# Modeling Spatio-Temporal Dynamics of BMPs Adoption for Stormwater Management in Urban Areas

^{1}

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## Abstract

**:**

^{2}= 0.67, PBIAS = 7.2) was used to simulate spatio-temporal patterns of household BMP adoption in two nearby watersheds (Watts Branch watershed between Washington, D.C., and Maryland; Watershed 263 in Baltimore), each of which are characterized by different socio-economic (population density, median household income, renter rate, average area per household, etc.) and physical attributes (total area, percentage of canopy in residential area, average distance to nearest BMPs, etc.). The BMP adoption rate was considerably higher at the Watts Branch watershed (14 BMPs per 1000 housing units) than at Watershed 263 (4 BMPs per 1000 housing units) due to distinct differences in the watershed characteristics (lower renter rate and poverty rate; higher median household income, education level, and canopy rate in residential areas). This research shows that adoption behavior tends to cluster in urban areas across socio-economic boundaries and that targeted, community-specific social interventions are needed to reach the NPS control goal.

## 1. Introduction

## 2. Study Areas

^{2}that partly extends into Washington, D.C., and partly into Prince George’s County, Maryland. It intersects with ten census tracts in Washington, D.C. (7803–9905), and five census tracts in Maryland (802,600–803,001), and it contains 13,327 residential lots where BMPs may be installed. Its population in 2010 was 48,168 people distributed among 20,536 households, and the population increased by nearly 15% in 10 years to 55,002 people occupying 22,021 households in 2020. The median household income increased by more than 40% over the same period, starting from USD 37,176 in 2010 and increasing to USD 52,798 in 2020. This watershed is considered to be healthy from a socio-economic perspective as it has undergone population and economic growth, a reduction in vacant lots, a reduction in poverty, and an increase in college education. In contrast, Watershed 263, which is in Baltimore City, Maryland, has a highly urban landscape and an area of approximately 7 km

^{2}. It intersects with 14 census tracts and contains 11,863 residential lots for possible BMP implementation. The population of this watershed decreased by 10% between 2010 and 2020, decreasing from 30,344 people to 27,594 people. The median household income increased by 18% from USD 27,125 in 2010 to USD 32,362 in 2020, but the vacancy rate, renting rate, and poverty rate all increased by approximately 10% during that period. The percentage of residents who attended college increased by nearly 40% during these 10 years, but the percentage of those with a bachelor’s degree did not change. From a socio-economic perspective, this watershed is considered to be less healthy than Watts Branch due to its mixed educational trajectory and increasing vacancy and poverty rates.

## 3. Materials and Methods

#### 3.1. BMP Data Used for Model Development

#### 3.2. Physical and Demographic Factors for BMP Adoption Model

#### 3.3. Potential BMP Adoption Models and Evaluation Metrics

^{2}), the percentage of bias (PBIAS), and the mean-square-error (MSE). The mathematical forms of these metrics are presented in Equations (2)–(4):

^{2}(also called the Nash–Sutcliffe efficiency coefficient, NSE), quantifies the amount of variance in the observed variable (y) that is explained by the model. A value of 1 (the maximum possible) indicates a perfect prediction. In linear regression, R

^{2}is equal to the square of the coefficient of linear correlation, but this equivalence breaks down under nonlinear parameterization approaches. PBIAS measures the average tendency of the predicted values to be larger or smaller than observed ones (it is the ratio of the mean error to the mean observed value). A value of 0 indicates perfect predictions. MSE is the mean of squared errors between the model output and observations, with 0 indicating a perfect fit once again. In addition to these metrics, for the case of linear regression, a t-test was conducted to evaluate the significance of each of the model’s input variables, with an early view towards potential model simplification.

^{2}relative to that obtained by LSE but no longer guarantee zero bias (and this also breaks the equivalence between R

^{2}and the square of the correlation coefficient). Both methods have found uses in machine learning as well as statistics. LASSO (least absolute shrinkage and selection operator) and ridge regression were developed to mitigate issues related to high degrees of covariance between model input variables, which may occur with the socio-economic variables that are in the present study. To this effect, LASSO regression adds an L1 regularization term ($\lambda \sum {|\beta}_{i}|$) into the ordinary regression system, while ridge regression adds an L2 regularization term ($\lambda \sum {\left|{\beta}_{i}\right|}^{2}$) [39]. These terms can be viewed as penalty terms in the form of the resulting optimization problem and serve as the trade-off bias accuracy for determination (or efficiency). In this study, both LASSO and ridge regressions were applied for the prediction of BMP adoption likelihood using the same dataset as that used for the ordinary least squares, and both regressions were evaluated using the 3 metrics discussed above and were compared with the linear regression model.

## 4. Results and Discussion

#### 4.1. Results of BMP Adoption Model Development

^{2}, are 0.51 and 0.52, respectively, which indicates that the model explains just over half (51% or 52%) of the observed variability in BMP adoption rates in the study area. LASSO and ridge regression approaches attempt to limit the negative impacts of correlated inputs by trading determination for bias. LASSO regression accordingly produced a model that has a slightly higher coefficient of determination than ordinary least squares (R

^{2}= 0.52) but at the cost of a negative bias, where the adoption rates are generally underpredicted. Ridge regression performs more poorly by providing no improvement in the coefficient of determination and causing a more significant underprediction than the LASSO model. Neither approach can be considered better than the ordinary least squares model in this study.

^{2}= 0.13) and produces predictions with the most bias out of the tested methods. The random forest model, on the other hand, explains the largest amount of observed variability in adoption rates at 67%, although it also tends to underpredict adoption, which is listed here by an average of over 7%; this suggests that it predicts low BMP adoption rates better than larger ones wherein most of its underpredictions would be located. The accurate prediction of the lower adoption rates corresponds to the preferred behavior for this model, which is targeted at the identification of zones with low likelihoods of spontaneous BMP installation, where social interventions should be focused for maximum return on environmental investments.

^{2}) [51]. This process breaks the relationship between the selected feature and the model’s output, resulting in a drop in the value of R

^{2}that reflects the degree to which the shuffled input impacts the accuracy of model predictions. The results of this process are presented in Figure 4 for each of the 21 model inputs and are expressed in terms of the reduction in R

^{2}resulting from shuffling out that input. Four of the model’s inputs stand out as most significant from this analysis: (1) average distance to the nearest BMP; (2) residential housing density; (3) percentage of residents with a college degree; and (4) average area per house. If these features were entirely uncorrelated with each other, then removing just the first two from the model (i.e., average distance to the nearest BMP and residential housing density), would decrease its coefficient of determination down to essentially zero, indicating their substantial importance. The percentage of residents with a college degree is also very important, as shuffling it out reduces the model’s R

^{2}value by 0.23 (from its original value of 0.67). Out of these four significant input features, two were also identified in the less accurate linear regression model: distance to BMPs and area per house. The less plausible features of the least squares model (median income and percentage of African American residents) are not identified as particularly significant in the more accurate random forest model. Conversely, the more plausible adoption factor of college education, which could reflect a better appreciation of environmental matters, is highlighted by this higher performing formulation.

#### 4.2. Application of the BMP Adoption Likelihood Model

#### 4.2.1. BMP Adoption Simulation Algorithm

- Step 1
- Based on the initial BMP density setting (e.g., 1 per 1000 housing units), randomly selected N residential parcels for BMP allocation. Set step $\mathrm{t}=0$.
- Step 2
- Calculate the distance of all residential lots to the nearest BMPs. Update the average minimum distance to BMPs for all census tracts.
- Step 3
- Predict the number ${\mathrm{n}}_{\mathrm{i}}$ new BMP adoption for census tract $\mathrm{i}$ based on the regression model.
- Step 4
- Randomly select ${\mathrm{n}}_{\mathrm{i}}$ residential parcels in census tract $\mathrm{i}$ for BMP adoption based on possibility $\mathrm{p}$ as detailed below:
- 4.1.
- For each residential lot, find the maximum distance to the nearest BMP and use the maximum value minus the current distance to the nearest BMP for each residential lot as the weight.
- 4.2.
- Calculate the allocation probability for each residential parcel as weight/sum_of_all_weights

- Step 5
- If the stop criterion is satisfied, terminate the process; else, set $\mathrm{t}=\mathrm{t}+1$, and go to Step 2.

#### 4.2.2. Baseline Simulation Results for BMP Adoption

^{2}vs. 556 m

^{2}), and poverty rate (29% vs. 13%) also favor Maryland above DC. Even though these tracts are in the same watershed, those located in Maryland correspond to “healthier” socio-economic conditions and have higher BMP adoption rates than those located in Washington, D.C. In contrast, all of the census tracts located in Watershed 263 have similar BMP adoption rates in the ten-year simulation results. Most tract-level BMP adoption rates increase in the first two or three years and then remain stable for the following seven years. The peak BMP adoption rate is between 3 and 10, with an average of 5 new BMPs per 1000 housing units per year. Compared with the census tracts in Watts Branch in Washington, D.C., about half of the census tracts in Watts Branch have a similar BMP adoption rate to that of Watershed 263. Overall, the BMP adoption rate is higher in Watts Branch than in Watershed 263, and this better performance results from the five “healthier” census tracts that are located in Maryland in this watershed.

^{2}) and 521 (about 70 BMPs per km

^{2}), respectively, for the duration of nine years. This difference in the level of implementation appropriately corresponds with differences in factors affecting BMP adoption rate in the two watersheds, such as median household income and poverty rate, all of which motivate the BMP adoption.

#### 4.2.3. BMP Adoption Response to Changing Conditions

#### 4.2.4. BMP Adoption and NPS Constituent Control

## 5. Conclusions

^{2}value of 0.67, PBIAS of −7.24, and MSE of 19.11. Based on this model, the spatio-temporal dynamics of BMP adoption behavior in two urban watersheds, Watts Branch (relatively “healthy”) and Watershed 263 (relatively “unhealthy”), were quantitatively analyzed. This research shows that distance to the nearest BMPs, education level, residential property (size, canopy value), and economic factors significantly impact BMP adoption. This simulation of BMP adoption in two watersheds also conforms to our estimation of “healthy” (Watts Branch) and “unhealthy” (Watershed 263) watersheds, where the BMP adoption rate in Watts Branch is much higher than that of Watershed 263. Even in the same watershed, “healthy” census tracts will have a much higher BMP adoption rate than “unhealthy” census tracts. Compared with the BMP adoption scenarios, to achieve 20% of residential parcels being covered by BMPs, Watts Branch will need 14 years; Watershed 263 will need more than 30 years. However, this three-fold longer time could not ensure the NPS pollutants control goal. A significant portion of the NPS pollutants hotspots are in open space, and other stakeholders aside from residents are needed to implement the BMPs.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Study area and locations. (

**a**) Relative location of the Washington, D.C., Watts Branch watershed and Watershed 263; (

**b**) census tracts and residential lots in Watershed 263; (

**c**) total BMPs installed between 2009 and 2020 in Washington, D.C.; (

**d**) census tracts and residential lots in Watts Branch.

**Figure 2.**BMPs installed through the RiverSmart Home project in Washington, D.C.; (

**a**) BMPs installed each year; (

**b**) Percentages of the different types of all BMPs installed between 2009 and 2020.

**Figure 3.**Illustration of a hyperplane used in support vector regression; (

**a**) decision trees used in random forest regression (

**b**).

**Figure 4.**Feature importance of the random forest regression model of BMP adoption likelihood identified using the input feature permutation approach.

**Figure 7.**Spatio-temporal BMP adoption in both watersheds in a three-year step. Red dots: predicted BMPs adoption, gray areas: residential lots; green lines: watershed boundary; (

**a**–

**d**) BMPs adoption in a 3-year step around Watts Branch Watershed, (

**e**–

**h**) BMPs adoption in a 3-year step around watershed 263.

**Figure 8.**Impacts of initial BMP density on BMP adoption in (

**a**) Watts Branch Watershed and (

**b**) Watershed 263.

**Figure 9.**BMP adoption rates simulated by the random forest model for ten years using 2010 and 2020 census tract data for Watts Branch and Watershed 263.

**Figure 11.**BMP allocation and nutrient hotspots in two watersheds. (

**a**) Map depicting 20% of residential lots covered by BMPs in Watts Branch in 14 years; (

**b**,

**c**) map depicting nitrogen and phosphorus output hotpots in Watts Branch, as calculated by SWAT simulation; (

**d**) map depicting 7.6% of residential lots covered by BMPs in Watershed 263; (

**e**,

**f**) map depicting nitrogen and phosphorus output hotpots in Watershed 263, as calculated by SWAT simulation.

Watts Branch | Watershed 263 | |||
---|---|---|---|---|

2010 | 2020 | 2010 | 2020 | |

Physical | ||||

Total area (km^{2}) | 18.81 | 7.43 | ||

Residential area (km^{2}) | 6.91 | 1.33 | ||

Total residential lots | 13,327 | 11,863 | ||

Demographic | ||||

Total population | 48,168 | 55,002 | 30,344 | 27,594 |

Total housing units | 20,536 | 22,021 | 16,668 | 17,054 |

Vacant rate (%) | 11 | 10 | 30 | 33 |

Renter rate (%) | 51 | 47 | 67 | 69 |

Poverty rate (%) | 24 | 21 | 35 | 39 |

College (%) | 22 | 27 | 16 | 22 |

Bachelor’s degree (%) | 8 | 13 | 9 | 9 |

Median household income | USD 37,176 | USD 52,798 | USD 27,125 | USD 32,362 |

Features | Copayment | Total Costs |
---|---|---|

Rain barrels | USD 50 or USD 70 per rain barrel, depending on the types (limit two) | USD 150 per rain barrel |

Shade trees | USD 0 per shade tree (no limit) | USD 50 per shade tree |

Rain gardens | USD 100 per 50 sq. ft. (USD 21/m^{2}) (limit two) | USD 86/m^{2} |

BayScaping (Native Landscaping) | USD 100 per 120 sq. ft. (USD 8.96/m^{2}) (limit two) | USD 13/m^{2} |

Permeable pavers | USD 10/sq. ft. (USD107/m^{2}) for replacing impervious surface with permeable pavers and/or USD 5/sq. ft. (USD 53.82/m^{2}) for removing and replacing impervious surface with vegetation; limit of USD 4000. | USD 128/m^{2} or USD 60/m^{2} |

Mean | Median | Std | Min | Max | |
---|---|---|---|---|---|

Physical features | |||||

Total area (m^{2}) | 988,714 | 601,065 | 1,338,461 | 171,894 | 11,417,542 |

Total residential area (m^{2}) | 234,567 | 165,268 | 228,058 | 0 | 1,392,595 |

Percentage of canopy in residential area (%) | 29.44 | 26.96 | 9.16 | 0 | 47.71 |

Average distance to nearest BMPs (m) | 275 | 154 | 298 | 0 | 2845 |

Demographic features | |||||

Total population | 3362 | 3072 | 1301 | 33 | 7436 |

Total household | 1658 | 1507 | 807 | 2 | 5375 |

Population/1000 m^{2} | 6 | 5 | 4 | 0 | 26 |

Household/1000 m^{2} | 3 | 3 | 3 | 0 | 17 |

Population/1000 residential m^{2} | 34 | 17 | 75 | 0 | 732 |

Household/1000 residential m^{2} | 15 | 8 | 25 | 0 | 196 |

Percentage of White (%) | 34.69 | 25.56 | 32.04 | 0.3 | 90.88 |

Percentage of Black (%) | 55.4 | 60.24 | 35.38 | 2.15 | 98.35 |

Percentage of Asian (%) | 3.16 | 2.1 | 3.44 | 0 | 21.27 |

Vacant rate (%) | 10.15 | 9.29 | 4.79 | 0 | 27.78 |

Renter rate (%) | 55.2 | 58.24 | 23.24 | 0 | 98.05 |

Median household income (USD) | 47,433 | 37,400 | 25,810 | 12,202 | 166,298 |

Median age | 35 | 35 | 7 | 20 | 63 |

Average area per house (m^{2}) | 172.59 | 124.27 | 234.91 | 0 | 2676.01 |

Poverty rate (%) | 14.15 | 8.5 | 14.34 | 0 | 58.1 |

College degree rate (%) | 18.52 | 18.34 | 8.79 | 0 | 42.86 |

Bachelor’s degree rate (%) | 20 | 20.15 | 11 | 1 | 48.34 |

BMPs adoptions from 2010 to 2019 | 77 | 41 | 107 | 0 | 619 |

Coefficient | Standard Error of Coefficient | t | p > |t| | |
---|---|---|---|---|

Physical | ||||

Total area (m^{2}) | −2.26 × 10^{−6} | 5.29 × 10^{−7} | −4.266 | 0 |

Total residential area (m^{2}) | 4.89 × 10^{−6} | 2.44 × 10^{−6} | 2.006 | 0.045 |

Percentage of canopy in residential area | 0.117 | 0.033 | 3.547 | 0 |

Average distance to nearest BMPs (m) | −0.0037 | 0.001 | −6.054 | 0 |

Demographic | ||||

Total population | −0.0004 | 0 | −0.878 | 0.38 |

Total household | 0.0003 | 0.001 | 0.333 | 0.739 |

Population/1000 m^{2} | −0.6524 | 0.223 | −2.921 | 0.004 |

Household/1000 m^{2} | 0.438 | 0.362 | 1.21 | 0.227 |

Population/1000 residential m^{2} | 0.1788 | 0.069 | 2.605 | 0.009 |

Household/1000 residential m^{2} | −0.1433 | 0.093 | −1.532 | 0.126 |

Percentage of White | −0.0647 | 0.045 | −1.442 | 0.149 |

Percentage of Black | −0.1077 | 0.037 | −2.903 | 0.004 |

Percentage of Asian | −0.1403 | 0.101 | −1.387 | 0.166 |

Vacant rate | −0.0422 | 0.037 | −1.137 | 0.256 |

Renter rate | −0.1316 | 0.012 | −11.23 | 0 |

Median household income (USD) | −0.0002 | 1.97 × 10^{−5} | −9.474 | 0 |

Median age | 0.0431 | 0.044 | 0.987 | 0.324 |

Average area per house | 0.0305 | 0.003 | 9.036 | 0 |

Poverty rate | −0.0264 | 0.018 | −1.483 | 0.138 |

College degree rate | −0.041 | 0.028 | −1.474 | 0.141 |

Bachelor’s degree rate | 0.0442 | 0.028 | 1.557 | 0.12 |

Const | 23.854 | 4.783 | 4.988 | 0 |

Coefficient | Standard Error of Coefficient | t | p > |t| | |
---|---|---|---|---|

Physical | ||||

Total area (m^{2}) | −1.86 × 10^{−6} | 3.78 × 10^{−7} | −4.916 | 0.000 |

Percentage of canopy in residential area | 0.1376 | 0.029 | 4.785 | 0.000 |

Average distance to nearest BMPs (m) | −0.0038 | 0.001 | −6.456 | 0.000 |

Demographic | ||||

Population/1000 m^{2} | −0.3351 | 0.056 | −5.982 | 0.000 |

Population/1000 residential m^{2} | 0.0643 | 0.012 | 5.269 | 0.000 |

Percentage of Black | −0.0740 | 0.009 | −7.996 | 0.000 |

Renter rate | −0.1548 | 0.009 | −17.373 | 0.000 |

Median household income (USD) | −0.0002 | 1.36 × 10^{−5} | −14.482 | 0.000 |

Average area per house | −0.0336 | 0.002 | −14.719 | 0.000 |

Const | 21.057 | 1.541 | 13.665 | 0.000 |

**Table 6.**Accuracy of the linear, LASSO, ridge, support vector, and random forest regression models of BMP adoption likelihood developed in this study.

Methods | ${\mathit{R}}^{2}$ | $\mathit{P}\mathit{B}\mathit{I}\mathit{A}\mathit{S}$ | $\mathit{M}\mathit{S}\mathit{E}$ |
---|---|---|---|

Linear regression | 0.51 | −1.88 | 28.09 |

Linear regression with features (p < 0.05) | 0.52 | −1.22 | 27.50 |

LASSO regression | 0.52 | −0.62 | 27.84 |

Ridge regression | 0.51 | −1.87 | 28.09 |

Support vector regression | 0.13 | −8.05 | 50.68 |

Random forest regression | 0.67 | −7.24 | 19.11 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Z.; Montas, H.; Shirmohammadi, A.; Leisnham, P.T.; Rockler, A.K.
Modeling Spatio-Temporal Dynamics of BMPs Adoption for Stormwater Management in Urban Areas. *Water* **2023**, *15*, 2549.
https://doi.org/10.3390/w15142549

**AMA Style**

Zhang Z, Montas H, Shirmohammadi A, Leisnham PT, Rockler AK.
Modeling Spatio-Temporal Dynamics of BMPs Adoption for Stormwater Management in Urban Areas. *Water*. 2023; 15(14):2549.
https://doi.org/10.3390/w15142549

**Chicago/Turabian Style**

Zhang, Zeshu, Hubert Montas, Adel Shirmohammadi, Paul T. Leisnham, and Amanda K. Rockler.
2023. "Modeling Spatio-Temporal Dynamics of BMPs Adoption for Stormwater Management in Urban Areas" *Water* 15, no. 14: 2549.
https://doi.org/10.3390/w15142549