There is no simple answer to this question and it is necessary to discuss some topics before any conclusions are written.

Initially, it is important to have an idea of ​​what is weather systems that cause rain - we have prepared an article about this topic, just access it here. Next, it’s important to know “how the weather forecast works?”. This article addresses this question in a simple way and here we will talk about it in more detail, highlighting the uncertainties present in atmospheric numerical models.

What is an atmospheric numerical model?

In summary, an atmospheric model is a set of mathematical and physical equations that represent the different atmospheric processes. The basic equations that describe the state of the atmosphere are:

These are the basic equations, but each physical process has a set of equations that represent it, called parameterization. There are different parameterizations to represent the same process, each one using a specific approach, resulting in different estimations depending on the objective of the simulation, the study area, etc.

However, both the basic equations and the parameterizations are approximations of the real, therefore, they have an associated error and are sources of uncertainties.

How does a model predict time?

For a model to forecast weather, it evolves the state of the atmosphere based on initial conditions. These conditions are obtained from a variety of instruments used to monitor the atmosphere: weather stations, weather balloons, radars, satellites, etc. With all this information, a global model can start its forecast, however, if these initial data have any kind of error, it will be transmitted to the model and its forecasts, generating yet another source of uncertainty.

The forecasts of a model are made on a grid, in which each of the different equations is calculated at a specific location (Figure 1). This information is integrated (interpolated), generating a spatial result at different times. It is important to remember that the atmosphere has 3 dimensions, therefore, this grid also extends vertically, with the same amount of points horizontally, but in several layers, generating a 3D representation of the atmosphere.

FIGURE 1: horizontal (left) and vertical (right) grids representations. Source: https://orchidas.lsce.ipsl.fr/.

The greater the number of points, the higher will be the horizontal resolution of the model, and the greater the number of vertical layers, the higher the vertical resolution of the model.

Increasing the resolution of a global model is no simple task. The computational power required increases considerably, moreover, not all equations were designed to work in such a high resolution. However, when necessary, a higher resolution forecast can be performed for a smaller region, by what is called a “regional model”, or “limited area model”. These models were specifically designed to work in high resolution and use as initial conditions the simulation of global models, therefore, the uncertainties of global models also end up passing to regional ones.

Is it possible to improve the forecast?

As technology and meteorology evolve, the models themselves also evolve. The equations are becoming more precise, the data observed are more numerous and of higher quality, the models are more consistent, and the computers are more powerful. All of this contributed to significant gains in the quality of weather forecasts.

So which model is the best? There is no definitive answer to this question. All models have uncertainties and will never be 100% faithful to what was observed. However, there are ways to achieve a better result, and one of these ways is to use a technique called an Ensemble (which is used by Agrosmart).

Due to many uncertainties present in the observed data used as initial conditions, on the models themselves and, especially due to the chaotic and dynamic nature of the atmosphere, it is not possible to ensure that one model result will be the correct forecast for a future state of the atmosphere. The ensemble guarantees, through statistical procedures, the most likely forecast to occur and, in many cases, the closest to the real world.

How does this work? Figure 2 uses a temperature forecast to exemplify an ensemble. Each model (blue line) starts from a different initial condition and produces a different forecast. With an ensemble, the forecast will be focused on the most likely outcome of all models (at the peak of the yellow part on the right vertical axis, where most of the model forecasted temperature).

FIGURE 2: Different temperature forecasts (blue line) from an initial condition (left vertical axis) generating different forecasts (right vertical axis). Source: Grönquist et al (2019).

Below, we present an example that shows the difficulty of making a weather forecast.

Case study of a weather forecast problem (14/07/2020).

On July 14, 2020, a storm hit the interior of Mato Grosso do Sul. Agrosmart Meteorological Stations recorded more than 35mm of rain in less than 30 min. On this day there was no precipitation forecast. What happened?

First, what was the atmospheric condition that day? There was no large-scale system influencing weather conditions, and in most of Brazil, there was good weather. On the Atlantic coast, it is possible to observe a Cold Front, but its influence on the continent seems to be weak on that day (Figure 3).

FIGURE 3: Infrared channel satellite image. The colors indicate the temperature of the top of the clouds, the closer to the red/pink, the colder the top, and the storm is expected to be stronger. Source: CPTEC.

The presence of the cold front may have contributed to the formation of the storm, but it was not the decisive factor. The storm occurred at the end of the day, probably due to the convective process, and it was formed by a single cell, indicating that it is a Mesoscale Convective System, a short duration system (a few hours at most) with small spatial extension. Figure 4 shows the life cycle of this system.

FIGURE 4: Satellite image similar to the previous one, for the period from 1700 UTC (14h local) - 2300 UTC (20h local) and cropped for Mato Grosso do Sul. Source: CPTEC.

This is a very difficult case to forecast, as it happens in a small area and has a short lifecycle. If this system were 100 km long and lasted for a few hours/days, a model with a resolution of 25 km, for example, could simulate such a system, as several points of the model would be within the area of ​​the system and the equations would reflect this phenomenon (Figure 5.a). In this case, the system is a few kilometers long and had a short duration, the same model would not be able to simulate the same, since, at most, only one point would be within the system area (Figure 5.b). In the latter case, the model would be “myopic” for this system.

FIGURE 5: Model grid and meteorological system representations.

Performing specific simulations for this case, with different configurations of the model (such as varying the characteristics of the grid and the parameterizations used), and even the inclusion of observed data in the middle of the simulation, maybe this kind of system would be simulated. However, this would be a case study and would deviate from the standard of a weather forecasting operating system.

Uncertainties

Atmospheric modeling and weather forecasting have evolved a lot in recent years and continue to evolve. Uncertainties have been reduced significantly in this process, but they still exist. It is very important to understand that weather forecasting is not an exact science and failures can occur.

We at Agrosmart are working around the clock to keep our forecasting system up to date with state-of-the-art atmospheric modeling, to ensure the most accurate forecast for our

References:

Grönquist, Peter & Ben-Nun, Tal & Dryden, Nikoli & Düben, Peter & Lavarini, Luca & Li, Shigang & Hoefler, Torsten. (2019). Predicting Weather Uncertainty with Deep Convnets. customers.

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