain to the (gray)2D domain are noted (gray) by are green noted triangles. by green The triangles. blue triangles The blue are triangles the locations are the where locations the regionalwhere the HLM regional streamflow HLM isstreamflow input into theis input XPSWMM into the model. XPSWMM The nested model. model Theand nested regional model model and outputsregional weremodel compared outputs towere observations compared at to the observ USGSations streamflow at the gaugeUSGS (yellowstreamflow squares). gauge The (yellow blue polylinessquares). (riverThe blue network) polylines were (river modeled network) by the HLMwere whilemodeled theblack by the polylines HLM while (river andthe black urban polylines drainage network)(river and are urban modeled drainage in XPSWMM. network) are modeled in XPSWMM.

3.3. Simulation Framework We setset upup thethe simulationsimulation frameworkframework toto comparecompare thethe impactsimpacts ofof radarradar rainfallrainfall spatiotemporalspatiotemporal resolutionresolution onon streamﬂowstreamflow predictionspredictions generatedgenerated byby thethe regionalregional modelmodel andand thethe nestednested regional–localregional–local model. A schematic of the framework is shown in Figure 3 3a.a. WeWe appliedapplied threethree radarradar rainfallrainfall productsproducts toto bothboth thethe regionalregional andand locallocal models,models, includingincluding • Multi-radarMulti-radar multi-sensor multi-sensor (MRMS) (MRMS) rainfall rainfall estima estimatestes which which were were rain-gauge-bias rain-gauge-bias corrected, corrected, with • withtemporal temporal resolution resolution of 1 h of and 1 h a and spatial a spatial resolution resolution of 1 km of 1 [50]; km [50]; • Stage IV rainfall estimates which were rain-gauge-bias corrected with a temporal resolution of 1 h and a spatial resolution of 4 km [51]; and

Atmosphere 2020, 11, 774 7 of 21

Stage IV rainfall estimates which were rain-gauge-bias corrected with a temporal resolution of 1 h • and a spatial resolution of 4 km [51]; and IFC rainfall estimates that did not include rain-gauge-bias correction, with a temporal resolution • of 1 h and 5 min and a spatial resolution of 500 m [52–54].

The radar rainfall estimates were compared to rainfall observations and daily accumulation records available from the NWS Coop rain gauge located just outside the city limits (Station ID: MHRI4) [55] (see Figure1). For the regional model, we generated initial conditions in the watershed using a spin-up period that started a minimum of three months before the selected events. In the local model, we set the initial soil moisture conditions to be partially dry with the simulation starting at least six hours before the onset of rain, which allowed time for the natural channels to fill from regional streamflow inputs. We set the initial state of the storm sewers and drainage network components to be empty. First, we generated regional runoff using the HLM model and used the streamflow outputs at various locations as the inflow boundary conditions to the XPSWMM model. The boundary conditions applied to the XPSWMM model included (1) spatially averaged radar rainfall estimates directly applied to the 2D domain and (2) the pre—simulated HLM streamflow as inflow boundary conditions to the stream network (Figure3). The results of the one-way-coupled, nested-model simulations were compared to the HLM model simulations and both were evaluated against measured USGS streamflow of the Maquoketa River (05416900-USGS, MCHI4-NWS) located downstream of the city. The results are referred to herein by the model configuration and the rainfall input used (IFC, Stage IV hourly and 5 min, and MRMS), where HLM refers to the regional model and XP—C2 is the nested regional–local model.

4. Results and Evaluation The model output was validated against two flood events (July 2010 and September 2016) during which the Maquoketa River stage exceeded the NWS major flood stage, resulting in nuisance flooding in Manchester. For both events, we compared the spatial pattern of the radar rainfall estimates over the region to each other. We also compared radar rainfall totals that occurred locally to a nearby NWS Coop rain gauge that had daily measurements. The primary method of validation we used was a statistical analysis to compare simulated streamflow to measured USGS observations. We used the most up-to-date rating curve to calculate the stage from the simulated discharge at the models (HLM and XP—C2) outlet. We used the root-mean-square error (RMSE) to quantify the difference between the modeled stage and the observed stage. To quantify the forecast error in the time series, we used the mean absolute error (MAE) and the coefficient of determination (R2) [56], and to measure the model’s ability to reproduce the magnitude and timing of the peak flows we used the peak error (PE) and the time to peak error (TPE) [56–59]. We considered the magnitude and timing of the peak and the rising and receding limb of the hydrograph when determining the suitability of the model to predict streamflow. Additionally, the model’s ability to capture the time to crest and the duration above the NWS major flood stage (6.1 m) was important for Manchester, because these statistics indicate significant flooding downtown. We considered the model’s performance suitable for streamflow predictions if it was able to predict the flood stage within 0.6–0.9 m of the rising limb, which is typically the error for issued flood warnings across Iowa [60]. In addition to streamflow statistics, we used a visual qualitative comparison to examine the urban model’s (i.e., XPSWMM) ability to generally reproduce the flood extent and depths for the two extreme rainfall events. We used non-georeferenced photos and drone footage to validate the performance of the local model to predict the flow of water in the urban environment.

4.1. Radar Rainfall Estimates During July 2010, the upper Maquoketa River basin and Manchester received 406 mm and 203 mm of rainfall, respectively (Figure4a). More recently, in September 2016, over 152 mm of rainfall occurred Atmosphere 2020, 11, 774 8 of 21 over Manchester in 17 h, while nearly 178 mm dropped over the upper Maquoketa River basin (FigureAtmosphere4b). 2020, 11, x FOR PEER REVIEW 8 of 22

(a)

(b)

Figure 4.4. (a) Radar rainfall accumulation estimates over the upper Maquoketa River Basin in mm for the July 2010 storm using Stage IV radar rainfall productproduct (left) and the Iowa Flood Center (IFC) radar rainfall product (right).(right). ( b) Radar rainfall accumulation estimates for the September 2016 storm using Stage IV (left) and MRMS radarradar rainfallrainfall productproduct (right).(right).

Note thatthat for for the the September September 2016 2016 storm, storm, the radarthe radar rainfall rainfall estimates estimates (MRMS (MRMS and Stage and IV) Stage showed IV) similarshowed spatial similar patterns spatial patterns and any diandfferences any differences in total accumulation in total accumulation are a result are of a theresult diff oferent the methodsdifferent usedmethods to create used to each create rainfall each product.rainfall product. The rainfall The ra productsinfall products with a with finer a spatialfiner spatial resolution resolution (IFC (IFC and MRMS)and MRMS) showed showed a variation a variation in the in distribution the distribution of the rainfallof the rainfall across theacross basins, the basins, but in general, but in general, the pattern the andpattern total and rainfall total wasrainfall similar was to similar Stage IV.to TheStage study IV. The area study had limited area had rainfall-gauge limited rainfall-gauge data, so the data, quality so controlthe quality check control was limitedcheck was for limited the radar for rainfallthe radar products. rainfall products. The radar The rainfall radar grids rainfall across grids all across three productsall three products were considered were considered equally uncertain equally and,uncertain given and, the lack given of rain-gaugethe lack of datarain-gauge in the area, data we in didthe notarea, reconstruct we did not or reconstruct adjust the precipitationor adjust the grids.precipitation As shown grids. in Table As shown1, the radarin Table rainfall 1, the products radar rainfall were products were used to compute the accumulated precipitation and maximum rainfall intensity of the storm over Manchester city limits. These measurements gave us information on the total rainfall but not the spatial distribution of the radar rainfall. We calculated the difference between the radar rainfall estimates and the NWS Coop rain gauge daily measurements. The accumulated radar rainfall

Atmosphere 2020, 11, 774 9 of 21 used to compute the accumulated precipitation and maximum rainfall intensity of the storm over Manchester city limits. These measurements gave us information on the total rainfall but not the spatial distribution of the radar rainfall. We calculated the diﬀerence between the radar rainfall estimates and the NWS Coop rain gauge daily measurements. The accumulated radar rainfall estimates were greater than the daily records measured at the NWS Coop rain gauge by 5–9% for Stage IV and MRMS and by 16–21% for IFC.

Table 1. Cumulative radar rainfall (mm) computed over Manchester using Stage IV, MRMS, and IFC products and the maximum rainfall intensity (mm h 1) for the July 2010 and September 2016 storms. · − The daily rainfall measurements from the NWS Coop rain gauge data near Manchester were compared to the radar rainfall estimates.

July 2010 Storm September 2016 Storm Cumulative Max Rainfall Cumulative Max Rainfall Product Rainfall (mm) Intensity (mm h 1) Rainfall (mm) Intensity (mm h 1) · − · − Stage IV 196 36 157 28 MRMS — — 157 33 IFC 224 43 168 28 NWS Coop rain gauge 185 — 145 —

4.2. Modeled Streamflow For the storm event of July 2010, the simulated hydrographs shown in Figure5a illustrate the skill of both the regional (HLM) and nested (XP—C2) models when predicting the rising limb of the hydrograph and the first peak. We also noticed that the nested model consistently generated a lower discharge compared to the regional model, which is discussed later. Both the nested and the regional models predicted the initial crest of the major flood stage earlier than what was observed, and also underestimated the rising limb by 0.3–0.5 m (Figure5b). After the first peak, the observed flood stage continued to increase, but the models showed a recession of the flood waters. The overall shape of the simulated hydrographs using both Stage IV and IFC radar rainfall estimates indicated that the models generated runoff from the rainfall occurring after the first peak, but there was a significant volume of water unaccounted for. The spatial and temporal variability of rainfall–runoff over the regional area was investigated, but no significant discrepancies in model routing and rainfall distribution were evident. The missing volume in the hydrograph may have been an issue of the total rainfall–runoff from the regional model and a discrepancy in the routing of high water levels in the floodplain where water is attenuated and stored. We noted that there might be downstream infrastructure creating backwater effects that were not represented in the local or regional model. One example is the breach of the Delhi Dam on 24 July 2010, located 17.7 km downstream of Manchester. The designed storage volume of the dam was 12,000 km3 and the breach released over 1960 m3 s 1, but it is unlikely to have resulted in a · − significant backwater effect that would account for the missing volume in the hydrograph [61]. Atmosphere 2020, 11, x FOR PEER REVIEW 10 of 22 Atmosphere 2020, 11, 774 10 of 21

(a)

(b)

Figure 5. The modeled discharge (m(m33⋅ss−11)) and and stage stage (m) (m) compared compared to to ( (a)) USGS USGS stage and ( b) discharge · − observations for July 2010. The simulated hydrographshydrographs are named according to the modelmodel (HLM(HLM oror XP-C2)XP-C2) andand thethe radarradar rainfallrainfall input.input. The models forcedforced with the IFC hourly radar rainfall product are redred (simulations(simulations HLM—FC—hHLM—FC—h andand XP—C2—IFC—h)XP—C2—IFC—h) whilewhile thosethose forcedforced withwith StageStage IVIV hourlyhourly radarradar rainfallrainfall areare blueblue (simulations(simulations HLM—StageHLM—Stage IVIV andand XP—C2—StageXP—C2—Stage IV).IV).

We computedcomputed statisticsstatistics forfor thethe firstfirst and second peaks of the hydrograph separately. We obtained root-mean-squaredroot-mean-squared error error (RMSE), (RMSE), mean mean absolute absolute error error (MAE), (MAE), coefficient coefficient of determination of determination (R2), peak (R2), peakerror error(PE), (PE),time to time peak to peakerror error(TPE), (TPE), time to time majo tor major flood floodstage stageerror, error,and duration and duration above above major majorflood floodstage. stage.The results The results are shown are shown in Table in 2. Table We 2saw. We th sawat both that the both nested the nested and regi andonal regional model modelhad skill had in skillreproducing in reproducing the magnitude the magnitude of the first of the peak first with peak a withPE of a less PE ofthan less 0.3 than m, 0.3but m, the but error the doubled error doubled when whenpredicting predicting the magnitude the magnitude of the ofsecond the second peak. peak.The en Thesemble ensemble of hydrological of hydrological predictions predictions could could be used be usedby city by officials city offi tocials predict to predict the time the timeat which at which the Maquoketa the Maquoketa River River will crest will crest6.1 m, 6.1 giving m, giving them them time to prepare. The recession was not included in this analysis because our main interest was in the model’s ability to capture the rising limb, peak, and duration above the flood stage.

Atmosphere 2020, 11, 774 11 of 21 Atmosphere 2020, 11, x FOR PEER REVIEW 11 of 22 time toTable prepare. 2. Statistical The recession analysis wascomparing not included the simulated in this st analysisages to USGS because observat our mainions for interest the first was and in the model’ssecond ability peaks to of capture the July the 2010 rising flood limb, and the peak, time and to crest duration and the above duration the above flood the stage. NWS major flood stage (6.1 m) for the first peak for model configurations HLM and XP—C2, using both Stage IV and TableIFC radar 2. Statistical rainfall products. analysis comparing the simulated stages to USGS observations for the first and second peaks of the July 2010 flood and the time to crest and the duration above the NWS major flood RMSE MAE PE Time to Crest Duration above Rainfallstage (6.1 Model m) for the first peak for model configurationsR2 HLMTPE (h) and XP—C2, using both Stage IV and IFC radar rainfall products.(m) (m) (m) 6.1 m Error (h) 6.1 m Error (h) Peak 1 RMSE MAE TPE Time to Crest Duration above StageRainfall IV HLM Model 0.32 0.28 0.98R 2 −0.04PE (m) 2.8 −1.0 −6.3 (m) (m) (h) 6.1 m Error (h) 6.1 m Error (h) XP—C2 0.30 0.23 0.99 0.10 2.0 0.3 −8.3 Peak 1 IFC—h HLM 0.43 0.39 0.98 −0.30 2.8 0.5 −5.5 Stage IV HLM 0.32 0.28 0.98 0.04 2.8 1.0 6.3 − − − XP—C2XP—C2 0.49 0.30 0.41 0.23 0.97 0.99 −0.11 0.10 1.3 2.0 1.5 0.3 −8.36.3 − PeakIFC—h 2 HLM 0.43 0.39 0.98 0.30 2.8 0.5 5.5 − − XP—C2 0.49 0.41 0.97 0.11 1.3 1.5 6.3 Stage IV HLM 1.5 1.4 0.99 1.17− 9.3 − Peak 2 XP—C2 1.6 1.5 0.99 1.17 9.3 IFC—hStage IV HLM HLM 1.3 1.5 1.2 1.4 0.99 0.99 0.62 1.17−4.3 9.3 XP—C2 1.6 1.5 0.99 1.17 9.3 IFC—h XP—C2 HLM 1.4 1.3 1.3 1.2 0.99 0.99 0.73 0.62 −4.8 4.3 − XP—C2 1.4 1.3 0.99 0.73 4.8 − For the September 2016 flood event, the impacts of the varying radar rainfall products on the modeledFor the streamflow September were 2016 more flood evident. event, In the Figure impacts 6a, ofwe the can varying see that radar the volume rainfall of products rainfall–runoff on the modeleddiffers significantly streamflow between were more each evident. radar rainfall In Figure product6a, we and can the see model that the realizations volume of were rainfall–runo arranged asff dianff ersuncertainty significantly band between around eachthe measured radar rainfall values. product The impact and the of modelthe temporal realizations resolution were of arranged the IFC asradar an uncertaintyrainfall estimate band was around tested the for measured this event values. but there The was impact no significant of the temporal change resolution in the results, of the so IFCmuch radar so that rainfall the estimatestreamflows was testedmodeled for using this event IFC but5 minute there wasand noIFC significant hourly overlaid change each in the other, results, as soshown much in so Figure that the 6b. streamflows The effect of modeled radar rainfall using resolution IFC 5 minute on the and response IFC hourly of the overlaid local eachmodel other, was asmore shown evidently in Figure seen6b. in The the estreamflowffect of radar predictions rainfall resolution compared on to thethe responseJuly 2010 offlood. the local model was more evidently seen in the streamflow predictions compared to the July 2010 flood.

(a)

Figure 6. Cont.

AtmosphereAtmosphere2020 2020,,11 11,, 774 x FOR PEER REVIEW 1212 of 2122

(b)

(c)

FigureFigure 6.6. The modeled dischargedischarge (m(m33⋅ss−1)) and and stage stage (m) (m) compared to (a) USGS stage andand ((b)) dischargedischarge · − observationsobservations forfor SeptemberSeptember 2016.2016. The simulated hydrographs are namednamed accordingaccording toto thethe modelmodel (HLM(HLM oror XP—C2)XP—C2) andand thethe radarradar rainfallrainfall input.input. TheThe modelsmodels forcedforced withwith thethe IFCIFC hourlyhourly radarradar rainfallrainfall productproduct areare redred (HLM—IFC—h,(HLM—IFC—h, XP—C2—IFC—h,XP—C2—IFC—h, XP—C2—IFC—5min)XP—C2—IFC—5min) whilewhile thosethose forcedforced withwith StageStage IVIV hourlyhourly radarradar rainfallrainfall areare blueblue (HLM—Stage(HLM—Stage IVIV andand XP—C2—StageXP—C2—Stage IV).IV). ModelsModels forcedforced withwith MRMSMRMS hourlyhourly radar radar rainfall rainfall are coloredare colo greenred green (HLM—MRMS (HLM—MRMS and XP—C2—MRMS). and XP—C2—MRMS). (c) The discharge (c) The fromdischarge the Eastern from the Tributary, Eastern which Tributary, drains which the eastern drains domain the eastern of the XPSWMMdomain of model,the XPSWMM shows how model, the hydrologicalshows how responsethe hydrological of Manchester response is signiﬁcantly of Manchester impacted is significantly by the spatial impacted and temporal by the resolution spatial and of thetemporal radar rainfallresolution input. of the radar rainfall input.

FromFrom thethe previousprevious experiments,experiments, wewe observedobserved thatthat usingusing hourlyhourly andand 55 minuteminute IFCIFC rainfallrainfall diddid notnot considerablyconsiderably changechange thethe streamﬂowstreamflow predictionspredictionsat at thethe USGSUSGS streamﬂowstreamflow gaugegauge onon thethe MaquoketaMaquoketa River. We extracted the flow in the Eastern Tributary to better understand the response of the urban model. In Figure 6c, it is clear that the higher resolution (both temporal and spatial) of the IFC rainfall

Atmosphere 2020, 11, 774 13 of 21

River. We extracted the flow in the Eastern Tributary to better understand the response of the urban model. In Figure6c, it is clear that the higher resolution (both temporal and spatial) of the IFC rainfall product did change the hydrological response of the Eastern Tributary. The IFC 5 minute rainfall allowed for a more detailed description of the transit of flows along the detailed urban drainage network, showing a rising of the hydrographs that could not be obtained with coarser rainfall inputs or coarser hydrological models. We saw that the models could predict the stage within less than 1 m of error (Table3), but none of the models or rainfall inputs significantly outperformed the others. Using the MRMS and Stage IV radar rainfall products, the nested model simulated the major flood level earlier than was observed by 2–3.5 h. It also predicted that the flood duration would be almost double the length of time that was observed. The hourly and 5 min HLM—IFC models generated a hydrograph that was similar in shape and volume to the observed hydrograph. However, the simulations were shifted ahead by 2–3 h because the lower discharge volume produced lower flow velocity in the routing model used by the HLM.

Table 3. Statistical analysis comparing the simulated stages to USGS observations for the September 2016 flood, and the time to crest and the duration above the NWS major flood stage (6.1 m) for model configurations HLM and XP—C2 using Stage IV, MRMS, and IFC (hourly and 5 min) radar rainfall products.

RMSE MAE PE TPE Time to Crest Duration above Rainfall Model R2 (m) (m) (m) (h) 6.1 m Error (h) 6.1 m Error (h) Stage IV HLM 0.7 0.6 0.89 0.51 2.0 3.5 5.5 − − XP—C2 0.6 0.5 0.88 0.33 0.5 2.2 4.2 − − MRMS HLM 0.7 0.6 0.88 0.96 0.8 3.5 6.8 − − XP—C2 0.6 0.5 0.90 0.81 0.0 2.6 5.9 − − IFC—5 min HLM 0.8 0.6 0.89 0.02 2.5 2.3 0.8 − − XP—C2 0.7 0.6 0.88 0.20 1.3 — — IFC—h XP—C2 0.7 0.6 0.84 0.20 1.3 — —

4.3. Modeled Flood Extents To better understand the performance of the local model as a flood-prediction tool, we evaluated the flood depths and extents from XPSWMM for both historical storms using visual comparison. We primarily looked at the downtown area of Manchester, because this area often experiences nuisance flooding and the city is a point of interest for potential drainage improvement projects. We compared the maximum water depths output from XPSWMM (XP—C2—IFC—h) to photos taken during the flood events. In Figure7, it is evident that the local model was able to reproduce the extent of flooding documented in downtown along E Main St. during the July 2010 flood. We have included diamond markers in both the model output and photos to facilitate the comparison. There are elements that reveal similarities between the flood depth map on the top panel and the aerial images; the access to the bridge on E Main St. when traveling west to east is not flooded; the flood depth in the building marked with the blue diamond is approximately half a meter, as indicated in the model output and the imagery. Figure8 compares the maximum depth outputs from the XPSWMM (XP—C2—Stage IV) model to aerial photos taken for the September 2016 flood. We saw that the model was able to recreate the flow around buildings and the pedestrian path, which acts as an earthen embankment restricting flow into and out of the river. The model correctly estimated the flood depth around the building marked with the red diamond, as an effect of the barrier created by the pedestrian path and the topography. The north side of the building marked in green and the east side of the purple diamond should not be flooded, as indicated by the model and the imagery. Atmosphere 2020, 11, 774 14 of 21 Atmosphere 2020, 11, x FOR PEER REVIEW 14 of 22

(a)

(b)

FigureFigure 7. 7The. The nested nested modelmodel was used used to to simulate simulate the the flood flood of July of July 2010 2010 in downtown in downtown Manchester. Manchester. (a) (a)The The maximum maximum depth depth output output from from XPSWMM XPSWMM (XP—C2—IFC—h) (XP—C2—IFC—h) was compared was compared visually to visually (b) photos to ( b) and aerial images of flooding provided by the City of Manchester. The points of interest are indicated photos and aerial images of flooding provided by the City of Manchester. The points of interest are indicated by colored diamond markers on both the photos and flood map. The orange arrow is pointing in the westbound direction along E Main Street. Atmosphere 2020, 11, x FOR PEER REVIEW 15 of 22

by colored diamond markers on both the photos and flood map. The orange arrow is pointing in the westbound direction along E Main Street.

Figure 8 compares the maximum depth outputs from the XPSWMM (XP—C2—Stage IV) model to aerial photos taken for the September 2016 flood. We saw that the model was able to recreate the flow around buildings and the pedestrian path, which acts as an earthen embankment restricting flow into and out of the river. The model correctly estimated the flood depth around the building marked with the red diamond, as an effect of the barrier created by the pedestrian path and the topography. The north side of the building marked in green and the east side of the purple diamond Atmosphereshould 2020not ,be11 ,flooded, 774 as indicated by the model and the imagery. 15 of 21

Atmosphere 2020, 11, x FOR PEER REVIEW 16 of 22 (a)

(b)

FigureFigure 8. The8. The nested nested model model was was used used to simulate to simulate the flood theof flood September of September 2016 in downtown2016 in downtown Manchester. (a)Manchester. The maximum (a) The depth maximum output fromdepth XPSWMM output from (XP—C2—Stage XPSWMM (XP—C2—Stage IV) was compared IV) was to compared (b) photos to and aerial(b) photos images and of floodingaerial images provided of flooding by the provided City of Manchester. by the City of The Manchester. points of interest The points are indicatedof interest by coloredare indicated diamond by markerscolored diamond on both markers the photos on both and floodthe photos map. and The flood orange map. arrow The orange is pointing arrow in is the pointing in the westbound direction along E Main Street. The newly built whitewater park in the westbound direction along E Main Street. The newly built whitewater park in the Maquoketa River is Maquoketa River is labeled as WW and the pedestrian path (orange line labeled PP) is shown to labeled as WW and the pedestrian path (orange line labeled PP) is shown to impede stormwater flow impede stormwater flow from downtown into the river. from downtown into the river. 5. Discussion In this section, we discuss the uncertainty in the data and models and its impacts on the streamflow predictions. We discuss the advantages and disadvantages of the models and the use of a nested regional–local modeling approach.

5.1. Uncertainty and General Observations Overall, for the two flood events evaluated, the nested modeling approach did not significantly improve the streamflow predictions compared to the regional HLM model. Additional examination is required to determine whether a different configuration of the local model would better resolve the characterization of the hydrograph recession. We evaluated the model’s performance primarily based on its ability to predict stages, because this is important for the city officials to make evacuation decisions. The uncertainty in the observed stages due to errors in the high end of the rating curves propagated into the evaluation of the model results. At extreme flood levels, like the flood of July 2010, the uncertainty associated with rating curves was prominent because we lacked physical measurements to help us quantify the storage of water in the floodplain at high flows. The rating curves traditionally ignore the less-known phenomenon of hysteresis [62], which is important for large events with unsteady flow. Model parameters are another source of error that will change

Atmosphere 2020, 11, 774 16 of 21

5. Discussion In this section, we discuss the uncertainty in the data and models and its impacts on the streamﬂow predictions. We discuss the advantages and disadvantages of the models and the use of a nested regional–local modeling approach.

5.1. Uncertainty and General Observations Overall, for the two flood events evaluated, the nested modeling approach did not significantly improve the streamflow predictions compared to the regional HLM model. Additional examination is required to determine whether a different configuration of the local model would better resolve the characterization of the hydrograph recession. We evaluated the model’s performance primarily based on its ability to predict stages, because this is important for the city officials to make evacuation decisions. The uncertainty in the observed stages due to errors in the high end of the rating curves propagated into the evaluation of the model results. At extreme flood levels, like the flood of July 2010, the uncertainty associated with rating curves was prominent because we lacked physical measurements to help us quantify the storage of water in the floodplain at high flows. The rating curves traditionally ignore the less-known phenomenon of hysteresis [62], which is important for large events with unsteady flow. Model parameters are another source of error that will change timing of the watershed response and the volume of runoff produced [24]. Without in situ measurements, modeling the amount of water that can be stored in the depressions in the land surface, vegetation and canopy, and the soil layers for watersheds with heterogenous terrain and landcover is difficult. There was also uncertainty in the downstream boundary condition, which impacted the ability of the model to reproduce any backwater effects from stormwater management structures or other kinds of impoundments along the floodplain. The accuracy of the nested approach for use in predicting streamflow is subject to the quality of the regional model and the quality of the finer-resolution data used in the local model. In this study, the uncertainty from the regional inflow applied to the local model was dominant compared to the small volume of runoff from the local model. For fluvial floods, the urban rainfall–runoff dynamics have a negligible impact on total streamflow. However, the impact of radar rainfall spatial and temporal resolution on streamflow predictions was more prominent across the regional model and the nested model. The performance of the nested model simulations did not exhibit systematic characteristics based on the individual rainfall products (e.g., no rainfall product resulted in larger runoff bias, etc.). This draws attention to the large uncertainty in rainfall inputs, which is a result of the non-linear, spatiotemporal patterns of rainfall. However, by using different, equally valid radar rainfall estimates, the ensemble of hydrological predictions envelop the observed hydrograph, thus implicitly accounting for the uncertainty in the radar rainfall input [63].

5.2. Model Application Another aim of this work was to test the nested modeling approach to determine whether it is suitable to apply in other areas of the state of Iowa where local models can be one-way coupled to the HLM model, which is actively providing streamflow forecasts [1]. By coupling the regional model to a local model, we can gain additional risk and hazard information that is useful to the local community. Because the XPSWMM model generates velocity and depth information in the 2D domain, we can use these outputs to give emergency responders and local officials hazard maps, such as the one shown in Figure9, to support their response. Other kinds of maps that the local hydrodynamic model can produce include road and property safety risk maps, which would aid in making decisions around closing off areas of a city (e.g., E Main St. in downtown Manchester). The XPSWMM model also outputs risk maps that highlight structures that might fail, such as bridges or dams (e.g., the Delhi Dam break). Atmosphere 2020, 11, x FOR PEER REVIEW 17 of 22

timing of the watershed response and the volume of runoff produced [24]. Without in situ measurements, modeling the amount of water that can be stored in the depressions in the land surface, vegetation and canopy, and the soil layers for watersheds with heterogenous terrain and landcover is difficult. There was also uncertainty in the downstream boundary condition, which impacted the ability of the model to reproduce any backwater effects from stormwater management structures or other kinds of impoundments along the floodplain. The accuracy of the nested approach for use in predicting streamflow is subject to the quality of the regional model and the quality of the finer-resolution data used in the local model. In this study, the uncertainty from the regional inflow applied to the local model was dominant compared to the small volume of runoff from the local model. For fluvial floods, the urban rainfall–runoff dynamics have a negligible impact on total streamflow. However, the impact of radar rainfall spatial and temporal resolution on streamflow predictions was more prominent across the regional model and the nested model. The performance of the nested model simulations did not exhibit systematic characteristics based on the individual rainfall products (e.g., no rainfall product resulted in larger runoff bias, etc.). This draws attention to the large uncertainty in rainfall inputs, which is a result of the non-linear, spatiotemporal patterns of rainfall. However, by using different, equally valid radar rainfall estimates, the ensemble of hydrological predictions envelop the observed hydrograph, thus implicitly accounting for the uncertainty in the radar rainfall input [63].

5.2. Model Application Another aim of this work was to test the nested modeling approach to determine whether it is suitable to apply in other areas of the state of Iowa where local models can be one-way coupled to the HLM model, which is actively providing streamflow forecasts [1]. By coupling the regional model to a local model, we can gain additional risk and hazard information that is useful to the local community. Because the XPSWMM model generates velocity and depth information in the 2D domain, we can use these outputs to give emergency responders and local officials hazard maps, such as the one shown in Figure 9, to support their response. Other kinds of maps that the local hydrodynamic model can produce include road and property safety risk maps, which would aid in making decisions around closing off areas of a city (e.g., E Main St. in downtown Manchester). The AtmosphereXPSWMM2020, 11model, 774 also outputs risk maps that highlight structures that might fail, such as bridges 17or of 21 dams (e.g., the Delhi Dam break).

FigureFigure 9. Maximum9. Maximum hazard hazard map map output output fromfrom XPSWMM (XP—C2—IFC—h) (XP—C2—IFC—h) for for the the July July 2010 2010 flood flood event, where red indicates high risk and blue is low risk (risk is a function of water depth and velocity event, where red indicates high risk and blue is low risk (risk is a function of water depth and velocity computed in the model). Photos from the July 2010 flood event provided by the city show scour in computed in the model). Photos from the July 2010 flood event provided by the city show scour in between buildings and turbulent flow through downtown streets. Atmospherebetween 2020 buildings, 11, x FOR and PEER turbulent REVIEW flow through downtown streets. 18 of 22

SinceSince the the hydrological hydrological importance importance of of the the urban urban rainfall–runo rainfall–runoffff dynamics dynamics is is heavily heavily dependent dependent on theon volume the volume and intensityand intensity of localized of localized rainfall rainfall [64], it[6 is4], probable it is probable that during that during extreme extreme regional regional rainfall events,rainfall they events, will havethey awill negligible have a negligible effect [65]. effect For the [65]. two For historical the two stormshistorical reported storms in reported this study, in itthis was thestudy, case it that was the the small case that ungauged the small tributaries ungauged and trib urbanutaries area and hadurban a minorarea had impact a minor on impact the Maquoketa on the Maquoketa River discharge [18,66]. However, by examining the response of the local model with and River discharge [18,66]. However, by examining the response of the local model with and without without subsurface drainage during a local rainfall event in Figure 10, we could see that it is crucial subsurface drainage during a local rainfall event in Figure 10, we could see that it is crucial for urban for urban models to be resolved at small spatial scales to better resemble the flow paths in an urban models to be resolved at small spatial scales to better resemble the flow paths in an urban landscape. landscape. Ignoring the details of storm sewers and ditches could significantly impact the accuracy Ignoring the details of storm sewers and ditches could significantly impact the accuracy of a city’s of a city’s flood profile for local rainfall events. flood profile for local rainfall events.

(a) (b)

FigureFigure 10. 10.The The maximum maximum ﬂood flood depths depths in in Eastern Eastern Manchester Manchester for for a a heavy heavy local local rainfall rainfall event event using using the XPSWMMthe XPSWMM model model where where (a) has (a) has the the stormwater stormwater system system (described (described in in Section Section 3.2 3.2)) activated activated andand (b) is overlandis overland ﬂow flow only. only.

Atmosphere 2020, 11, 774 18 of 21

6. Conclusions In this study, we used a nested regional–local model to investigate the impacts of the spatiotemporal resolution of radar rainfall inputs and urban rainfall–runoff dynamics on streamflow predictions in an urban–rural watershed. We applied this modeling approach to the community of Manchester and found that the model was able to predict the flood levels while also providing reasonably accurate forecasts of the magnitude and timing of peak streamflow. The model tended to estimate the peak of the hydrograph slightly earlier than what was observed. Though the model cannot generate a single definitive forecast, it can be used to generate an ensemble of hydrological predictions which are suitable for warning against the worst possible flood. The nested model’s ability to capture the crest time and duration above the NWS major flood stage, despite the various uncertainties in rainfall input, could be used as a tool to assist the community in preparing for potential fluvial and pluvial flooding. We determined that the hydrological importance of the urban rainfall–runoff dynamics is heavily dependent on a localized rainfall event and intensity. The local urban hydrodynamics do not significantly contribute to streamflow predictions during extreme regional rainfall events, but they are important at smaller tributary basins, where there are fewer observations available for validation. While streamflow outputs from a regional model are necessary for forecasting a riverine-induced flood, ignoring the impacts of the stormwater network could have major implications for the predicted flood risk. During peak river flows, the capacity of the stormwater infrastructure to mitigate any additional local rainfall–runoff would be limited, thus posing a potential flood risk for the urban district. Capturing the storm movement across a watershed is important for streamflow predictions and the response of the urban drainage system. This study showed how the spatial and temporal variability of radar rainfall inputs will impact streamflow predictions in regional, local, and nested models. For the September 2016 event, the modeled streamflow resulted in various hydrological responses resulting from the varying spatial resolution of the radar rainfall inputs, but it was less sensitive to the temporal resolution. In contrast, for this same storm event, the urban catchment was sensitive to the variations of the radar rainfall inputs in both time and space. Because of the uncertainty associated with radar rainfall estimates, we advocate for using an ensemble hydrological prediction rather than a deterministic approach. By using multiple rainfall forcing and model configurations, we generated an ensemble of model realizations that provide an estimate for the range of potential streamflow observations at the USGS streamflow gauge. Using a nested modeling approach is an effective method for integrating models built at varying scales. By using a nested modeling approach, we were able to integrate a fine-resolution urban model to a large-scale, simplified model. In doing so, we took advantage of the HLM’s good characterization of regional runoff and XPSWMM’s ability to capture fine-scale flooding in an urban landscape to generate useful flood-relevant information for Manchester. The nested modeling approach adds value to the community because of the detailed flood information (hazard maps, maximum flood depths and extents, etc.) the local model is able to generate at a fine resolution, which can be used to aid decision-makers who need to allocate mitigation resources to high-risk areas.

Author Contributions: Conceptualization, L.E.G. and W.F.K.; methodology, L.E.G. and W.F.K.; software, L.E.G. and F.Q.; validation, L.E.G., F.Q. and W.F.K.; formal analysis, L.E.G.; data curation, L.E.G. and F.Q.; writing—original draft preparation, L.E.G.; writing—review and editing, L.E.G., F.Q. and W.F.K.; visualization, L.E.G.; supervision, W.F.K.; funding acquisition, W.F.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Iowa Flood Center and conducted while L.E.G. was a graduate student at the University of Iowa. Acknowledgments: Ryan Wicks and others at Fehr and Graham provided data on Manchester’s infrastructure and records of the floods. The local USACE and IDNR agencies provided data, reports, and HEC-RAS models of the Maquoketa River near Manchester. Conflicts of Interest: The authors declare no conflict of interest. Atmosphere 2020, 11, 774 19 of 21

References

1. Krajewski, W.F.; Ceynar, D.; Demir, I.; Goska, R.; Kruger, A.; Langel, C.; Mantilla, R.; Niemeier, J.; Quintero, F.; Seo, B.-C.; et al. Real-time flood forecasting and information system for the state of iowa. Bull. Am. Meteorol. Soc. 2017, 98, 539–554. [CrossRef] 2. Buchmiller, R.C.; Eash, D.A. Floods of May and June 2008 in Iowa; Iowa Department of Natural Resources: Des Moines, IA, USA, 2010; pp. 1–20. 3. Weber, L.J.; Muste, M.; Bradley, A.A.; Amado, A.A.; Demir, I.; Drake, C.W.; Krajewski, W.F.; Loeser, T.J.; Politano, M.S.; Shea, B.R.; et al. The Iowa Watersheds Project: Iowa’s prototype for engaging communities and professionals in watershed hazard mitigation. Int. J. River Basin Manag. 2018, 16, 315–328. [CrossRef] 4. Quintero, F.; Krajewski, W.F.; Seo, B.-C.; Mantilla, R. Improvement and evaluation of the Iowa Flood Center Hillslope Link Model (HLM) by calibration-free approach. J. Hydrol. 2020, 584, 124686. [CrossRef] 5. Quintero, F.; Krajewski, W.F.; Mantilla, R.; Small, S.; Seo, B.-C. A Spatial–dynamical framework for evaluation of satellite rainfall products for flood prediction. J. Hydrometeorol. 2016, 17, 2137–2154. [CrossRef] 6. Schmitt, T.G.; Thomas, M.; Ettrich, N. Analysis and modeling of flooding in urban drainage systems. J. Hydrol. 2004, 299, 300–311. [CrossRef] 7. Salvadore, E.; Bronders, J.; Batelaan, O. Hydrological modelling of urbanized catchments: A review and future directions. J. Hydrol. 2015, 529, 62–81. [CrossRef] 8. Mitchell, V.G.; Duncan, H.; Inman, M.; Rahilly, M.; Stewart, J.; Vieritz, A.; Holt, P.; Grant, A.; Fletcher, T.D.; Coleman, J.; et al. State of the Art Review of Integrated Urban Water Models. In Proceedings of the 6th International Conference on Novatech, Lyon, France, 25–28 June 2007. 9. Knebl, M.R.; Yang, Z.-L.; Hutchison, K.; Maidment, D.R. Regional scale flood modeling using NEXRAD rainfall, GIS, and HEC-HMS/RAS: A case study for the San Antonio River Basin Summer 2002 storm event. J. Environ. Manag. 2005, 75, 325–336. [CrossRef] 10. Neal, J.C.; Odoni, N.A.; Trigg, M.A.; Freer, J.E.; Garcia-Pintado, J.; Mason, D.C.; Wood, M.; Bates, P.D. Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models. J. Hydrol. 2015, 529, 169–183. [CrossRef] 11. Salas, F.R.; Somos-Valenzuela, M.A.; Dugger, A.; Maidment, D.R.; Gochis, D.J.; David, C.H.; Yu, W.; Ding, D.; Clark, E.P.; Noman, N. Towards real-time continental scale streamflow simulation in continuous and discrete space. JAWRA J. Am. Water Resour. Assoc. 2018, 54, 7–27. [CrossRef] 12. Teng, J.; Jakeman, A.J.; Vaze, J.; Croke, B.F.W.; Dutta, D.; Kim, S. Flood inundation modelling: A review of methods, recent advances and uncertainty analysis. Environ. Model. Softw. 2017, 90, 201–216. [CrossRef] 13. Bisht, D.S.; Chatterjee, C.; Kalakoti, S.; Upadhyay, P.; Sahoo, M.; Panda, A. Modeling urban floods and drainage using SWMM and MIKE URBAN: A case study. Nat. Hazards 2016, 84, 749–776. [CrossRef] 14. Mark, O.; Weesakul, S.; Apirumanekul, C.; Aroonnet, S.B.; Djordjević,S. Potential and limitations of 1D modelling of urban flooding. J. Hydrol. 2004, 299, 284–299. [CrossRef] 15. Domingo, N.D.S.; Refsgaard, A.; Mark, O.; Paludan, B. Flood analysis in mixed-urban areas reflecting interactions with the complete water cycle through coupled hydrologic-hydraulic modelling. Water Sci. Technol. 2010, 62, 1386–1392. [CrossRef] 16. Russo, B.; Sunyer, D.; Velasco, M.; Djordjević,S. Analysis of extreme flooding events through a calibrated 1D/2D coupled model: The case of Barcelona (Spain). J. Hydroinform. 2015, 17, 473–491. [CrossRef] 17. Chen, A.S.; Evans, B.; Djordjević,S.; Savić,D.A. A coarse-grid approach to representing building blockage effects in 2D urban flood modelling. J. Hydrol. 2012, 426–427, 1–16. [CrossRef] 18. Bermúdez, M.; Neal, J.C.; Bates, P.D.; Coxon, G.; Freer, J.E.; Cea, L.; Puertas, J. Quantifying local rainfall dynamics and uncertain boundary conditions into a nested regional-local flood modeling system. Water Resour. Res. 2017, 53, 2770–2785. [CrossRef] 19. Villarini, G.; Krajewski, W.F. Review of the different sources of uncertainty in single polarization radar-based estimates of rainfall. Surv. Geophys. 2010, 31, 107–129. [CrossRef] 20. Wright, D.B.; Smith, J.A.; Villarini, G.; Baeck, M.L. Long-term high-resolution radar rainfall fields for urban hydrology. JAWRA J. Am. Water Resour. Assoc. 2014, 50, 713–734. [CrossRef] 21. Emmanuel, I.; Andrieu, H.; Leblois, E.; Janey, N.; Payrastre, O. Influence of rainfall spatial variability on rainfall-runoff modelling: Benefit of a simulation approach? J. Hydrol. 2015, 531, 337–348. [CrossRef] Atmosphere 2020, 11, 774 20 of 21

22. Ochoa-Rodriguez, S.; Wang, L.P.; Gires, A.; Pina, R.D.; Reinoso-Rondinel, R.; Bruni, G.; Ichiba, A.; Gaitan, S.; Cristiano, E.; Van Assel, J.; et al. Impact of spatial and temporal resolution of rainfall inputs on urban hydrodynamic modelling outputs: A multi-catchment investigation. J. Hydrol. 2015, 531, 389–407. [CrossRef] 23. Krajewski, W.F.; Kruger, A.; Singh, S.; Seo, B.-C.; Smith, J.A. Hydro-NEXRAD-2: Real-time access to customized radar-rainfall for hydrologic applications. J. Hydroinform. 2013, 15, 580–590. [CrossRef] 24. Smith, B.K.; Smith, J.A.; Baeck, M.L.; Villarini, G.; Wright, D.B. Spectrum of storm event hydrologic response in urban watersheds. Water Resour. Res. 2013, 49, 2649–2663. [CrossRef] 25. Bruni, G.; Reinoso, R.; Van de Giesen, N.C.; Clemens, F.H.L.R.; Ten Veldhuis, J.A.E. On the sensitivity of urban hydrodynamic modelling to rainfall spatial and temporal resolution. Hydrol. Earth Syst. Sci. 2015, 19, 691–709. [CrossRef] 26. Wang, L.-P.; Ochoa-Rodríguez, S.; Van Assel, J.; Pina, R.D.; Pessemier, M.; Kroll, S.; Willems, P.; Onof, C. Enhancement of radar rainfall estimates for urban hydrology through optical flow temporal interpolation and Bayesian gauge-based adjustment. J. Hydrol. 2015, 531, 408–426. [CrossRef] 27. Thorndahl, S.; Einfalt, T.; Willems, P.; Nielsen, J.E.; Ten Veldhuis, M.-C.; Arnbjerg-Nielsen, K.; Rasmussen, M.R.; Molnar, P.Weather radar rainfall data in urban hydrology. Hydrol. Earth Syst. Sci. 2017, 21, 1359–1380. [CrossRef] 28. Peleg, N.; Blumensaat, F.; Molnar, P.; Fatichi, S.; Burlando, P.Partitioning the impacts of spatial and climatological rainfall variability in urban drainage modeling. Hydrol. Earth Syst. Sci. 2017, 21, 1559–1572. [CrossRef] 29. Fletcher, T.D.; Andrieu, H.; Hamel, P. Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art. Adv. Water Resour. 2013, 51, 261–279. [CrossRef] 30. Liu, Y.; Gupta, H.V. Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework. Water Resour. Res. 2007, 43.[CrossRef] 31. Eash, D.A. Floods of July 23–26, 2010, in the Little Maquoketa River and Maquoketa River Basins, Northeast Iowa; Open-File Report 2011-1301; U.S. Geological Survey: Reston, VI, USA, 2012. 32. Innovyze. XPSWMM Reference Manual; XPSWMM and XPStorm Resource Center: Portland, OR, USA, 2016. 33. Small, S.J.; Jay, L.O.; Mantilla, R.; Curtu, R.; Cunha, L.K.; Fonley, M.; Krajewski, W.F. An asynchronous solver for systems of ODEs linked by a directed tree structure. Adv. Water Resour. 2013, 53, 23–32. [CrossRef] 34. USDA. Natural Resources Conservation Service Web Soil Survey. Available online: http://websoilsurvey. nrcs.usda.gov/ (accessed on 20 July 2017). 35. Knighton, J.; White, E.; Lennon, E.; Rajan, R. Development of probability distributions for urban hydrologic model parameters and a Monte Carlo analysis of model sensitivity. Hydrol. Process. 2014, 28, 5131–5139. [CrossRef] 36. Rawls, W.J.; Brakensiek, D.L.; Miller, N. Green-ampt infiltration parameters from soils data. J. Hydraul. Eng. 1983, 109, 62–70. [CrossRef] 37. Iowa Geodata. Available online: https://geodata.iowa.gov/dataset/high-resolution-land-cover-iowa-2009- 564 (accessed on 20 July 2017). 38. Arrault, A.; Finaud-Guyot, P.; Archambeau, P.; Bruwier, M.; Erpicum, S.; Pirotton, M.; Dewals, B. Hydrodynamics of long-duration urban floods: Experiments and numerical modelling. Nat. Hazards Earth Syst. Sci. 2016, 16, 1413–1429. [CrossRef] 39. USDA. National Resources Conservation Service: Manning’s (Roughness) Coefficient. Available online: https://www.nrcs.usda.gov/wps/portal/nrcs/detail/national/water/manage/hydrology/?cid=stelprdb104570 (accessed on 20 July 2017). 40. Brown, J.D.; Spencer, T.; Moeller, I. Modeling storm surge flooding of an urban area with particular reference to modeling uncertainties: A case study of Canvey Island, United Kingdom. Water Resour. Res. 2007, 43, 1–22. [CrossRef] 41. Syme, W.J. Flooding in urban areas–2d modelling approaches for buildings and fences. In Proceedings of the Engineers Australia 9th National Conference on Hydraulics in Water Engineering, Darwin, Australia, 23 September 2008. 42. Schubert, J.E.; Sanders, B.F. Building treatments for urban flood inundation models and implications for predictive skill and modeling efficiency. Adv. Water Resour. 2012, 41, 49–64. [CrossRef] 43. Smith, G.P.; Wasko, C.D.; Miller, B.M. Modelling the influence of buildings on flood flow. In Proceedings of the 52th Floodplain Management National Conference, Batemans Bay, Australia, 21–24 February 2012. 44. Bellos, V.; Tsakiris, G. Comparing various methods of building representation for 2D flood modelling in built-up areas. Water Resour. Manag. 2015, 29, 379–397. [CrossRef] Atmosphere 2020, 11, 774 21 of 21

45. Gironás, J.; Niemann, J.D.; Roesner, L.A.; Rodriguez, F.; Andrieu, H. Evaluation of methods for representing urban terrain in stormwater modeling. J. Hydrol. Eng. 2010, 15, 14. [CrossRef] 46. Jankowfsky, S.; Branger, F.; Braud, I.; Gironás, J.; Rodriguez, F. Comparison of catchment and network delineation approaches in complex suburban environments: Application to the Chaudanne catchment, France. Hydrol. Process. 2013, 27, 3747–3761. [CrossRef] 47. Rodriguez, F.; Bocher, E.; Chancibault, K. Terrainrepresentation impact on periurban catchment morphological properties. J. Hydrol. 2013, 485, 54–67. [CrossRef] 48. Mignot, E.; Paquier, A.; Haider, S. Modeling floods in a dense urban area using 2D shallow water equations. J. Hydrol. 2006, 327, 186–199. [CrossRef] 49. Fewtrell, T.J.; Bates, P.D.; Horritt, M.; Hunter, N.M. Evaluating the effect of scale in flood inundation modelling in urban environments. Hydrol. Process. 2008, 22, 5107–5118. [CrossRef] 50. Zhang, J.; Howard, K.; Langston, C.; Kaney, B.; Qi, Y.; Tang, L.; Grams, H.; Wang, Y.; Cocks, S.; Martinaitis, S.; et al. Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimation: Initial operating capabilities. Bull. Am. Meteorol. Soc. 2016, 97, 621–638. [CrossRef] 51. Lin, Y.; Mitchell, K.E. The NCEP Stage II/IV hourly precipitation analyses: Development and applications. In Proceedings of the Preprints 19th Conference on Hydrology, American Meteorological Society, San Diego, CA, USA, 9–13 January 2005; pp. 2–5. 52. Seo, B.-C.; Krajewski, W.F.; Quintero, F.; ElSaadani, M.; Goska, R.; Cunha, L.K.; Dolan, B.; Wolff, D.B.; Smith, J.A.; Rutledge, S.A.; et al. Comprehensive evaluation of the ifloods radar rainfall products for hydrologic applications. J. Hydrometeorol. 2018, 19, 1793–1813. [CrossRef] 53. Seo, B.C.; Krajewski, W.F. Correcting temporal sampling error in radar-rainfall: Effect of advection parameters and rain storm characteristics on the correction accuracy. J. Hydrol. 2015, 531, 272–283. [CrossRef] 54. Seo, B.C.; Krajewski, W.F.; Mishra, K.V. Using the new dual-polarimetric capability of WSR-88D to eliminate anomalous propagation and wind turbine effects in radar-rainfall. Atmos. Res. 2015, 153, 296–309. [CrossRef] 55. Iowa State University Iowa Environmental Mesonet. Available online: https://mesonet.agron.iastate.edu/ sites/locate.php (accessed on 15 August 2017). 56. Krause, P.; Boyle, D.P.; Bäse, F. Comparison of different efficiency criteria for hydrological model assessment. Adv. Geosci. 2005, 5, 89–97. [CrossRef] 57. Reusser, D.E.; Blume, T.; Schaefli, B.; Zehe, E. Analysing the temporal dynamics of model performance for hydrological models. Hydrol. Earth Syst. Sci. 2009, 13, 999–1018. [CrossRef] 58. Legates, D.R.; McCabe, G.J. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour. Res. 1999, 35, 233–241. [CrossRef] 59. Jachner, S.; Boogaart, G.; Petzoldt, T. Statistical methods for the qualitative assessment of dynamic models with time delay (R Package qualV). J. Stat. Softw. 2007, 22.[CrossRef] 60. Zalenski, G.; Krajewski, W.F.; Quintero, F.; Restrepo, P.; Buan, S. Analysis of national weather service stage forecast errors. Weather Forecast. 2017, 32, 1441–1465. [CrossRef] 61. Fiedler, W.; King, W.; Schwanz, N. Independent Panel of Engineers: Report on Breach of Delhi Dam; Iowa Department of Natural Resources: Des Moines, IA, USA, 2010. 62. Lee, K.; Firoozfar, A.R.; Muste, M. Technical Note: Monitoring of unsteady open channel flows using the continuous slope-area method. Hydrol. Earth Syst. Sci. 2017, 21, 1863–1874. [CrossRef] 63. Quintero, F.; Sempere-Torres, D.; Berenguer, M.; Baltas, E. A scenario-incorporating analysis of the propagation of uncertainty to flash flood simulations. J. Hydrol. 2012, 460–461, 90–102. [CrossRef] 64. Javier, J.R.N.; Smith, J.A.; Meierdiercks, K.L.; Baeck, M.L.; Miller, A.J. Flash flood forecasting for small urban watersheds in the baltimore metropolitan region. Weather Forecast. 2007, 22, 1331–1344. [CrossRef] 65. Ogden, F.L.; Raj Pradhan, N.; Downer, C.W.; Zahner, J.A. Relative importance of impervious area, drainage density, width function, and subsurface storm drainage on flood runoff from an urbanized catchment. Water Resour. Res. 2011, 47, 1–12. [CrossRef] 66. Neal, J.; Schumann, G.; Bates, P. A subgrid channel model for simulating river hydraulics and floodplain inundation over large and data sparse areas. Water Resour. Res. 2012, 48, 1–16. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).