Development of Operational Weather Forecasting Shaped by the “Triple-In” Properties of Numerical Models

Operational weather forecasting has reached a turning point. It is possible that it could be reshaped by the “Triple-In” properties of “indispensability”, “inexactitude” and “incompleteness” of numerical models. The indispensability of numerical models is a salient feature of current operational weather forecasting. But inexactitude is rooted in almost all numerical schemes, and incompleteness of numerical models will always exist due to the extreme complexity of the Earth system.   

The intrinsic qualities of the Triple-In properties in numerical models determine the advancement of meteorological development, and also the future framework of operational weather forecasting. Indispensability means that the numerical model has the ability and potential to describe the evolution of the atmosphere or Earth system – a cardinal principle for a strategic plan for meteorological advancement. But inexactitude and incompleteness indicate that products obtained directly from numerical weather prediction (NWP) contain uncertainties. Therefore, updated operation should focus on minimizing the unavoidable uncertainties. The inexactitude requires that efforts should be taken to enhance the precision of NWP in meteorological centres. The incompleteness highlights that more research attributes are needed for Earth system modelling.


A new era for forecasting

Since the end of the twentieth century, the United States National Academy of Science (NAS) has been exploring how national meteorological services can continuously improve weather forecasting and related products and services (National Research Council, 1999). In a road map for the future, NAS emphasized the need and opportunities for continuing modernization. A recent review paper (Benjamin et al, 2019) that traced the evolution of forecasting over the last 100 years – splitting them into four eras – pointed out that the next 30 years will be a new era. Its characteristics will include, for example, more automation of forecasting process and increasingly complexity across all time/space scales for numerical environmental weather prediction.

The statement at the Eighteenth World Meteorological Congress (Cg-18) that WMO has now reached a turning point in its history is in line with the ideas above. A fundamental governance reform was approved at Cg-18 to make WMO more integrated and ready to operate in a seamless Earth system framework, across its main domains of weather, climate, water and environment. Some changes will therefore take place in weather forecasting and its associated processes.

Whether it would be possible to conduct weather forecasting based on scientific, mathematical principles was seriously discussed over 100 years ago. Theoretical developments since then have provided understanding of atmospheric dynamics and physical processes, which builds a foundation for numerical models and significantly contributes to the continuous improvement of operational NWP. Taking the evolution of reanalysis products as an example, Figure 1 shows the climatic summer precipitation (1979–2002) from Global Precipitation Climatology Project (GPCP) products and different reanalysis products over East Asia. Precipitation from reanalysis data can reflect the ability of numerical models to produce all the precipitation-related processes. As shown in Figure 1, compared with GPCP, ERA40 (based on a model released in 2001) significantly underestimates the precipitation over East Asia, especially that over south-eastern China. In contrast, ERAIM (model released in 2006) overestimates the precipitation in south-eastern China. The ERA5 (2016) reasonably reproduces the value and pattern of the observed precipitation. The differences between the three generations of reanalysis data highlight the remarkable improvements of numerical model systems over the years.


Intrinsic qualities of numerical models

Figure 1. Climatic summer ((June, July and August)) precipitation (1979–2002)

Figure 1. Climatic summer ((June, July and August)) precipitation (1979–2002) from GPCP products and different reanalysis products (ERA40, ERAIM and ERA5)

Triple-In – indispensability, inexactitude and incompleteness – properties are inherent in numerical models. Such models are indispensable for modern weather forecasting and will be the most important cornerstone for seamless digital operation into the future. In accord with the seamless Earth system framework of the new era, NWP models are advancing towards mature Earth system modelling.

However, the Earth system is a complex hierarchy and so its numerical model system is also complex. Correspondingly, the inexactitude and incompleteness of the numerical model will always exist everywhere, and will lead to long-term uncertainties in NWP. Such permanent uncertainty determines the development direction of meteorology, and also the future framework of operational weather forecasting.

Indispensability – As stated by Charney (1951), “the atmosphere exhibits no periodicities of the kind that enable one to predict the weather in the same way one predicts the tides.” Instead of a simple set of causal relationships, all atmospheric phenomena are the result of complex influences of a combination of non-synchronous, non-uniform and non-equilibrium factors. Due to the overwhelming complexity of atmospheric processes, only a numerical model has the ability and potential to comprehensively grasp the multiscale and nonlinear forcing and describe the evolvement of the atmosphere. As numerical modelling has matured over the past 30 years, NWP, which is performed every day at major operational centres, has unquestionably become dominant in the forecasting process. The indispensability of the numerical model has therefore been a salient feature of modern operational forecasting.

Inexactitude – The starting point for a numerical model is a series of basic laws governing atmospheric dynamics: Newton’s second law of motion, the first law of thermodynamics and the law of conservation of mass. To be stored and processed on a computer, the continuous field variables in the equations describing the basic laws must be discretized. Spatial and temporal discretizations can lead to errors. In numerical models, only disturbances larger than a certain pre-defined spatial scale are explicitly considered. The effects of smaller-scale processes must then be estimated from the larger-scale model state, which is referred to as parameterization.

Even for models with a horizontal resolution of several kilometres, many processes including cloud microphysics, radiative transfer, turbulence and shallow cumuli, still need to be parameterized. And parameterization always produces large biases. For example, the moisture phase change, a key process for most weather and climate phenomena, is parameterized, which leads to large biases in models.

Many processes, such as surface flux, cumulus convection, cloud microphysics and radiation, are necessary to describe the moisture phase change and its influences. Due to the extreme complexity and limited knowledge, moisture-related processes, such as cloud and feedback, remain the largest source of uncertainties in models. Besides the model itself, the initial state for the model also contains biases from the observational data. In summary, the inexactitude is rooted in the numerical model and numerical prediction.

Incompleteness – The atmosphere is significantly influenced by the other components of the Earth system. The oceans, cryosphere, land surface, hydrology, composition and eco-systems all have an important impact on weather prediction. Some environmental interactions have been included in numerical prediction systems for decades. With advances in atmosphere models, an increasing number of interacting processes among various Earth system components have been implemented, and more details of these processes have been resolved.

The Earth system model is an attempt to encapsulate everything known about the Earth system, which involves the atmosphere, biosphere, geosphere, hydrosphere and cryosphere, along with all of the interconnections and feedbacks among them. However, present understanding of the interactions among various components is far from sufficient. Many important processes are still missing in model systems. Moreover, the demand for describing interactions has increased rapidly, along with the improvement of numerical models. For example, after moving to convective-scale resolution, it is becoming increasingly important to include a realistic representation of the effects of large cities for reliable predictions of temperature and precipitation. The incompleteness of numerical models is rooted in the extreme complexity of the evolvement of the Earth system at various scales.


New framework for operational weather forecasting

Figure 2. New framework of operational weather forecasting

Figure 2. New framework of operational weather forecasting

The framework for operational weather forecasting should be updated and redefined. Due to its indispensability, the numerical model for the Earth system will certainly be the centre of operational forecasting in the coming seamless era. Continuous research and development is the only way to overcome the inexactitude and incompleteness of numerical models. The Triple-In properties of numerical models highlight the research attributes of the overall meteorological undertaking. As illustrated in Figure 2, the new framework of the operational weather forecast can be divided into four sections.

Strategical layout: towards modelling a perfect, seamless Earth system framework – In the lower quarter of Figure 2, the indispensability of the numerical model determines the strategical layout of future operational forecasting: building a reliable seamless Earth system modelling framework and making best use of the model outputs in an objective way. This is the primary principle of designing scientific research, technical development and operation tasks. The right- and left-hand quarters of Figure 2 show deployments to improve the current numerical model systems, which aim at precision and perfection. The upper quarter represents efforts to optimize NWP results with recognition of uncertainty.

Capacity-building on enhancing model precision – The right-hand quarter of Figure 2 shows the needs to improve the precision of the model system and for more accurate and efficient mathematical expression and numerical techniques to be designed. Spatiotemporal resolution should be increased, fundamental meteorological research on physical and chemical processes should be carried out, and more reliable data assimilation methods should be developed. Considering the new demand of seamless prediction, innovative and refined evaluation should be designed and conducted to understand and trace the source of biases in the model system. At the same time, more field campaigns should be designed and conducted to promote understanding of key dynamical and physical processes in the atmosphere and improve model performance. For example, the Third Tibetan Plateau Atmospheric Scientific Experiment (TIPEX-III) (Zhao et al., 2018) and the Southern China Monsoon Rainfall Experiment (SCMREX) (Luo et al., 2017) have been conducted in China.

The operational NWP system should also be updated to improve precision. For example, in short-term forecasting, high-resolution regional models with mesoscale processes explicitly resolved should be used. The focus at this spatiotemporal scale is the rapid update cycle and the involvement of fine-scale forcing such as complex urban or mountain boundaries.

Figure 3. Mean observed

Figure 3. Mean observed (a) and ECMWF Integrated Forecasting System model 12–36 h forecast (b) of daily mean rainfall (units: mm/d) average over western China for May to June 2019. The target region over the northern edge of Sichuan Basin is marked by a black dashed line. (c) Regional averaged diurnal curves of accumulated rainfall of heavy rainfall events (with intensity in peak hours greater than 5 mm/3 h) in observations (black line) and the model forecast (blue line). (d) Regional averaged percentage of total precipitation distributed with different hourly intensity for observation (black line) and model forecast (blue line).

Capacity-building on completing Earth system components – The left-hand quarter of Figure 2 shows the needs to further complete the Earth system components. Interactions among various subsystems should be analysed. A method to effectively couple all the components should be explored, and coupling assimilation should be designed to optimally combine available observations from the entire Earth system. To advance scientific knowledge on the climate and Earth system, long-term, continuous, stereoscopic and integrated observations for major components (atmosphere, hydrosphere, cryosphere, land surface and biosphere) and the interactions among them should be deployed and implemented.

The China Meteorological Administration (CMA) has selected five observatories with “good climate representativeness, complete historical observation data, and mature basic conditions of observation stations” to conduct a pilot experiment at the National Climate Observatories since 2006. In 2019, CMA launched 24 National Climate Observatories to conduct continuous observations for the Earth system. These 24 observatories cover typical underlying surfaces such as grassland, forest, farmland, mountain, wetland, desert, marine, lake and urban areas, and represent weather and climate characteristics of 16 key zones of the climate system in China. The long-term observations from these stations will promote studies on exchanges of mass, moisture and energy and interactions among Earth system, and also supply reliable metrics for evaluation of the coupled model system.

The “whole” Earth system model should be used for full seamless weather and environment forecasting. As the model’s resolution increases, more features of the ocean, sea ice and land surface will be resolved, and a much wider range of chemical and biological processes should be involved and properly reproduced.

Real-time operation: understanding uncertainties in the products and designing objective algorithms and corrections – Real-time operational forecasting will focus on the uncertainties of the numerical prediction system, corresponding to the upper quarter of Figure 2. First, it is necessary to improve the scientific understanding of weather and climate features at a fine scale and in a seamless way. Second, it is necessary to design precise metrics for evaluating key model behaviour and critical processes and for understanding the uncertainties. Third, based on in-depth evaluation, it is necessary to make good use of big data and innovate intelligent automatic techniques to objectively correct the products of the numerical prediction system. Through state-of-the-art validation and emendation, a forecaster can minimize the uncertainties of the current numerical model system and produce a high-quality forecast.

The forecast of heavy rainfall events over the northern edge of Sichuan Basin (in south-western China) is shown as an example in Figure 3. Comparison between the pre-summer mean (May–June) daily rainfall distribution from China Merged Precipitation Analysis (CMPA) (Figure 3(a)) and ECMWF 24 h forecast (12–36 h) (Figure 3(b)) reveals that the model forecast generally reproduces the heavy rainfall centres over south-western China. The location and magnitude of rainfall centres are comparable in the target region (marked by black dashed lines in Figure 3).

However, while the subdaily rainfall characteristics are considered, evident biases are found in the model forecast. For the diurnal variation of heavy rainfall events (with intensity in peak hours greater than 5 mm/3 h), the peak hour in the model is 3 h earlier than that in the observation (Figure 3(c)). For the distribution of rainfall amount with different intensities, the model tends to overestimate (underestimate) the accumulated amount of weak (strong) rainfall (Figure 3(d)). Based on the recognition of model biases, subdaily relationships (diurnal cycle and intensity structure) between model outputs and observation can be established. By using these relationships, the correction of model outputs for a specific heavy rainfall event can be done in two steps: first, the temporal evolution is postponed by 3 hours from the beginning of the heavy rainfall event at 0200 local time (LT) on 27 June 2019; second, the distribution of rainfall amount with different intensity in each 3 h model output is adjusted.

Figure 4 compares the original ECMWF model forecast and corrected results against observations for a heavy rainfall event over the target region. It can be seen that by reducing the portion of weak rainfall, the weak rainfall around the heavy rainfall centre is partly eliminated, and the rainfall is stronger in large centres. Also noted at a subdaily timescale, the corrected peak time is consistent with the observation (Figure 4(e)). The regional averaged rainfall distribution with different intensity (Figure 4(f)) after correction (red line) is more realistic compared with the original model outputs (blue line).


Distribution of observed model forecast

Figure 4. Distribution of observed (a), model forecast (b) and correction of accumulated rainfall model outputs of the heavy rainfall event from 0200 LT on 27 June 2019 to 2300 LT on 28 June 2019. (e) Temporal evolution of regional averaged rainfall during the heavy rainfall event from observation (black line), ECMWF forecast (blue line) and ECMWF forecast after correction (red line). (f) Same as (e), but for the accumulated regional mean rainfall amount of precipitation with different hourly intensity.


The way ahead

Based on an in-depth understanding of the intrinsic qualities of numerical models (Triple-In), a strategy for weather operational forecasting facing the coming new era is proposed. The indispensability of numerical models has established their core position in operational systems.

Three directions should be deployed to overcome the intrinsic uncertainties of the model. To reduce inexactitude, the precision of the model system should be improved according to major simulation and forecast biases. To overcome incompleteness, key new processes in the climate or Earth system should be recognized, understood and properly involved in the model system. To make best use of indispensable up-to-date numerical models, results should be thoroughly evaluated and corrected according to inherent deviations. The three directions are closely related and have a unified core of research, which is key to pushing development of operational forecasting forward.



We thank ZHANG Wenjian, Paolo Ruti, ZHOU Heng, XU Xianghua and NA Xiaodan for their helpful feedback on the manuscript.



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Charney, J.G., 1951: Dynamic forecasting by numerical process. In: Compendium of Meteorology (T.F. Malone, ed.). Boston, American Meteorological Society.

Luo, Y., R. Zhang, Q. Wan, et al., 2017: The Southern China Monsoon Rainfall Experiment (SCMREX). Bulletin of the American Meteorological Society, 98(5):999–1013.

National Research Council, 1999: A Vision for the National Weather Service: Road Map for the Future. National Academies Press.

Zhao, P., X. Xu, F. Chen, et al. (2018): The third atmospheric scientific experiment for understanding the Earth–atmosphere coupled system over the Tibetan Plateau and its effects. Bulletin of the American Meteorological Society, 99(4):757–776.



Rucong Yu, China Meteorological Administration (CMA)

Jian Li, State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences

Pengqun Jia, CMA Training Centre


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