1. Introduction

The rise and fall of sea levels on the Earth is referred to as “tide”, which is a Low German word for “time”. Tides originate from combined effects of gravitational forces exerted by the Moon and Sun, and the Earth’s rotation. More specifically, the gravitational pull of the Moon and Sun results in a high tide, respectively. If both are in a straight line the combined pull causes higher tides as well as lower tides. Overall, tidal heights and timing are affected by the coastline and near-shore bathymetry, whereas the four stages are low tide, flood tide, high tide, and ebb tide.

Figure 1: Origin of tides by Encyclopaedia Britannica, Inc. (https://www.britannica.com/science/tide retrieved on: July 22, 10 AM)

 

Above mentioned factors such as Sun and Moon gravitation influence the tidal signal and frequencies. These factors, also referred to as tidal constituents, affect the tidal signal on different time periods of (half) days, months, and even years. Tidal constituents can also interact with each other and combined there is a list of hundreds of constituents of which 37 are generally known to have the biggest impact on tides. Overall, these constituents are used to predict the tides.

2. Ocean tide model

One of the widely used benchmark tide models, the basic ocean tide model 10 (DTU10) developed by the Technical University of Denmark, is based on the global hydrological FES2004 (Finite Element Solutions) using additional 18 years of satellite altimetry measurements. The sea level data were analyzed to obtain the phase and amplitude of the 9 major tidal constituents. Including bathymetry, the model’s performance is accurate over the open oceans. However, the model exhibits lower accuracy near the shoreline. The lower accuracy can, in part, be explained by DTU10 only taking into account the astronomical tide signal and neglecting weather influences such as precipitation and wind. The two following Figures 2 and 3 show the DTU10 performance near the coast compared to tide gauge measurements in Brest (France) and Cuxhaven (Germany), respectively.

Figure 2: Tide gauge measurement in Brest (France) compared to DTU10 model prediction

 

Figure 3: Tide gauge measurement in Cuxhaven (Germany) compared to DTU10 model prediction

 

For both locations, the DTU10 tide model predicts a lower amplitude as well as a phase shift of up to three hours. The forecast of the lower amplitude becomes more apparent at the Cuxhaven station, as tides were recorded during the winter storm “Sabine”. Between February 10 and 14, the tide prediction is up to 3 m lower than the measured tide. To address this, researchers at Meteomatics were eager to develop and implement a new approach, which is from hereon referred to as the Tide Weather Model (TWM).

3. Meteomatics near-coast improvements – Tide Weather Model (TWM)

Driven by previous models’ inaccuracies in coastal regions, researchers here at Meteomatics set out to improve tide predictions in these areas using worldwide observational data from thousands of tide gauges. Moreover, our researchers took advantage of the power of the Meteomatics API to include weather conditions with the overall objective to better forecast tides in coastal areas.

The following Figures 4 and 5 show the result of the TWM without including weather data compared to the previous DTU10 approach for Brest and Cuxhaven, respectively.

Figure 4: Comparison between TWM (tide only) and DTU10 with tide measurements at Brest (France)

 

Figure 5: Comparison between TWM (tide only) and DTU10 with tide measurements at Cuxhaven (Germany)

 

The phase shift that was previously observed in the DTU10 model vanishes completely in the TWM when considering tides only. However, there are still high residual deviations between the modelled and observed height of the amplitude. This residual was successfully eliminated by a novel consideration of weather effects using our first-hand data streams, as shown in Figures 6 and 7.

Figure 6: Comparison between TVM (weather conditions included) and DTU10 with tide measurements at Brest (France)

 

Figure 7: Comparison between TVM (weather conditions included) and DTU10 with tide measurements at Cuxhaven (Germany)

 

As known from other parameters of the Meteomatics API, TWM is seamlessly interpolated onto each queried coordinate.

 

4. Conclusions

The newly developed TWM shows a great performance, especially in coastal regions, through the use of tide gauge observations and taking into account the local weather conditions. The new model has gone live in our API in July as shown in the image below.

Figure 8: TWM tide prediction inspected on our Cesium data visualization platform. Colors show levels from -500 cm to 500 cm and demonstrate the high regional variability in near-coastal regions as well as the channel.