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Mathematical Models In Numerical Weather Prediction

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The first attempt to predict weather numerically required a larger workforce. With the development of powerful computers and better modelling techniques, numerical weather prediction has returned to models that are quite similar to the earliest model. The simple-basic equations are used as the forecast equations in Numerical Weather Prediction. The weather data at a particular station for a short range over a particular region is considered. The parameters such as minimum temperature, maximum temperature and relative humidity is calculated based on the mathematical relations over different periods with the timeseries data collected. The results obtained show that NWP can estimate the weather conditions more precisely and accurately.

Keywords: Numerical Weather Prediction, minimum temperature, maximum temperature, time-series, precisely, accurately


Weather forecasting stations are systems that allow forecasting of daily, weekly or monthly weather conditions. To predict weather of a particular region over a fixed duration is a tedious process. The early approaches couldn’t handle unstructured data and missing data and hence resulted in misinterpreted output. The early numerical predictions involved a larger number of work forces and continuous observations. The deployed models needed curious work to be done manually and prediction was tough. Due to rapid change in the weather conditions, the parameters considered had to be revised to meet these changes. It also required gathering up of historical data and filling in the missing data.


The goal of this project is to design a mathematical model for predicting weather forecast. It would take into consideration of the parameters such as minimum temperature, maximum temperature, humidity, average temperature. Mathematical models are models designed on the basis of physics. It also considers the data mining techniques and strategies to deal with the historic data and the missing data. We also calculate the probability of the error occurrence in the resulted output. Data mining is the key to obtain future predictions. It also evolves as an important tool in understanding thee patterns and its evolutions to the mark. Weather forecasting serves a true purpose to travellers, business-men, farmers and many others. It helps in keeping a track of the storms, floods, rainfall, snowfall, etc. In our project, we will mainly try to predict rainfall using a mathematical model as well as some of the data mining techniques and strategies.

Literature Survey

Since the weather in India is unpredictable, an approach must be developed to forecast weather efficiently. By forecasting weather precisely we can prevent and overcome many hazards that could lead to great loss to a nation. So, in order to do this, Hidden Markov Model was chosen. A Hidden Markov Model (HMM) may be a statistical Markov model during which the framework being modelled is assumed to be a Markov chain with in hidden (secret) states. In this paper HMM is employed to predict weather using Markov chain property. The training of the model and probability of occurrence of an event is calculated by observing weather data for last 21 years. The data is firstly categorized based on standard values set apart. The result obtained shows that our model is reliable and works very well in predicting weather for next 5 days based on today’s weather pattern. Much of the work has been carried out on HMM and it has been used for various purposes like for Speech Recognition, Pattern Matching and

Bioinformatics and so on. Related work has been done to predict weather also by using HMM. Predicting weather for a large number of unstructured data required training using annoted data. Usage of Viterbi algorithm made the deployment expensive.

In general, a short-term weather foresee within 3 hours is difficult as a result of lack of surface weather data and limitations of computation resources. However, such a short-term prediction is getting more and more anticipated in several industrial situations such as transportation, retailing business, agriculture, and energy management as well as our daily life. To keep up with these huge demands, services based on very short- term weather forecast began to be provided. Data sources for such kind of forecast are private companyowned surface sensor networks in addition to nationowned surface sensors. Some surface weather sensors of private companies are more densely distributed than nation-owned sensors. We call these surface weather sensor network as dense weather patterns. Among them, for example, POTEKA sensors are located in roughly every 2 to 3 km and provide observed data every minute through mobile network. Those dense sensors are spreading its locations over the world. However, a data mining technique for such a device has not been well developed. In this paper, we propose a deep learning architecture specifically developed for the short-term weather forecasting based on the dense weather station device. It is important to use dense data to obtain a precise prediction. The tensor learning methodology is applicable to predict other elements such as precipitation and solar radiation.

Our proposal consists of two folds: point prediction model and tensor prediction model. The point prediction model is useful for forecasting exactly on the location of the dense weather station.

The tensor prediction model interpolates the prediction of the point prediction model to cover whole range of locations around the interested area. It is shown that our model outperforms the existing state-of-the-art methods such as XGBoost and support vector machines using a large real observed data. A data-mining methodologies for dense weather data is developed, and a short-term local weather forecasting method using dense weather data is proposed. Because the weather stations in the network considered in this study are located every 2 to 3 km, it is useful to conduct short-term local forecast at the location of the weather stations.

Traditionally speaking, the error rate of growth is taken into account unpredictable due to the uncertainty of unavoidable errors in data collection. A new kind of errors can be detected in the forecast with a non-uniform continuity index. The results based on a simulation of the T213 ECMWF model support our new founded facts that the errors caused by non-uniform continuity between the forecast fields and analysis fields is a new founded error contamination mechanism in numerical weather models. Comparing the figures with each other among the figures of geographical distribution patterns of real initial fields, we could see that there are more points which uniform continuity condition are not satisfied in those initial fields when prevalent in the meridian circulation. There still exist many flaws in these models For example, the non-uniform continuity exists in real atmosphere but there are fewer nonuniform continuity grid-points existing in our forecasting products with the time integration steps for our models.

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A framework for analyzing weather radar (DBz) images as spatial point processes is presented. Weather radar images are modeled for the purpose of predicting their evolution in time and thereby providing a basis for short-period precipitation forecasts. An observed image sequence is modeled as a set of individual rain cells that are the outcome of a marked 2+1D spatial point process. To each point giving the place and time of maturation of a rain cell is assigned a vector of possibly time-varying features such as intensity, duration, extent, shape and velocity. The point process is a doubly stochastic spatial point process with a clustering mechanism determined by the mesoscale situation. Also determined by the mesoscale situation are prior distributions for the elements of the feature vector. A scheme for fitting this type of model to an observed sequence of weather radar images is presented. The aim of the present work has been exploration of the evolution of cell features given an incremental fitting strategy, not the estimation of model parameters. A new, incremental scheme for fitting point process models to radar images was presented. The method shows promising results for a simple sequence of radar images of a situation with dissipating precipitation.

The potential of two numerical weather prediction models in quantitative precipitation forecasting over a tropical region is examined. The precipitation observations being produced from the Fifth Generation Penn State and Weather Research and Forecasting (WRF) models had been statistically verified. The statistical verification indicates that the basis mean squared error (RMSE) increases for higher rainfall rate, though the models have performed quite satisfactorily in certain cases during heavy rainfalls that cause flood. It is also shown that the longer the rainfall forecast duration, the upper the probability of detection (POD) and therefore the lesser probability to be the false alarm ratio (FAR). This results in a precisely potential of the models in producing QPF for flood forecasts. It lacks in producing more reliable and accurate QPF.

The fifth-generation NCAR/Penn State Mesoscale Model, MM5, has been used to forecast storms spanning a year in nearby regions at 5-km resolution. MM5 predicted temperatures and those observed by the passive millimeterwave Advanced Microwave Sounding Units (AMSU) were compared. MM5-forecasted surface precipitation rate, peak vertical wind, and water paths for rainwater, snow, graupel, the sum of rainwater, snow, and graupel, cloud liquid water, and cloud ice were also compared with AMSU estimates. Results show that MM5 forecasts statistically agree with those observed by AMSU. MM5 over-forecast large ice particles for some storms. Morphology, intensity, and area of storms forecasted by MM5 are generally similar to AMSU observations, but with location differences. MM5 can provide useful high-resolution forecasts for tropical storms about 8 hours in advance. Forecast accuracy could be improved by using higher-resolution and more accurate initial and boundary conditions, satellite data for location correction during the forecast, and a more accurate weather prediction model.

It evaluates MM5 weather forecasts for tropical storms at high spatial resolution. MM5 can provide useful highresolution forecasts about 8 hours in advance. Due to rapid change and small horizontal extent of convective instabilities and errors in MM5 physics , it results in some basic errors. These systems, which are employed by meteorology in our country, are often both difficult and costly for individual use. Smart weather stations are being developed that can be used individually in order to get rid of such problems. In this study, a sensible meteorological observation post has realized for the monitoring of weather when changing during the day. the info that received from the temperature, humidity, pressure and rain sensors within the air base , are processed by an Arduino-based processor then estimated weather information has been given to users. The study results have been compared with results obtained from meteorology and the results have been seen to be close to each other.

Station DHT11 temperature and humidity sensor, BMP180 pressure sensor and rain sensors from Arduino uno outputs obtained by processing on the control card, has been transferred to an LCD display visible to users. The data received from the sensors are weather conditions. Using Arduino cards gives limited library for storage and hence dense data cannot be calculated.

Weather forecasting is determination of the right values of weather parameters and furthermore the future weather condition based on these parameters. In this study different weather parameters were collected from national climate data center then using Long-short term memory(LSTM) technique ,the neural network is trained for different combinations. In prediction of future weather condition using LSTM the neural network is trained using different combinations of weather parameters, the weather parameters used are temperature, precipitation, wind speed, pressure, dew point visibility and humidity. After training of LSTM model using these parameters the prediction of future weather is done. A proposed model for weather forecasting system is implemented using recurrent neural network with LSTM technique. It is observed that Long-Short Term Memory neural network gives substantial results with high accuracy among the other weather forecasting techniques. Training a Recurrent Neutral Network is a very difficult task. It cannot process very long sequence as an activation function.

The effective information extracting from sounding data is important for severe weather forecasting. The atmospheric structure analysis has been done with V- 3θ, which is different from the synoptic chart forecasting. This research introduces the calculation and programming of the V-3θ plot, and analyses the typical severe weather events. The results show this method could extract the atmospheric structure and transition information ahead and improves the disaster weather prediction. The new way for improving severe weather forecasting is introduced, which digs up sufficiently the structure and transition information in atmospheric data. The multi-parameters V – 3θ plot is designed based on the structure analysis of the atmosphere elements. Additionally, extreme weather events account for $485 billion in US economic damage, with this number expected to inflate as global warming increases the frequency and intensity of natural disasters. The purpose is to develop an inexpensive infrastructure of weather stations, to create more accurate forecasting networks for citizens and governmental officials of third world and developing countries.

This research will compare the precision of inexpensive weather stations to commercial grade weather nodes, and data gathered from the National Oceanic and Atmospheric Administration (NOAA). Finally, the research will assess the forecasting accuracy of the inexpensive forecasting technology systems, against popular weather media such as The Weather Channel© and the National Weather Service.

The ultimate goal of this developmental project is to install the inexpensive weather infrastructure in developing countries, in order to help government officials accurately forecast and prepare for critical weather events. It is an inexpensive weather forecasting infrastructure, that would allow citizens and government officials to be notified and prepare for extreme weather events. It can be concluded though this system was effective in accurately recording data and forecasting in the short term, it was not able to correctly forecast long term weather condition.

Case-Based Reasoning (CBR) techniques are being studied and adopted in weather forecast applications. Many subtle issues remain to be resolved for CBR to be a practical problem solver. It establishes a CBR system for localscale and short-term weather forecast at an airport. Real data based tests have shown the effectiveness and comparative advantages of the proposed method.

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Mathematical Models In Numerical Weather Prediction. (2022, February 27). Edubirdie. Retrieved March 27, 2023, from
“Mathematical Models In Numerical Weather Prediction.” Edubirdie, 27 Feb. 2022,
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