This percentage was used as the fog climatology level in the reliability diagram Fig. What is the quality of this observational dataset? Table 3 shows a seasonal and geographic distribution of fog events over eastern China: the east coast has more fog events and the western interior lands fewer; the southeast coast has more fog in the cold season and the northeast coast more fog in the warm season.
This seasonal and geographic distribution demonstrated by Table 3 is generally in agreement with 50 yr of fog statistics in China, as reported by Liu et al.
This fact is indeed reflected in Table 3. For example, Tianjin reported 12 foggy days in July and Qingdao reported 9 days in June and 8 days in July, which were significantly more than other cities during the same months.
All this suggests that the observational fog data collected are reliable. By the way, based on Liu et al. Otherwise, more fog events would have been evaluated. Figure 2 shows the monthly verification statistics from the NMM and ARW control forecasts note that given no distinguishing differences in performance between the and h forecasts, all the statistical scores throughout this paper were averaged over both the and h forecasts to increase the sample size.
Although all forecasts with the exception of the multivariable-based NMM forecast in the summer season underestimate the number of fog events, the multivariable-based method exhibits less bias is closer to value 1. This can be further confirmed from the HR plot shown in Fig. The hit rate of the LWC-only approach is particularly low near zero for the ARW model in the winter and summer seasons, which demonstrates that the LWC-only method is not reliable, although the LWC-only method was only slightly worse than the multivariable-based method in May.
Given the fact that more diagnostic parameters are included by the logical operator or in the new method [Eq. Therefore, this new multivariable-based fog detection algorithm will be employed in the rest of this study. To examine in detail the effectiveness of different diagnostic rules and how well the multivariable diagnosis in fog forecasting does from a single model, a large-scale fog event is presented below.
The event occurred over a large area along the east coast of China on the morning of 7 April Fig. The sea level pressure map not shown indicates that the entire costal region from south to north was controlled by a steady high pressure system centered on the Beijing—Tianjin region.
This high pressure system caused a stable planetary boundary layer and a weak surface wind environment along the coast Fig. The air over the water was nearly saturated, as shown in Fig. The cloud-top and -base forecasts are presented in Figs. Figure 3b indicates that the surface wind directions were mostly southeasterly warm and moist over land and northwesterly cold over the water.
Over land, the southeasterly wind brought warm and moist air toward the north warm advection , which was gradually cooled down during its transport and was further cooled down by strong radiative cooling near the ground along the southern coast during the night of 6 April clear sky under high pressure. Over the water, on the other hand, the northwesterly cold-air movement cold advection cooled the near-saturated air above the water down to its condensation temperature.
Under such a favorable combination of wind, temperature, and humidity conditions, a large-scale marine-radiation fog episode developed both on land and over the water along the coast from Hangzhou and Shanghai in the south to Qingdao, Tianjin, Dalian, and Beijing in the north, during the early morning of 7 April as shown in Fig. The large-scale fog region shown in Fig. The fog mostly dissipated over land after BT, although it still remained over the water, as can be seen from satellite images not shown.
It was not clear whether or not fog developed in the northeast area near Dalian because no fog data were available from there for this fog event. During this large-scale fog episode, numerous traffic interruptions including local traffic tie-ups, shutdowns of several highways, closures of sea harbors, and hours-long delays for many airlines were reported in all the affected cities.
Several casualties from a series of fatal car accidents on highways were also reported by local police offices. The societal impacts of accurate fog forecasting are high in such major events.
If the LWC-only approach is used, the fog forecast in this case would be significantly underpredicted. From the above analysis, we can expect that the fog was of the advection type over water and of the radiation type on land along the southern coast.
But the LWC-only approach failed to detect both types of fog over most of the region. By using the multivariable diagnosis, however, the fog areas derived from the NMM and the ARW control forecasts were obviously expanded as shown in Figs. As a result, the NMM with the multivariable diagnosis successfully predicted the fog events in Shanghai and over the water to the south of Dalian and the east of Qingdao, as shown in Fig.
This fog case demonstrates that by using the LWC-only approach the single models in the SREF system would seriously underforecast the fog, while using the multivariable diagnosis would greatly improve the forecast. Although the forecast fog areal coverage was still smaller than the observed, it is much better than the forecast made with the LWC-only approach cf. As with the two control forecasts, fog occurrence 1 or 0 can also be diagnosed for all perturbed ensemble members.
Based on all individual member forecasts, the probability relative frequency of fog occurrence can be calculated.
A probabilistic forecast can be evaluated both probabilistically and deterministically. By comparing the single control forecasts and their corresponding same model ensemble-based forecasts, the benefits from the ensemble-based forecasts are obvious and are true for both models. But the overall combined score measured by ETS Fig. Apparently, the bias parallels the behavior of HR MR.
Because of the shrinkage in the forecast area, HR MR should be expected to decrease increase with the increase in probability thresholds. Considering that fog is a relatively rare event, on many occasions there should be no fog in both the forecast and the observation, which implies that the correct rejection rate CRR must be quite high for all kinds of fog forecasts.
In other words, CRR will be less sensitive to which model groups or probability thresholds are selected. This characteristic is indeed shown in Fig. The above results demonstrate a clear benefit from the ensemble approach over a single deterministic run in two ways.
Second, the ensemble-based forecast can provide useful information to various types of users with their own unique requirements, objectives, and economic values. For example, some users may prefer a higher hit rate and need not worry about the false alarm rate, while others may be the opposite. This is a situation that ensemble-based forecasts can serve well but a single forecast cannot.
To further demonstrate the value of probabilistic forecasts over a deterministic forecast, probability itself was also evaluated in terms of a probabilistic score. Figure 6a shows the BSS over each month for both the NMM-ensemble-based and ARW-ensemble-based probabilistic forecasts, where the control run of the corresponding base model was used as the reference forecast for each model.
Clearly, both ensembles show skill over their own single control forecast for the entire verification period from February to August. The mean BSS averaged over all 7 months is shown in Fig. In addition to Fig. Since the skill was systematically reduced for all ensembles when switching the reference from the ARW control forecast to the NMM control forecast, this indicates that the single NMM control forecast might, on average, outperform the single ARW control in predicting fog.
This is in agreement with the previous results revealed by scores such as the ETS of Figs. To demonstrate meteorologically why ensemble-based fog forecasts work better than a single forecast, the 6—7 April fog episode is examined again with the member SREF-B08RDP ensemble. Figure 7 shows that the ensemble spreads or forecast variations among ensemble members were quite significant over the fog area: 1. From Eq. When taking a closer look at Fig.
Given a large forecast variation in basic fields from one member to another, it is unlikely that a single member could capture the whole picture, but the combined forecast from all members might do a better job.
This is exactly the case here. For example, the 9-h control forecasts with multivariable diagnosis failed to predict the whole picture of the fog event Figs. Although the ARW control forecast had a tiny indication of fog near Shanghai and Hangzhou, the predicted fog scales were too small to show any confidence Fig. However, if information from all the individual ensemble members is combined, the situation can be greatly improved.
For example, the ensemble-mean forecast of LWC only in Fig. Note that there was uncertainty in the fog observations in the area northeast of Dalian, as mentioned above.
This case clearly demonstrates how and why an ensemble-based forecast would be superior to and more beneficial than a single forecast.
To examine if model diversity in both the physics and dynamics can add extra value to an IC-uncertainty-only based ensemble as suggested by Mullen et al. Therefore, it is important to keep in mind that the results from the first experiment should reflect a combined impact from both the multimodel approach and increased ensemble size from 5 to 10 members. When comparing the ETS of the three ensembles shown in Fig.
It is a big gain with contributions from both the multimodel approach and the membership increase. In light of the fact that forecast skill with a 0.
Therefore, an improvement of It is inferred that the contribution of the increase in the member size from 5 to 10 members is also significant. The superiority seen in the deterministic aspect is also true for the probabilistic aspects. For example, the BSS of Fig. To better understand where the improvement came from, the BS has been decomposed into three components of reliability , resolution , and uncertainty [Eq.
The result is shown in Table 4. By comparing the multimodel member SREF-B08RDP second column ensemble with either the NMM third column or ARW fourth column ensembles, it can be seen that the main improvement was in the reliability although the resolution was also noticeably improved.
The improvement in the uncertainty is, however, very small. After excluding the ensemble size effect, a similar result was also observed from the second experiment; that is, the main improvement between a single-model ensemble third or fourth columns and a multimodel ensemble fifth column is in the reliability.
This is particularly true when the ensemble size is very small, such as in the five-member second experiment, where there was no improvement in resolution but merely a reflection of the original quality of the base models the resolution of the combined ensemble was somewhere between that of the NMM and ARW ensembles, considering the fact that the NMM performed slightly better than the ARW, as seen previously in this study. Regarding the impacts of ensemble size, it is useful to keep in mind that BS or BSS has a theoretical cap or limit for a given ensemble size Richardson This same pattern of behavior is also observed using other measuring metrics Du et al.
This pattern implies that a probabilistic forecast cannot reach its full skill if the ensemble size is too small, especially for low-predictability events like fog. In this sense, increasing the ensemble size from 5 to 10 members should have made a significant contribution equally as important as the multimodel approach to the ensemble performance seen in this study, an argument that can be apparently confirmed by comparing the second column with the fifth column in Table 4.
However, it is expected that the ensemble size impacts will be much smaller when the ensemble size exceeds 10 members Du et al. For example, in an experiment combining two member ensembles, one might find that the impacts from the increased ensemble size from 50 to members are much less than those from the multimodel effect.
Figure 8 shows the ROC diagram for each of these four ensembles. Again, given that the improvement in the ROC area of the 5-member NMM—ARW ensemble over the NMM or ARW ensembles is small, the contribution of the ensemble size increase from 5 to 10 members is obviously important to the quality of the ensemble-based probabilistic forecast in this experiment with a small ensemble size, for the same reasons discussed in the last paragraph.
The small impacts of a multimodel approach on ROC are due to the nature of the score, which mainly reflects the resolution but not the reliability aspect of a probabilistic forecast. This is consistent with the result revealed in Table 4. To evaluate the joint distribution of forecasts and observations over various probabilities, the reliability diagrams of the four ensembles are compared in Fig.
The no-skill line is generated in such a way that it is evenly divided between the perfect forecast diagonal line and the climatology Wilks A probabilistic forecast is considered to be skillful if its reliability curve is above the no-skill line and to have resolution if the curve is above the climatology line. Therefore, Fig. This problem has been noticeably corrected by the five-member multimodel NMM—ARW ensemble, which once again shows the positive contribution of the multimodel approach to probabilistic distributions.
The combined benefits of a multimodel approach and an increase in ensemble size are obvious from this study. Apparently, the results shown by Fig. A new multivariable-based diagnostic fog-forecasting method has been proposed. Its fog diagnosis is based on the following five basic model variables: model lowest-level liquid water content LWC , cloud top, cloud base, m wind speed, and 2-m relative humidity.
Since all of these base variables are available from a model postprocessor, this fog diagnostic algorithm can also be included as part of a model postprocessor and, therefore, fog forecasts can now be provided conveniently and centrally as direct NWP model guidance to forecasters and end users.
The selection of these five variables, their thresholds, and influence on fog forecasting focusing on 2-m RH and surface wind were discussed to provide some insights into similar works in the future. This method can easily be adapted to other NWP models. The practical application of this method is obvious, especially to the transportation community of air, sea, and land as well as navy or marine-related operations.
By comparing this new multivariable method to a commonly used method—the LWC-only based approach—it is found that the newly proposed multivariable fog diagnostic method has a much higher detection capability in current operational NWP models. Reasons why the multivariable approach works better than the LWC-only method were also illustrated in a case study.
To assess fog-forecast skill and account for forecast uncertainty, this fog-forecasting algorithm is then applied to a multimodel-based Mesoscale Ensemble Prediction System. To verify the performance of a probabilistic forecast, the following four scores were employed: Brier score BS and its decomposition, Brier skill score BSS , relative operating characteristic ROC , and reliability diagrams reliability.
Verification was focused on the and h forecasts. By comparing the performance between single-value forecasts and ensemble-based forecasts, the benefits of an ensemble approach over a single deterministic approach were clearly shown. The ensemble-based forecasts were, in general, statistically superior to a single-value forecast in fog forecasting.
A case was also presented to demonstrate meteorologically why ensemble-based forecasts work better and are socially more beneficial than single-value forecasts. By further comparing forecasts between those from the single-model ensemble and the two-model ensembles, it was shown that the performance of ensemble-based forecasts could be further improved by using a multimodel approach.
The multimodel approach is an effective way in which to enhance the ensemble technique to improve the reliability but not the resolution and uncertainty aspects of probabilistic forecasts. For a small-sized ensemble such as the one in this study, the increase in its membership is also important in improving the quality of the probabilistic forecasts, although this importance is expected to decrease when the ensemble size increases. To summarize and give a quick comparison, Fig.
We can see that steady improvement was made through each of those steps, with two big jumps, one associated with the use of the new multivariable fog detection method and the other associated with the combining of the two single-model ensembles a mixed contribution of the multimodel approach and the ensemble size increase. A problem with this fog diagnostic method is that it can predict only fog occurrence but not fog intensity.
In the real world, predicting fog intensity is as important as predicting its occurrence in traffic planning and control of land, air, and sea.
This problem might be solved by applying a newer diagnostic method suggested by Zhou and Ferrier , since this newer method can resolve fog liquid water content on the grid scale. Although this newer method was developed for radiation fog, it could be easily expanded to cover other types of fog by adding advection terms. An extra variable needed for this method is turbulence intensity, which is usually available from a model postprocessor.
Thus, both fog occurrence and intensity could then be systematically verified over North America within the framework of ensemble prediction. At the same time, it will be also interesting and useful to then compare the ensemble-based fog forecasts to the statistical approaches such as the MOS and neural network—based methods. We also thank Dr. We acknowledge Drs. The fog algorithm development work was partially supported by an FAA project.
Our special appreciation goes to Ms. Last but not least, the suggestions from Drs. Glenn White and Robert Grumbine of EMC, as well as three anonymous reviewers, gave us opportunities to improve our final version. Citation: Weather and Forecasting 25, 1; The highest ETS of all combinations is shown in boldface. Decomposition of BS into reliability, resolution, and uncertainty for the four ensembles. Boldface indicates the lowest values for reliability, uncertainty, and BS, and the highest value for resolution.
Sign in Sign up. Advanced Search Help. What is the difference between advection and radiation fog? Meteorologist and weather router Chris Tibbs on everything you need to know about fog at sea. Knowing how your variety of fog has formed will give you a better idea of how long it is going to last.
Radar and AIS help to make navigating in fog safer, but it is still an unnerving experience to sail in visibility of less than 1,m. Foghorns are hard to pinpoint and the rumble of large engines seem closer than they actually are. It usually feels as if you are sailing around in circles.
At some stage all of us will encounter fog and it will have been generated by one of three processes. Advection fog — the widespread fog that covers large sea areas — is caused when a warm moist air mass moves over a cold sea. The cold sea cools the air above to below its dew-point, causing moisture in the air to condense. Fog is formed from the numerous water droplets. This happens over a large area and will persist until there is a change in the air mass.
This can take anything from hours to days. In one recent Round Britain Race, we started from Calais in fog and returned down the North Sea in even thicker fog; it did lift a little for a while in between. It was a fairly memorable race, but not for the right reasons. Various locations are prone to fog with a given weather pattern. Indeed, it can be so common that the fog receives a local name — the Haar or sea fret along the east coast of England and Scotland, for example.
To do this we must consider; the amount of sunshine and how strong the sun is at a particular time of year, the wind speed and direction and whether they will change, how much cloud there is, whether there will be any rain, how much heat the ground has absorbed, and so on.
If any of those variables is different, even by a small amount, it will have a knock-on effect throughout the forecast. How do you forecast fog? You might also like. Fog is one of the most common weather conditions in the UK, particularly throughout autumn and winter, but do you know when fog becomes mist, or how you can catch fog?
Read more. A fog so thick and polluted it left thousands dead wreaked havoc on London in
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