# Error Analysis on ESA’s Envisat ASAR Wave Mode Significant Wave Height Retrievals Using Triple Collocation Model

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Data Description

#### 2.1. Envisat ASAR Wave Mode Data

_{s}could be obtained by

**Figure 1.**Envisat ASAR imagette acquired on (

**a**) 01 August 2008 20:49:43; (

**b**) 1 January 2007 01:52:24; and (

**c**) 30 October 2008 22:08:29; with the image variance of 2.34, 1.02 and 1.30, respectively.

#### 2.2. Buoy Data

**Figure 2.**Locations of the 152 collocated buoys used in the validation. 54 of the buoys, deployed in the deep and open ocean are represented by red dots.

#### 2.3. Wavewatch III SWH Hindcast

## 3. Triple Collocation Error Model

_{buoy}(from NDBC buoy observation), H

_{ASAR}(from Envisat ASAR wave mode product) and H

_{ww}

_{3}(from ww3 wave model hindcast), with their independent random errors (e

_{buoy}, e

_{ASAR}and e

_{ww}

_{3}), are related to the hypothetical true significant wave height H linearly as shown below:

_{buoy}, β

_{ASAR}and β

_{ww3}in Equation (2) can be eliminated by introducing new variables ${H}_{X}^{\prime}={H}_{X}/{\mathrm{\beta}}_{\mathrm{X}}$, ${e}_{{X}^{\prime}}^{\prime}={e}_{X}/{\mathrm{\beta}}_{\mathrm{X}}$ (with subscript X standing for buoy, ASAR, and ww3, respectively), and then eliminate the unknown truth H utilizing the assumption of independent errors in order to obtain

_{ASAR}= 1, β

_{ww}

_{3}= 1 and scales H

_{ASAR}and H

_{ww}

_{3}with β

_{ASAR}and β

_{ww}

_{3}. In addition, first estimates for the errors and the calibration constants are determined using Equation (3) and a neutral regression [36], respectively. In the next step, H

_{ASAR}and H

_{ww}

_{3}are scaled with the newly found estimates for β

_{ASAR}and β

_{ww}

_{3}, and then the errors and the calibration constants are determined again, until the convergence is achieved.

_{buoy}) and the calibration coefficients of β

_{ASAR}and β

_{ww}

_{3}were calculated.

## 4. Triple Collocation and Error Analysis

#### 4.1. Collocation Criteria and Collocated Results

**Figure 3.**Collocation example of Envisat ASAR and NDBC buoy when the maximum collocation distance is set to be 50 km.

**Figure 4.**Histograms of triple collocation numbers with the all buoys (

**left**), and those in the deep and open ocean (

**right**). The red lines represent the collocation numbers of 1500.

#### 4.2. Triple Collocation Comparison Results

**Table 1.**Estimates of calibration coefficients, RMSE and SI for the triple collocated SWH datasets from all the 152 buoys, Envisat ASAR and ww3 model hindcasts.

Collocation Distance (km) | Calibration Coefficients | RMSE (m) | SI | |||||
---|---|---|---|---|---|---|---|---|

β_{ASAR} | β_{ww}_{3} | RMSE_{buoy} | RMSE_{ASAR} | RMSE_{ww}_{3} | SI_{buoy} | SI_{ASAR} | SI_{ww}_{3} | |

50 | 0.9495 | 0.9583 | 0.2427 | 0.5660 | 0.2330 | 11.93% | 27.84% | 11.82% |

60 | 0.9478 | 0.9618 | 0.2599 | 0.5725 | 0.2254 | 12.75% | 28.08% | 11.37% |

70 | 0.9510 | 0.9670 | 0.2698 | 0.5738 | 0.2254 | 13.33% | 28.26% | 11.39% |

80 | 0.9558 | 0.9716 | 0.2864 | 0.5710 | 0.2148 | 14.18% | 28.08% | 10.83% |

90 | 0.9583 | 0.9743 | 0.3027 | 0.5665 | 0.2042 | 15.08% | 28.00% | 10.33% |

100 | 0.9604 | 0.9771 | 0.3068 | 0.5617 | 0.2039 | 15.37% | 27.87% | 10.34% |

110 | 0.9619 | 0.9822 | 0.3191 | 0.5607 | 0.1953 | 16.08% | 27.94% | 9.92% |

120 | 0.9649 | 0.9842 | 0.3295 | 0.5646 | 0.1925 | 16.59% | 28.03% | 9.74% |

130 | 0.9642 | 0.9852 | 0.3366 | 0.5663 | 0.1897 | 16.90% | 28.04% | 9.56% |

140 | 0.9629 | 0.9866 | 0.3415 | 0.5678 | 0.1921 | 17.03% | 27.98% | 9.61% |

150 | 0.9631 | 0.9886 | 0.3466 | 0.5698 | 0.1938 | 17.23% | 28.00% | 9.65% |

160 | 0.9622 | 0.9904 | 0.3522 | 0.5721 | 0.1969 | 17.43% | 28.02% | 9.74% |

170 | 0.9609 | 0.9917 | 0.3557 | 0.5762 | 0.1986 | 17.55% | 28.15% | 9.79% |

180 | 0.9592 | 0.9920 | 0.3575 | 0.5773 | 0.2012 | 17.60% | 28.17% | 9.88% |

190 | 0.9581 | 0.9917 | 0.3605 | 0.5787 | 0.2017 | 17.71% | 28.22% | 9.89% |

200 | 0.9583 | 0.9927 | 0.3643 | 0.5789 | 0.2021 | 17.90% | 28.23% | 9.90% |

**Table 2.**As in Table 1, but for collocated datasets with the 54 buoys only in the deep and open ocean.

Collocation Distance (km) | Calibration Coefficients | RMSE (m) | SI | |||||
---|---|---|---|---|---|---|---|---|

β_{ASAR} | β_{ww}_{3} | RMSE_{buoy} | RMSE_{ASAR} | RMSE_{ww}_{3} | SI_{buoy} | SI_{ASAR} | SI_{ww}_{3} | |

50 | 0.9044 | 0.9614 | 0.2176 | 0.5017 | 0.1887 | 9.61% | 23.62% | 8.59% |

60 | 0.8989 | 0.9622 | 0.2253 | 0.5131 | 0.1875 | 9.85% | 24.02% | 8.45% |

70 | 0.9034 | 0.9637 | 0.2289 | 0.5122 | 0.1799 | 10.05% | 23.97% | 8.14% |

80 | 0.9069 | 0.9650 | 0.2376 | 0.5108 | 0.1789 | 10.47% | 23.92% | 8.12% |

90 | 0.9091 | 0.9661 | 0.2433 | 0.5094 | 0.1792 | 10.76% | 23.95% | 8.16% |

100 | 0.9075 | 0.9663 | 0.2415 | 0.5095 | 0.1848 | 10.75% | 24.14% | 8.46% |

110 | 0.9055 | 0.9662 | 0.2442 | 0.5072 | 0.1837 | 10.92% | 24.20% | 8.46% |

120 | 0.9057 | 0.9669 | 0.2545 | 0.5167 | 0.1779 | 11.36% | 24.57% | 8.16% |

130 | 0.9046 | 0.9666 | 0.2596 | 0.5188 | 0.1790 | 11.55% | 24.61% | 8.19% |

140 | 0.9042 | 0.9687 | 0.2669 | 0.5227 | 0.1778 | 11.81% | 24.67% | 8.08% |

150 | 0.9049 | 0.9699 | 0.2677 | 0.5236 | 0.1819 | 11.84% | 24.69% | 8.25% |

160 | 0.9034 | 0.9712 | 0.2676 | 0.5284 | 0.1870 | 11.78% | 24.82% | 8.43% |

170 | 0.9028 | 0.9716 | 0.2700 | 0.5330 | 0.1866 | 11.85% | 24.99% | 8.39% |

180 | 0.9024 | 0.9722 | 0.2699 | 0.5343 | 0.1896 | 11.82% | 25.01% | 8.50% |

190 | 0.9016 | 0.9719 | 0.2717 | 0.5363 | 0.1910 | 11.89% | 25.09% | 8.55% |

200 | 0.9014 | 0.9723 | 0.2738 | 0.5383 | 0.1899 | 11.98% | 25.10% | 8.51% |

**Figure 5.**Scatter plots of the comparison results with all the 152 buoys, for Envisat ASAR vs. NDBC buoys (

**the left panels**), Envisat ASAR vs. ww3 model (

**the middle panels**), and ww3 model vs. NDBC buoys (

**the right panels**). The collocation distances between ASAR and buoy in the plots from upper to bottom panels are 50 km, 100 km, 150 km and 200 km, respectively. The numbers in the color bar represent the number of collocated data points per 0.1 m histogram bins.

**Figure 6.**As in Figure 5, but for datasets with 54 buoys only in the deep and open ocean.

#### 4.3. Error Analysis on Collocation Distance

**Figure 7.**Change of Envisat ASAR wave mode SWH errors as functions of the collocation distance. Circles and lines refer the RMSEs of ASAR SWH estimated from triple collocations and the regression lines, respectively. Blue and red symbols indicate the results from all buoys and deep-and-open-ocean buoys, respectively.

#### 4.4. Discussion on Error of Envisat ASAR Wave Mode SWH in Coastal Waters

^{R}and velocity bunching MTF [1]:

^{v}the orbital velocity transfer function and j

^{2}= −1. And K, k

_{y}and k

_{y}are wavenumber, and its components in azimuth and radar look direction, respectively.

#### 4.5. Discussion on the Triple Collocation Results

## 5. Conclusions

## List of All Acronyms

ASAR | Advanced Synthetic Aperture Radar |

CDIP | Coastal Data Information Program |

Envisat | Environmental Satellite |

ECMWF | European Centre for Medium-Range Weather Forecasts |

ERS | European Remote Sensing Satellite |

IFREMER | Institut Français de Recherche pour l’Exploitation de la Mer |

IOWAGA | Integrated Ocean Waves for Geophysical and other Applications |

MEDS | Marine Environmental Data Service |

MTF | Modulation Transfer Function |

NDBC | National Data Buoy Centre |

NOAA | National Oceanic and Atmospheric Administration |

RAR | Real Aperture Radar |

RMSE | Root Mean Square Error |

SAR | Synthetic Aperture Radar |

SI | Scatter Index |

SWH | Significant Wave Height |

ww3 | WaveWatch III |

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Wang, H.; Zhu, J.; Yang, J. Error Analysis on ESA’s Envisat ASAR Wave Mode Significant Wave Height Retrievals Using Triple Collocation Model. *Remote Sens.* **2014**, *6*, 12217-12233.
https://doi.org/10.3390/rs61212217

**AMA Style**

Wang H, Zhu J, Yang J. Error Analysis on ESA’s Envisat ASAR Wave Mode Significant Wave Height Retrievals Using Triple Collocation Model. *Remote Sensing*. 2014; 6(12):12217-12233.
https://doi.org/10.3390/rs61212217

**Chicago/Turabian Style**

Wang, He, Jianhua Zhu, and Jingsong Yang. 2014. "Error Analysis on ESA’s Envisat ASAR Wave Mode Significant Wave Height Retrievals Using Triple Collocation Model" *Remote Sensing* 6, no. 12: 12217-12233.
https://doi.org/10.3390/rs61212217