# Topographic Wetness Index as a Proxy for Soil Moisture in a Hillslope Catena: Flow Algorithms and Map Generalization

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}m

^{−3}(VWC) from a network of moisture sensors over time. By examining some of the possible sensitivities of the TWI algorithm, we intended to find the algorithm calculation settings that result in moisture values more closely correlated to the record of wetting and drying that we see in the network of soil moisture sensors positioned in various locations at the site.

## 2. Materials and Methods

^{3}/m

^{3}with the factory calibration on a typical mineral soil; resolution is 0.001 m

^{3}/m

^{3}(METER Group, Pullman, WA, USA). No special site-specific calibration was performed [62]. Readings were logged on a Decagon EM50 data logger (METER Group, Pullman, WA, USA).

^{3}/m

^{3}volumetric moisture from a functional moisture sensor were assumed to represent saturated soil and were imputed with the value 0.5 m

^{3}/m

^{3}. Similarly, any moisture readings less than 0.03 m

^{3}/m

^{3}from a functional moisture sensor were assumed to represent dry conditions and were imputed to the value 0.03 m

^{3}/m

^{3}. These values were chosen as the upper and lower range for saturated and dry mineral soils in the study landscape based on the reported error of the sensors and the soil water retention curves published by the National Cooperative Soil Survey Laboratory Data database of the United States Department of Agriculture for the soils at the site [63]. More details of data handling are given in the coverage of statistical methods below.

_{M}is a modified specific catchment area, t is the so-called “suction factor,” a parameter entered by the user, SCA

_{Max}is the maximum stable value for SCA

_{M}obtained through the iterations, and β is slope. The iterative algorithm allows adjacent pixels to contribute flow and continues for as long as the modified specific catchment area is less than the new modified specific catchment area. Increasing slope values and increasing t values both diminish the influence of adjacent pixels, thereby lessening the modification of the original specific catchment area. In the Saga GIS software, the default t value is set to 10 but can be modified by the user. In the original publication introducing the SWI, the equation above is given with a constant value of 15 (where the value t is placed in the above equation) [75] (Böhner and Selige, 2004). The formula parsed above was confirmed with the developers of the algorithm (J. Böhner 2021, personal communication, 2 November 2021). Following other authors [38], we tested the sensitivity of the t factor for its influence on the correlation between the SWI and observed soil moisture. While some authors [38] found that higher values of t led to greater coefficients of determination between the SWI and the observed soil moisture the highest value they chose to examine was t = 256. We increased our tested values by doubling orders of magnitude from t = 10 to t = 10

^{64}. This high value was chosen as the endpoint because the output of SWI rasters began to converge when t values were set between t = 10

^{32}and t = 10

^{64}.

#### Statistical Analysis

- Mean VWC for each month (April 2017–December 2021). A moisture-sensor-month combination was only included if the sensor gave readings for at least 10 unique days during that month.
- Mean VWC for each year (2017–2021). A sensor-year combination was only included if the sensor gave readings for at least 7 unique months, in each of which there were at least 10 unique days of readings.
- Grand mean VWC for the entire measurement period.
- Mean VWC by day during three months in the water year representing recharge, saturation, and use periods in the water year, represented in November, April, and September for the years 2017, 2018, 2019, 2020, and 2021.

- We fit a linear regression of VWC on TWI using data from all sensors with valid readings for the given time slice, then used that regression to generate predicted values for all sensors.
- We fit a linear regression of VWC on TWI and the depth of the sensor using data with valid readings during the time slice, then used that regression to generate predicted values for all sensors.
- We fit a linear regression of VWC on TWI using spatially blocked cross-validation (CV). Each cross-validation had as many folds as there were sensors used to fit the regression. For each CV fold, we omitted all data points from a single sensor (1 to 3 data points depending on how many moisture probes were connected to the logger). The sensors attached to a single logger are spatially adjacent, making this is a conservative approach to address potential spatial autocorrelation in soil moisture unrelated to TWI. Within each fold, we fit the regression to all data except for the value(s) from the held-out sensor, then predicted the value(s) from the held-out sensor. We combined the predicted values from each CV fold, resulting in a vector of predicted values corresponding to all observed values.
- We fit another linear regression using spatially blocked CV in the same way as above but included both TWI and depth of the moisture sensor as predictors.

## 3. Results

^{4}to t = 10

^{16}. When elevation models were resampled to 7 m, however, single-flow algorithms performed at a similar or sometimes better level. The D8 algorithm applied to a resampled 7 m elevation model gave the best performance for predicting annual soil moisture of all algorithms. Filtering was a better strategy for map generalization when using multiple flow direction algorithms while resampling was better for single-flow direction algorithms.

^{4}gave the best performance; however, when DEM was resampled to larger pixel sizes, the best t factors were t = 10

^{16}, 10

^{32}, and 10

^{64}. As t was increased, its influenced was diminished and the output from SWI more closely resembled output from MFD v = 1.1 algorithm (but r values were slightly higher for SWI with t values > 10

^{8}than for TWI MFD v = 1.1). The best performing configurations for SWI were those applied to DEMs that had been either resampled to 3 m to 7 m pixel resolution, or filtered with a Gaussian filter of 2 sigma to 2.5 sigma, or a simple circular smoothing filter of 4 to 5 m. In the cases of filtered DEMs of 1 m resolution, performance improved with increasing suction factor values until t = 10

^{4}, with a modest decrease thereafter (Table 2). In the case of resampled DEMs performance increased with increasing suction factor until t = 10

^{16}for the DEMs resampled to the 3 to 7 m pixel sizes.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Site of modelling and volumetric water content measurements. The white circles indicate the locations of the soil moisture sensors. The green lines indicate elevation contours at the specified elevations in meters. Elevation is color-coded with blues indicating lower values and reds higher values.

**Figure 3.**Process of hydrological correction, flow algorithm application, and calculation of the 26 TWI output rasters for each elevation model for the study site.

**Figure 4.**Daily median soil moisture values at 15 cm. Shaded regions represent the 25th and 75th percentile soil moisture values and illustrate spatial variability at each timestep. Green line represents the median value of VWC for the sensors in locations with TWI values greater than 7.4; Orange dashed line represents the median VWC for the sensors in locations with TWI values less than 7.4 (using D8 algorithm) [14].

**Figure 5.**Selected output examples of TWI. Each row shows the effect of increasing a single factor on a set of TWI calculations. Terms used: v = convergence index value; w = pixel resolution; t = SAGA wetness index suction factor; r = Pearson correlation between TWI and average observed soil moisture; σ = standard deviation (meters) of the Gaussian curve used for DEM filtration.

**Figure 6.**Relationship between TWI and measured annual soil moisture for all models examined. Black dots represent models without any cross-validation. Cyan dots represent models run on generalized DEMs with cross validation. Red dots represent cross-validated models that run on DEMs with no initial generalization. Dots are set to a transparency level such that darker colors represent greater density of data points.

**Figure 7.**Correlation between TWI calculated with several flow algorithms and the measured mean soil moisture for the 5-year measurement period. Terms used: Braun = Braunschweiger Reliefmodel; D8 = deterministic 8 cell; DEMON = digital elevation model networks; Dinf = deterministic infinity; KRA = aspect-driven kinematic routing; MDinf = multiple triangular flow direction; “MFD, v = 1.1” = Multiple flow direction with convergence factor v = 1.1; MFDmd = multiple flow direction with maximum downslope gradient adjustment; Rho8 = stochastic single-direction flow algorithm; “SWI, t = 10”, “SWI, t = 10^4”, and “SWI, t = 10^16” = SAGA wetness index with a suction t-factor value of 10, 10

^{4}, and 10

^{16}respectively.

**Figure 8.**(

**left**) Selected months for all available years representing recharge (November), saturation (April), and use (September) periods. (

**right**) Pearson correlation strength between VWC measured at all depths and the topographic wetness index calculated with the D8 algorithm [14] on a 7 m resampled DEM for selected months. Each boxplot summarizes the data distribution of daily values for the given month.

**Figure 9.**(

**A**) Landform classification using GEOMORPHONS algorithm [52] and TWI. The output of the GEMORPHONS algorithm color coded to show landscape classes. (

**B**) TWI calculated with the D8 algorithm at high resolution. (

**C**) TWI calculated after resampling. (

**D**) TWI calculated after filtering. Terms used: w = pixel resolution; r = Pearson correlation between soil moisture and TWI; σ = sigma of the Gaussian curve for Gaussian filtering. Higher visualizations of TWI in (

**B**–

**D**), are darker blue, but TWI is shown on a unique relative scale for each image.

**Figure 10.**Influence of the suction factor (t) on the performance of the SAGA wetness index at DEM generalized to different grid cell resolutions (w). Pearson correlation between observed grand mean moisture and index value is indicated by “r”.

**Table 1.**Pearson correlation coefficients between average TWI from all tested algorithms and observed monthly moisture volumetric water content average values. The coefficients shown are the mean r values of TWI models with measured monthly mean soil moisture.

Model with Surface Measurements Only | Model with Depth | Cross-Validated Model with Depth | |
---|---|---|---|

DEM resolution (w) | r | r | r |

1 | 0.202 | 0.328 | −0.135 |

2 | 0.355 | 0.453 | 0.129 |

3 | 0.412 | 0.501 | 0.210 |

4 | 0.418 | 0.504 | 0.231 |

5 | 0.449 | 0.534 | 0.282 |

7 | 0.449 | 0.536 | 0.287 |

10 | 0.432 | 0.520 | 0.251 |

SSC window ^{a} | |||

Radius (m) | r | r | r |

1 | 0.251 | 0.371 | −0.031 |

2 | 0.307 | 0.411 | 0.053 |

3 | 0.347 | 0.444 | 0.099 |

4 | 0.406 | 0.493 | 0.196 |

5 | 0.419 | 0.503 | 0.215 |

7 | 0.422 | 0.507 | 0.232 |

10 | 0.403 | 0.492 | 0.199 |

Gaussian filter ^{b} | |||

Sigma (m) | r | r | r |

0.5 | 0.261 | 0.366 | −0.043 |

1.0 | 0.327 | 0.424 | 0.075 |

1.5 | 0.353 | 0.447 | 0.112 |

2.0 | 0.389 | 0.478 | 0.169 |

2.5 | 0.403 | 0.491 | 0.184 |

3.5 | 0.409 | 0.495 | 0.200 |

5.0 | 0.407 | 0.495 | 0.208 |

^{a}Simple smooth circular filter window applied to a 1 m DEM.

^{b}Gaussian filter applied to a 1 m DEM.

**Table 2.**Pearson correlation between grand mean VWC for the measurement period 2017–2021 and SAGA Wetness Index with increasing t values after DEM filtration.

Gaussian DEM Filtration | |||||||
---|---|---|---|---|---|---|---|

---------- sigma ---------- | |||||||

Suction Factor (t) | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.5 | 5.0 |

--- r --- | |||||||

1 × 10^{1} | 0.422 | 0.444 | 0.458 | 0.439 | 0.459 | 0.450 | 0.456 |

1 × 10^{2} | 0.507 | 0.542 | 0.562 | 0.565 | 0.577 | 0.562 | 0.512 |

1 × 10^{4} | 0.573 | 0.568 | 0.580 | 0.581 | 0.584 | 0.582 | 0.557 |

1 × 10^{8} | 0.562 | 0.534 | 0.553 | 0.573 | 0.576 | 0.568 | 0.541 |

1 × 10^{16} | 0.489 | 0.514 | 0.547 | 0.579 | 0.583 | 0.573 | 0.541 |

1 × 10^{32} | 0.513 | 0.521 | 0.548 | 0.579 | 0.583 | 0.573 | 0.541 |

1 × 10^{64} | 0.399 | 0.521 | 0.548 | 0.579 | 0.583 | 0.573 | 0.541 |

Filtration with simple circular averaging filter | |||||||

---------- filter radius, m ---------- | |||||||

Suction Factor (t) | 1 | 2 | 3 | 4 | 5 | 7 | 10 |

--- r --- | |||||||

1 × 10^{1} | 0.425 | 0.437 | 0.435 | 0.435 | 0.453 | 0.444 | 0.454 |

1 × 10^{2} | 0.513 | 0.533 | 0.553 | 0.564 | 0.577 | 0.550 | 0.492 |

1 × 10^{4} | 0.585 | 0.565 | 0.577 | 0.581 | 0.589 | 0.577 | 0.537 |

1 × 10^{8} | 0.546 | 0.516 | 0.556 | 0.578 | 0.579 | 0.563 | 0.516 |

1 × 10^{16} | 0.558 | 0.479 | 0.553 | 0.584 | 0.583 | 0.565 | 0.516 |

1 × 10^{32} | 0.548 | 0.492 | 0.554 | 0.584 | 0.587 | 0.564 | 0.516 |

1 × 10^{64} | 0.548 | 0.492 | 0.554 | 0.584 | 0.587 | 0.564 | 0.516 |

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## Share and Cite

**MDPI and ACS Style**

Winzeler, H.E.; Owens, P.R.; Read, Q.D.; Libohova, Z.; Ashworth, A.; Sauer, T.
Topographic Wetness Index as a Proxy for Soil Moisture in a Hillslope Catena: Flow Algorithms and Map Generalization. *Land* **2022**, *11*, 2018.
https://doi.org/10.3390/land11112018

**AMA Style**

Winzeler HE, Owens PR, Read QD, Libohova Z, Ashworth A, Sauer T.
Topographic Wetness Index as a Proxy for Soil Moisture in a Hillslope Catena: Flow Algorithms and Map Generalization. *Land*. 2022; 11(11):2018.
https://doi.org/10.3390/land11112018

**Chicago/Turabian Style**

Winzeler, Hans Edwin, Phillip R. Owens, Quentin D. Read, Zamir Libohova, Amanda Ashworth, and Tom Sauer.
2022. "Topographic Wetness Index as a Proxy for Soil Moisture in a Hillslope Catena: Flow Algorithms and Map Generalization" *Land* 11, no. 11: 2018.
https://doi.org/10.3390/land11112018