# High-Resolution Spatio-Temporal Estimation of Net Ecosystem Exchange in Ice-Wedge Polygon Tundra Using In Situ Sensors and Remote Sensing Data

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^{2}

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## Abstract

**:**

## 1. Introduction

_{2}sink [7].

_{2}effluxes are significantly higher in the centers of HCPs than in the ones of LCPs, which suggests that future polygon degradation could lead to an increase in soil CO

_{2}efflux.

## 2. Materials and Methods

#### 2.1. NGEE-Arctic Site

#### 2.2. Datasets

#### 2.2.1. Remote Sensing Data

#### 2.2.2. Tram and Flux Datasets

_{2}flux data, along the tram transect on eight different occasions during 2014. The soil moisture (dielectric permittivity) and fluxes were recorded at 21 of the 137 tram stations. Soil moisture was estimated using dielectric permittivity measurements from a time domain reflectometer. Small-scale net CO

_{2}fluxes between tundra surface and atmosphere were measured with a transparent closed-dynamic chamber connected to a Los Gatos Research, Inc. (San Jose, CA, USA) portable Greenhouse Gas Analyzer in the same manner as in Wainwright et al. [12] and Vaughn et al. [17]. For each measurement, the chamber was placed on a PVC base (30 cm diameter, installed ~15 cm deep) approximately 24 h prior to measurement. Fluxes were calculated from the slope of the linear section of greenhouse gas concentrations versus time. The chamber flux measurements were done during the day mostly between 11:00 and 20:00 (73% samples are between 11:00 and 15:00).

_{2}fluxes (AmeriFlux ID US-NGB [18]) were measured on a 3.75 m tall tripod in the vicinity of the tram setup, employing a Gill R3-50 sonic anemometer (Gill, Lymington, UK) together with a LI-COR LI-7500A CO

_{2}/H

_{2}O gas analyzer (LI-COR, Lincoln, NE, USA). We followed the standard calibration and data QA/QC procedures as widely applied across the Ameriflux network (ameriflux.lbl.gov, accessed on 7 July 2021). The tower-based NEE was averaged NEE between 11:00 and 20:00 each day. We assume that NEE in our study is representing the daytime average NEE (NEEday).

#### 2.3. Integration Strategy

**x**

_{t}= {x

_{i,t}| i = 1, …, n} representing NDVI at all pixels (the number of pixels is n) at Day t. We denote a data vector by

**z**

_{t}= {z

_{j,t}| j = 1, …, m}, which is a collection of data at Day t, including (1) the NDVI measurements at tram locations (1 ≤ j ≤ m

_{T}; the number of the tram measurements is m

_{T}), and (2) the gI data at pixels (m

_{T}+ 1 ≤ j ≤ m

_{T}+ m

_{VI}= m; the number of gI data pixels is m

_{VI}). At each time step, the data vector is described as a function of the state vector by the state-observation equation:

**z**

_{t}= H

**x**

_{t}+ K

**u**+

**w**(t)

**u**is a unit vector (a vector containing all elements equal to one with the length of m). Physically, the observation equation (Equation (2)) describes all the data as a function of target variables (NDVI in our case), so that—within the estimation framework—this equation transfers the information from the data to the target variables. H and K include the correlation parameters describing the data value as a function of NDVI at each pixel. At the tram pixels, the data are the direct measurements of NDVI:

_{j,t}= x

_{i,t}+ w

_{T},

_{T}follows an independent identically distributed (i.i.d.) zero-mean normal distribution with a fixed variance, representing a measurement error. For the non-tram locations, we assume that the j-th gI data is linearly correlated with NDVI at the i-th pixel such that:

_{j,t}= a

_{V}(t) x

_{i,t}+ b

_{V}(t) + w

_{V}(t),

_{V}(t) and b

_{V}(t) are the time-varying slope and intercept parameters in the linear correlations, and w

_{V}(t) represents the uncertainty in the correlations. We assume that w

_{V}(t) follows a zero-mean normal distribution with the variance (σ

_{V}) of the residual in the linear correlations. In Equation (2), the transfer matrix H is represented by:

_{j,i}= 1, if j-th tram station corresponds to i-th pixel (1 ≤ j ≤ m

_{T})

= a

_{V}(t), if j-th gI data corresponds to i-th pixel (m

_{T}+ 1 ≤ j ≤ m).

_{j,j}= 0, if j-th tram station corresponds to i-th pixel (1 ≤ j ≤ m

_{T})

= b

_{V}(t), if j-th gI data corresponds to i-th pixel (m

_{T}+ 1 ≤ j ≤ m).

_{V}(t), b

_{V}(t), and σ

_{V}are co-estimated at each time step during the Kalman filter. At each time step, the linear correlation is evaluated between the NDVI and gI, at the tram locations, and then the correlation parameters and the residual variance are calculated.

**x**

_{t}

_{+1}= A

**x**

_{t}+ B

**u**+

**v**(t)

**v**(t) represents the deviation from the linear model such as natural fluctuation. Although the time evolution of NDVI can be described by a mechanistic model, we use a data-driven, first-order autoregressive (AR1) model in this study, adapted from the spatio-temporal integration approach developed by Chen et al. (2013). In our model, the general form of Equation (7) is changed to:

_{i,t+1}= x

_{i,t}+ v

_{i}

_{i,t}to x

_{i,t}

_{+1}with the magnitude v

_{i}(in Equation (7), the matrix A is an identity matrix, and the matrix B is zero). This implementation is the same as Rastetter et al. [56] who implemented the temporal evolution of leaf area index (LAI) using the Kalman filter. Rastetter et al. [56] assumed that the change of LAI in each time step was small and hence the systematic change component could be approximated to be zero, and that the observation equation (equivalent to Equation (2) above) could transfer the information related to the temporal evolution in LAI from the data within the Kalman filter. Similarly, we assume that the daily change in NDVI is relatively small so that v

_{i}follows an i.i.d. zero-mean normal distribution with a fixed variance. The variance of v

_{i}is determined from taking the variance of the NDVI difference (x

_{i,t}

_{+1}—x

_{i,t}) at all the tram locations. Although the systematic increase and decrease are not included in this formulation, such temporal dynamics are captured based on the tram information represented in Equation (3) with the Kalman filter.

**x**

_{t}and its estimation variance (the algorithm is described in Appendix A). The Kalman filter consists of prediction and update at each time step. In the prediction step, the state transition equation (Equation (7)) is used to predict the state vector (i.e., NDVI at all the pixels) at the next time step

**x**

_{t}

_{+1}from the previous time step

**x**

_{t}. In the update step (or correction step), the estimate of the state vector is improved or corrected by including the tram NDVI and airborne gI data through the observation equation (Equation (2)). In this update step, the information transfers from the data to the target variables (e.g., the estimates of NDVI). The covariance of the state vector is estimated at each step; each diagonal element of the covariance matrix is the estimation variance σ

_{xi,t}, representing the uncertainty in the estimates.

_{i,t}) is a function of NDVI such that:

_{i,t}= f(x

_{i,t}) + ε

_{t},

_{t}in this relationship. To account for the uncertainty in this relationship, we used the variance propagation formula, in which the variance of y

_{i,t}is |f’(x

_{i,t})|

^{2}σ

_{xi,t}+ σ

_{y}, where f’ is the first derivative of the function f, and σ

_{xi,t}is the estimation variance of NDVI at pixel i and time step t derived from the Kalman filter, and σ

_{y}is the variance of the residual in the NEEday-NDVI relationship. Once the NEEday map is created, we computed the weighted average of NEEday (Equation (9)) within the EC flux tower footprint to compare with the NEEday from the EC flux tower data. The weights were calculated based on the contribution of each pixel to the tower data in the footprint model.

**z**

_{t}. The Kalman filtering approach has been used extensively for remote sensing and environmental science applications as well as for integrating ecosystem or land surface models with eddy-covariance flux tower data [39,56]. Our unique contribution is to seamlessly integrate spatio-temporal disparate datasets sampled over a range of spatial and temporal scales, which addresses the particular challenge of integrating spatially extensive but temporally sparse data with high frequency but spatially sparse data.

## 3. Results

^{2}= 0.57 and p-value of <1 × 10

^{−13}). On the other hand, the correlations between the airborne-based gI (one-time acquisition) and the tram-based NDVI (multiple acquisitions) change over time (Figure 6b). The Spearman correlation coefficients are −0.10 (p-value 0.26), 0.63 (p-value < 0.01), 0.65 (p-value < 0.01) and −0.01 (p-value 0.92) on Days 182, 206, 221 and 256, respectively. While the correlations are not significant in the shoulder seasons, they are higher in the middle of the growing season when the NDVI and NEE are most spatially heterogeneous.

^{−4}. Since the EC data has large scatter, we smoothed data with the moving average of the 15-day window to represent the seasonal variability. Different from earlier studies (e.g., Rasteter et al., 2010), the tower data were not included in the estimation, and we did not calibrate any parameters according to the flux tower data. We would note that the flux-tower data often have large deviation and scattering (Fox et al., 2008).

## 4. Discussion

^{2}/s across the site, the range of which is larger than that of the flux tower-measured NEE across different drained lake basins in this region [21]. This can possibly be attributed to the spatial averaging effect that occurs for the flux tower data, which is unable to resolve the spatial variability of fluxes associated with microtopography in ice-wedge polygons. Nor can such microtopographic variability be captured by the low-resolution satellite-based estimations of NDVI and NEEday.

_{2}uptake (i.e., high NDVI and NEEday) than other features across different polygon types, and also that the troughs have higher values than LCP centers, even though they both had high soil moisture. This is possibly because low centers tended to have deep ponded water and anoxic conditions that inhibit vegetation growth [13]. In terms of temporal variability, both NDVI and NEEday were low at the dry rims and the center of HCPs throughout the season, while they were more dynamic at the troughs and center of LCPs. Although both NDVI and NEE changed over time, their correlation was consistent along the same curve. In addition, the spatial heterogeneity of NDVI and NEEday was persistent during most of the growing season such that the high NDVI and NEEday regions tended to be the same throughout the season. This is why a single image of gI was able to describe the spatial heterogeneity. This is consistent with the previous findings on the relationship between soil moisture and plant vigor by Dafflon et al. [24], using soil electrical conductivity from electrical resistivity tomography (ERT), and greenness index from pole- and UAS-mounted cameras.

## 5. Summary

_{2}uptake than the centers of LCPs, and the HCP areas have a larger spatial coverage of troughs. Our results suggest the importance of considering microtopographic features for carbon exchange, and the need to integrate multi-type multiscale datasets to capture the microtopographic effects on the spatio-temporal dynamics of NDVI and NEE.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{t}, ${\widehat{\sigma}}_{i,t}$, is the estimation variance at each pixel, representing the uncertainty in ${\widehat{\mathit{x}}}_{t}$.

**x**

_{t}from the previous step. The state transition equation (Equation (7)) is used to predict the expected value of the state vector as ${\widehat{\mathit{x}}}_{t|t-1}$ based on the estimate at the previous time step ${\widehat{\mathit{x}}}_{t-1}$:

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**Figure 1.**Schematic diagrams of different polygon types and polygon features (from Wainwright et al., 2015): (

**a**) low-centered, (

**b**) flat-centered and (

**c**) high-centered polygons. In this study, we defined rims only when the polygon edges are higher than the centers.

**Figure 2.**(

**a**) High-resolution LiDAR digital elevation model (DEM) over the NGEE Arctic site (elevation in meters), (

**b**) orthorectified airborne RGB image, and (

**c**) greenness index (gI) computed from the RGB image. In the plots, the black line is the tram location. In (

**a**), the same DEM was used as Hubbard et al. (2013) and Wainwright et al. (2015).

**Figure 3.**(

**a**) Tram system installed at the NGEE-Arctic site, and (

**b**) the aerial image of the tram track location with the point-measurement locations. In (

**a**), the tram moves on two rails, carrying a sensor package on its arm. The flux chambers can be seen on the ground.

**Figure 4.**The structure of the multiscale data integration. The black boxes represent different types of datasets (fluxes, tram NDVI, gI) at different spatial and temporal scales. The red boxes represent the target variables to estimate; i.e., spatially and temporally continuous NDVI and NEE. The blue lines represent the correlations obtained from the datasets. The red lines represent the estimation based on those datasets and correlations.

**Figure 5.**Spatiotemporal variability of observed properties along the tram transect: (

**a**) LiDAR-based elevation with the polygon type-feature definition, (

**b**) NDVI on the different day of year (DOY), (

**c**) soil moisture (as dielectric permittivity K

_{a}) and (

**d**) NEE. In (

**b**), the NDVI data are shown on selected DOYs. All the measurement dates are shown for soil moisture in (

**c**) and for NEE in (

**d**).

**Figure 6.**Correlations between (

**a**) NDVI and NEEday based the chamber flux measurements on DOY 182, 206, 221 and 256, and (

**b**) NDVI and gI (measured on 7 August 2013). In (

**b**), NDVI was measured on different dates, while gI values are from the one-time data acquisition.

**Figure 7.**Changes of NDVI over the site in 2014 on (

**a**) DOY 185, (

**b**) DOY 210 and (

**c**) DOY 240, and the changes of NEEday (in μmol/m

^{2}/s) over the site on (

**d**) DOY 185, (

**e**) DOY 210 and (

**f**) DOY 240. In each plot, the black line represents the tram location, and the white triangle is the flux tower location.

**Figure 8.**Comparison between the daytime averaged flux tower NEEday (black squares) and the estimated NEEday (weighted-average within the tower footprint) during the growing season. The thick red line represents the mean estimate, while the thin red lines represent the 99-percent confidence interval.

**Table 1.**Spatial average of NEEday and NDVI temporal average (Av.) over the growing season in each polygon type-feature combination. The standard deviation (SD) is also shown. The spatial coverage is the area of each polygon feature within each polygon type (The total area is normalized to 1).

Av. NDVI | (SD) | Av. NEEday, μmol/m ^{2}/s | (SD) | Spatial Coverage | ||
---|---|---|---|---|---|---|

LCP | Trough | 0.59 | (0.014) | −3.4 | (0.64) | 0.14 |

Center | 0.52 | (0.010) | −2.1 | (0.41) | 0.36 | |

Rim | 0.44 | (0.011) | −1.4 | (0.34) | 0.5 | |

FCP | Trough | 0.58 | (0.016) | −3.2 | (0.63) | 0.29 |

Center | 0.48 | (0.016) | −1.7 | (0.37) | 0.21 | |

Rim | 0.41 | (0.016) | −1.1 | (0.27) | 0.5 | |

HCP | Trough | 0.56 | (0.013) | −2.8 | (0.56) | 0.5 |

Center | 0.43 | (0.012) | −1.2 | (0.30) | 0.5 |

**Table 2.**Spatial average of NEE and NDVI temporally averaged (Av.) over the growing season in each polygon type, and the spatial average of peak NEE and NDVI in each polygon type.

Av. NDVI | (SD) | Av. NEEday, μmol/m^{2}/s | (SD) | |
---|---|---|---|---|

LCP | 0.49 | (0.011) | −2.4 | (0.42) |

FCP | 0.48 | (0.016) | −2.3 | (0.43) |

HCP | 0.50 | (0.012) | −2.6 | (0.45) |

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## Share and Cite

**MDPI and ACS Style**

Wainwright, H.M.; Oktem, R.; Dafflon, B.; Dengel, S.; Curtis, J.B.; Torn, M.S.; Cherry, J.; Hubbard, S.S.
High-Resolution Spatio-Temporal Estimation of Net Ecosystem Exchange in Ice-Wedge Polygon Tundra Using In Situ Sensors and Remote Sensing Data. *Land* **2021**, *10*, 722.
https://doi.org/10.3390/land10070722

**AMA Style**

Wainwright HM, Oktem R, Dafflon B, Dengel S, Curtis JB, Torn MS, Cherry J, Hubbard SS.
High-Resolution Spatio-Temporal Estimation of Net Ecosystem Exchange in Ice-Wedge Polygon Tundra Using In Situ Sensors and Remote Sensing Data. *Land*. 2021; 10(7):722.
https://doi.org/10.3390/land10070722

**Chicago/Turabian Style**

Wainwright, Haruko M., Rusen Oktem, Baptiste Dafflon, Sigrid Dengel, John B. Curtis, Margaret S. Torn, Jessica Cherry, and Susan S. Hubbard.
2021. "High-Resolution Spatio-Temporal Estimation of Net Ecosystem Exchange in Ice-Wedge Polygon Tundra Using In Situ Sensors and Remote Sensing Data" *Land* 10, no. 7: 722.
https://doi.org/10.3390/land10070722