Latent Heat Nudging in the Canadian High-Resolution (2.5 km) Regional Deterministic Prediction System

Dominik Jacques aEnvironment and Climate Change Canada, Dorval, Quebec, Canada

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Daniel Michelson aEnvironment and Climate Change Canada, Dorval, Quebec, Canada

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Abstract

This study examines the application of latent heat nudging (LHN) for the assimilation of radar-derived precipitation rates in the 2.5-km High-Resolution Deterministic Prediction System (HRDPS) operated by Environment and Climate Change Canada. One goal of this study is to document the overall impact of applying LHN in the most recent operational implementation of the HRDPS. On average, for 110 forecasts conducted over a 2-month period in 2016, LHN is shown to improve a composite NWP index (measuring the average change in RMSE over many variables and observation types) by ∼1.5% compared to a control experiment with no LHN. For winds between 400 and 100 hPa, reductions in RMSE between 1% and 4% are found for lead times up to 48 h. For precipitation, improvements for lead times up to 6 h are shown. Another goal of this study is to quantify the relative contributions for certain components of the LHN implementation. The features being investigated are the inclusion of LHN within the assimilation cycle, the use of idealized heating profiles and the conservation of relative humidity. The 2-month forecasting experiments are conducted with these components deactivated in turn. By comparing these experiments, it is found that the inclusion of LHN in the assimilation cycle has the largest impact. It is also found that the use of idealized profiles in locations where precipitation is observed but not simulated is a critical aspect of this implementation of LHN. A case study is also provided to illustrate the impact of LHN on altitude winds.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dominik Jacques, dominik.jacques@ec.gc.ca

Abstract

This study examines the application of latent heat nudging (LHN) for the assimilation of radar-derived precipitation rates in the 2.5-km High-Resolution Deterministic Prediction System (HRDPS) operated by Environment and Climate Change Canada. One goal of this study is to document the overall impact of applying LHN in the most recent operational implementation of the HRDPS. On average, for 110 forecasts conducted over a 2-month period in 2016, LHN is shown to improve a composite NWP index (measuring the average change in RMSE over many variables and observation types) by ∼1.5% compared to a control experiment with no LHN. For winds between 400 and 100 hPa, reductions in RMSE between 1% and 4% are found for lead times up to 48 h. For precipitation, improvements for lead times up to 6 h are shown. Another goal of this study is to quantify the relative contributions for certain components of the LHN implementation. The features being investigated are the inclusion of LHN within the assimilation cycle, the use of idealized heating profiles and the conservation of relative humidity. The 2-month forecasting experiments are conducted with these components deactivated in turn. By comparing these experiments, it is found that the inclusion of LHN in the assimilation cycle has the largest impact. It is also found that the use of idealized profiles in locations where precipitation is observed but not simulated is a critical aspect of this implementation of LHN. A case study is also provided to illustrate the impact of LHN on altitude winds.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dominik Jacques, dominik.jacques@ec.gc.ca

1. Introduction

This study is a follow-up to Jacques et al. (2018), which examined the impact of latent heat nudging (LHN; originally proposed by Manobianco et al. 1994; Jones and Macpherson 1997) in the Regional Deterministic Prediction System (RDPS). Operating with a grid spacing of 10 km, the RDPS is currently being phased-out and is expected to be replaced by the High-Resolution Deterministic Prediction System (HRDPS) running at 2.5 km (Fig. 1). Given the encouraging results that were obtained by applying LHN in the 10-km RDPS, it was decided to implement it in the 2.5-km HRDPS.

Fig. 1.
Fig. 1.

The 2.5-km “high-resolution” HRDPS is nested within the 10-km regional system that is itself nested in the 15-km global system. Measurements from the Canadian radars (red outlines) and the American radars (white outlines) that are within the HRDPS domain are assimilated.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

A survey of convective-scale operational systems (Gustafsson et al. 2018) mentions many meteorological centers using LHN. These include the MetOffice (Jones and Macpherson 1997; Macpherson 2001), Deutscher Wetterdienst (Stephan et al. 2008), and MeteoSwiss (Leuenberger and Rossa 2007). LHN is also in operational use at the Korea Meteorological Administration (Shin et al. 2022). Diabatic initialization of latent heating through a digital filter, a method related to LHN (Benjamin et al. 2016; Gustafsson et al. 2018) is used at the National Oceanic and Atmospheric Administration. The studies mentioned above generally indicate that LHN improves precipitation forecasts up to lead times of 6–15 h.

As discussed in Jacques et al. (2018), the primary motivation for implementing LHN into Environment and Climate Change Canada’s (ECCC) prediction system was to establish a baseline against which other precipitation assimilation approaches could be evaluated. Indeed, LHN was recently compared to an experimental “deterministic non-Gaussian” approach and the local ensemble transform Kalman filter (LETKF), both assimilating radar-derived accumulations of precipitation in log units (Buehner and Jacques 2020). It was found that LHN could provide approximately half of the longer-lived (∼48 h) improvements on wind and temperature brought by the other methods at a negligible cost and without having to rely on a forecast ensemble.

Studies performed in other centers also found that LHN is not easily replaced by more sophisticated approaches such as the direct assimilation of reflectivities in 4D-Var (Hawkness-Smith and Simonin 2021) or EnKF-type systems (Bick et al. 2016; Gastaldo et al. 2021). For these reasons, it is expected that LHN will continue to be used and investigated alongside alternatives until it can be replaced.

In an operational context, one motivation for replacing LHN is that it requires two parallel data flows, one for the assimilation of conventional (i.e., non-radar) observations (in the 4D-EnVar framework at ECCC), and another for the assimilation of radar-derived precipitation rates by LHN in the atmospheric model itself. Another drawback of LHN is that it is not as simple as it may first appear. Its different components need to be chosen and tuned for optimal results. Finally, the heuristic nature of LHN is at odds with the more formal framework used for the assimilation of other observation types. Despite these issues, it is believed that the benefits brought by LHN (shown later in this manuscript) are sufficient to justify the added complexity to the forecasting system.

The main goal of this study is to document the operational implementation of LHN in the HRDPS. The occasion is also taken to discuss some of the factors that most impact the LHN performance. While the basic idea of LHN is simple: latent heating profiles are scaled for a better correspondence between the simulated and observed precipitation, a number of choices have to be made for an operational implementation of LHN. For example, decisions have be made about what to do in cases where there is no precipitation in the model and therefore no latent heating profiles to scale. Other choices include whether to include LHN within the assimilation cycle or not, whether to conserve relative humidity along with temperature changes and what to do about frozen precipitation. Also, mitigating measures may or may not be applied to improve the poor relationship between latent heating and precipitation in kilometer-scale models with explicit microphysics (Stephan et al. 2008). As always with radar observations, the removal of nonmeteorological targets and the application of comprehensive quality controls remains a challenge requiring customized solutions.

To better understand some of these contributions, we conducted six experiments, each one consisting of 110 forecasts launched twice daily over a two month period during summer of 2016. One experiment is a control run where the LHN is completely deactivated, another is the fully fledged LHN implementation that became operational in December 2021. The four other experiments are presented to assess the impact of certain features of LHN in isolation. Average verification scores over the two month period are used to compare the different experiments against the control. A case study is also provided to examine the impact of LHN on winds high in the atmosphere.

This article begins by describing the observations, the HRDPS, and the implementation of LHN in sections 2, 3, and 4, respectively. The methodology is found in section 5, which describes the experiments that are performed and the evaluation methods. Results are presented in section 6. Even though LHN only directly affects vertical profiles of temperature and moisture, we will see that it also impacts winds above 500 hPa. Section 7 is a case study that gives some clues as to the process that can explain the significant and sustained impact of LHN on winds. Finally, section 8 provides conclusions.

2. Source data

The source data for LHN comprises quality-based radar composites/mosaics at 2.5-km horizontal resolution, based on pseudo-CAPPIs (constant altitude plan position indicators) of reflectivity at an altitude of 1 km above ground level. These composites are generated by the BALTRAD toolbox (http://git.baltrad.eu; Michelson et al. 2018) as described in (Jacques et al. 2018). In the operational version of the product currently in use (Michelson et al. 2020), the depolarization ratio (Kilambi et al. 2018) is used as the basis for the identification and removal of nonmeteorological targets.

Before the assimilation, the source reflectivities are converted to precipitation rates using the NEXRAD convective reflectivity (Z) to rain-rate (R) relation:
Z=300R1.4.

This is a change from Jacques et al. (2018) where the Marshall–Palmer exponential drop size distribution (Marshall and Palmer 1948) was assumed with the ZR relationship Z = 200R1.6 (Marshall and Gunn 1952). This change is motivated by the fact that LHN is tested only in the summer months where convective reflectivities are more frequently encountered. In preliminary tests conducted with different ZR relationships (not shown here), the application of LHN was not found to be very sensitive to this parameter. That said, the use of a single ZR on such a large domain and period will unavoidably lead to over and under estimation of precipitation in many cases. A more sophisticated approach to infer precipitation rates from radar measurements should be investigated in future work.

After conversion to precipitation rates, the radar observations are then passed through a median filter with a window of 3 × 3 grid points to remove isolated echoes often associated with observational noise. Last, a smoothing filter consisting of a circular boxcar average with a radius of 4 km (Fig. 2a) is applied. This smoothing is performed to remove the small-scale features that the model is not capable of representing. Through trial and error, it was determined that this smoothing window produces precipitation rates whose spectral densities, estimated with the discrete cosine transform (Denis et al. 2002) and illustrated in Fig. 2b, best matched that of the modeled precipitation. The end result is smoothed precipitation rates (Fig. 2d) with a texture that is more similar to modeled precipitation rates (Fig. 2e) than the unaltered observations (Fig. 2c).

Fig. 2.
Fig. 2.

(a),(b) BALTRAD composites are smoothed to remove the small-scale features that the model is not capable of representing. This is done by using a circular smoothing stencil in (a) and producing fields of precipitation rates in (b) whose spectral density match more closely with those simulated by the model. By eye, (d) the filtered observations have a texture that better resembles that of the (e) model than (c) its unfiltered counterpar. (f),(g) BALTRAD’s quality index is filtered using the same process.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

An interesting feature of the BALTRAD reflectivity composites is that each individual grid point comes with a quality index giving an appreciation for the quality of the measurement. This index ranges between zero and one with zero indicating lowest quality and 1 indicating highest quality. Figures 2f and 2g illustrate how the quality index is passed through the same median and boxcar filtering as for the precipitation rates.

3. HRDPS

The HRDPS is a 2.5-km local-area model covering a large portion of Canada and approximately half of the continental United States (Fig. 1). It is driven by the 10-km RDPS and operates with a time step of one minute. The HRDPS was originally described by Milbrandt et al. (2016) and has since been the object of a few upgrades. To avoid confusion, the newer system used in this study will be referred to as HRDPS-IC3 for Innovation Cycle 3. This system became operational in December 2021.

On the modeling side, HRDPS-IC3 is different from its older counterparts in that it uses the P3 microphysical scheme (Morrison and Milbrandt 2015; Morrison et al. 2015; Milbrandt and Morrison 2016), the Town Energy Balance (TEB) land-scheme (Masson 2000) and turbulent orographic form drag (Beljaars et al. 2004).

HRDPS-IC3 operates with its own continuous assimilation cycle. Every 6 h, all nonradar observations are assimilated within an 4D-EnVar system similar to those described by Buehner et al. (2015) and Caron et al. (2015). The assimilation results in a 4D increment to winds, temperature, moisture, and surface pressure that is applied using the incremental analysis update (IAU; Lee et al. 2006) method during the next model integration. As illustrated in Fig. 3, the 4D increment is available every hour during the assimilation window. These hourly increment fields are then applied to prognostic variables during model integration. With IAU, the initial conditions used for a given forecast are exactly the same as those of the background provided to the assimilation system. During the first 6 h of model integration, the hourly increment generated by the assimilation system is gradually applied to gently bring the model solution closer to observations.

Fig. 3.
Fig. 3.

Diagram representing the concurrent but independent application of IAU and LHN during the first 6 h of model integration.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

Consistent with previous approaches used at ECCC, the start time of a given forecast (T0) is defined as the center of its assimilation window even if the model starts being integrated 3 h earlier. Negative lead times are used to indicate times between the start of the model integration and T0. For example, the model integration for a 1200 UTC forecast (T0) starts at 0900 UTC (T0 − 3 h) with the analysis increment applied for 6 h until 1500 UTC (T0 + 3 h). The assimilation of radar-derived precipitation rates using LHN is also performed during the 6-h IAU period but it is completely independent from the assimilation of other observations. Figure 3 is presented to illustrate the application of IAU and LHN within the GEM model.

In HRDPS-IC3, the application of LHN is completely independent from the assimilation of nonradar observations by the 4D-EnVar system. One major difference between the two approaches is that the 4D-EnVar system uses a previous forecast (the background) to estimate the 4D increment that will be applied in the next model integration through IAU. LHN does not use a previous forecast but uses the precipitation, temperature and moisture of the ongoing model integration as input along with radar-inferred precipitation. This approach allows LHN to adapt its action depending on the (possibly rapid) evolution of the simulation. For example, once LHN succeeds in bringing the simulated precipitation closer to observations, it will be less active during subsequent time steps.

4. LHN implementation

With LHN, vertical profiles of latent heating (lh) are scaled according to the ratio of the precipitation rates (pr) observed by radar and those predicted by the model:
prratio=prradarprmodel,
such that
lhfinal=prratio×lhinitial,
with lhinitial representing the model’s initial latent heating profile and lhfinal representing the heating profile after the application of LHN. The general idea is to provide more heating, and increase the atmospheric instability, where more precipitation is desired and vice versa.
Our implementation of LHN is coded within the Global Environmental Multiscale Model (GEM) in the same manner as a column-type physical parameterization. As in Jones and Macpherson (1997), we use an incremental form of Eq. (3):
lhfinal=lhinitial+lhincrement=lhinitial+(prratio1)×lhinitial.

To avoid too large modifications of temperatures by LHN, prratio is not allowed to be larger than 1.5 or smaller than 1/1.5. These limits on prratio are slightly more conservative than those previously used in Jacques et al. (2018). This change, along with the overall reduction of the intensity at which LHN is applied (mweight discussed in the next section) were established to compensate for the smaller model time step that causes LHN to be applied 10 times more often than in our previous implementation at 10 km.

As suggested by Dixon et al. (2009) among others, LHN is only allowed to change positive values of the latent heating profiles. Also, LHN is applied every minute (the model time step) even if the temporal resolution of radar observations is 10 min. The same observations are simply reused until new ones become available.

Five components of our implementation of LHN are now separately discussed.

a. Modulation factors

The intensity with which LHN is applied is controlled by multiplying lhincrement by a modulation factor m:
mtotal=mtime×mqi×mtemperature×mweight,
such that Eq. (4) becomes
lhfinal=lhinitial+mtotal×(prratio1)×lhinitial.

The different factors contributing to mtotal are defined as follows.

  1. mtime

    LHN is applied every time step during the first 6 h of model integration. Even in a continuous cycle using IAU, it takes a few time steps for the modeled precipitation to develop and stabilize. Applying LHN during this transient period is not desirable so it is initially turned off and activated slowly. This is achieved with mtime, a modulation coefficient that depends on the model’s time step, t in minutes, following:
    mtime=(0,t<10t910,10t<201,20t360.
    As illustrated in Fig. 3, mtime completely switches LHN off during the first 10 min of model integration and then incrementally activates it during the following 10 min.
  2. mqi

    LHN may only be applied when and where radar observations are available. This is done with mqi, which is the quality index (Fig. 2g) associated with the radar observations at each grid point in the domain. Modulation by the quality index causes LHN to be applied with more force in the presence of good observations. For a given radar, the quality index decreases with range creating a gradual transition between the areas where radar observations are available and where they are not.

  3. mtemperature

    Radar observations in cold conditions present all kind of difficulties that we wished to avoid in this first operational implementation of LHN. Primarily, the estimation of precipitation rates from frozen or partially frozen hydrometeors comes with larger errors. Also, winter systems often have limited vertical extent such that the 1-km pseudo-CAPPIs used here can miss significant areas at medium to distant ranges where precipitation occurs.

    For these reasons, LHN is deactivated in cold conditions by letting mtemperature depend on the model’s temperature (K) at an altitude of 1 km AGL (T1km):
    mtemperature=(0,T1km<273T1km2735,273T1km<2781,278T1km.
    In winter months, LHN will typically be active over the western maritime region and, depending on the weather, in areas along the southern border of the HRDPS. In experiments not shown here, LHN was found to bring no statistically significant changes to the overall performance of HRDPS-IC3 during the winter months.
  4. mweight

    Finally, mweight is a user-defined “master” weight that controls the overall intensity at which LHN is applied. Through prior testing, it was determined that mweight = 0.2 gives the overall best results. This value is used in all LHN experiments presented here.

b. Idealized profiles

In locations where there is precipitation in the observations but not in the model, there is no latent heating profile to scale and Eq. (6) cannot be applied. In the literature, this situation is sometimes handled by using the latent heating profile of a nearby precipitating grid point (Manobianco et al. 1994; Jones and Macpherson 1997). In preparation work for Jacques et al. (2018) we found this approach to be problematic when the chosen latent heating profiles would suddenly change at the boundaries between computational tiles. When this happened, abrupt changes in latent heating caused artifacts in the simulated precipitation.

As an alternative solution, “idealized” latent heating profiles, that depend on the precipitation rates at the surface, have been proposed in Jacques et al. (2018). These profiles are defined for different intervals of precipitation intensity and are somewhat similar to the climatological profiles discussed in Leuenberger and Rossa (2007). Because of changes in resolution and microphysical parameterizations, these profiles had to be updated for use of LHN in HRDPS-IC3.

When we consider a large number of latent heating profiles simulated by HRDPS-IC3 (Fig. 4 in gray), we see that there is a lot of variability, especially for higher precipitation rates. Variability is much lower if we consider only the profiles displaying latent heat release at the lower levels (Fig. 4 in blue). In the context of LHN, low-level heating is of interest since it maximizes the increase in instability and makes it more likely for the model to generate precipitation where desired. The idealized profiles shown in orange are constructed to approximately follow these profiles. In locations where precipitation is observed but not simulated, these idealized profiles are used by LHN such that
lhfinal=lhinitial+mtotal×lhidealized.
Fig. 4.
Fig. 4.

When binned in different precipitation rate categories, profiles of latent heating/cooling (in gray) show great variability. This variability can be reduced by selecting only the profiles displaying low-level heating (in blue). The idealized profiles in red are used by LHN in cases where there is precipitation in the observations but not in the model.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

c. Horizontal smoothing

LHN relies on the assumption that the latent heat release in a column is proportional to the precipitation rates at the surface. In kilometer-scale models this assumption is not well fulfilled because the hydrometeors may only contribute to surface precipitation some time later and some distance away from the location of condensation and latent heat release.

To mitigate this space/time delay and allow the use LHN at kilometer-scale resolutions, Stephan et al. (2008) proposed that the vertically averaged precipitation flux be considered by LHN instead of precipitation at the surface. Here, we propose a different approach where both the precipitation and the latent heating rates are horizontally smoothed to reinforce the relationship between precipitation and latent heating. This smoothing is independent from, and should not be confused with, the smoothing of observations described in section 2.

Motivation for this smoothing is provided in Fig. 5 which shows color coded histograms describing the relationship between precipitation rates and the column-sum of positive (upper half) and negative (lower half) latent heating rates. In the 10-km RDPS, Fig. 5a, hydrometeors are not explicitly parameterized and the relationship between latent heat release (upper half of the figure) and precipitation rates approximately follows a power law. In the 2.5-km HRDPS-IC3 with explicit microphysics, Fig. 5b, the relationship is more complicated and, considering the logarithmic scale, displays a lot more scatter.

Fig. 5.
Fig. 5.

Color-coded histograms for the column sum of latent heat release (+ve) and cooling (−ve) as a function of precipitation rates. (a) At a resolution of 10 km, coarsely parameterized microphysics enforce a good relation between latent heating above and the precipitation at the ground. (b) At 2.5 km, the added complexity deteriorates this relationship. (c) Horizontal smoothing of both the precipitation rates and latent heating helps to improve the correspondence between the two.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

When both the precipitation rates and latent heating are horizontally smoothed, Fig. 5c, the scatter between latent heating and precipitation rates is reduced. The smoothing being applied here consists in a convolution with an isotropic 2D Gaussian kernel whose decay, here σsmooth = 3, is a function of distance expressed in grid point units. More smoothing can further improve this relationship but it becomes impractical to apply because of the decomposition of the domain for parallel integration.

The negative values in Figs. 5a–c represent the column sum of latent cooling related to the evaporation of condensed water. The relationship between this cooling and precipitation rates is poor irrespective of model resolution or smoothing. This justifies the application of LHN only on latent heating.

d. Moisture adjustments

LHN primarily adjusts model temperatures but it is often suggested (Manobianco et al. 1994; Jones and Macpherson 1997, among others) that moisture also be modified to conserve the relative humidity that was originally forecasted. Such modification of moisture to preserve relative humidity is tested in this study. This procedure only considers the temperature changes resulting from the application of LHN. No distinction is made as to whether an existing latent heating profile is scaled or if an idealized profiles is used.

e. LHN in the cycled assimilation system

HRDPS-IC3 operates within a continuous assimilation cycle where each forecast becomes the background state for the next assimilation period. An advantage of such cycling is that the assimilated observations result in a better background which results in better analyses and better forecasts and so on. Unfortunately, performing cycled experiments is time consuming because the forecasts and analyses must be executed sequentially.

For research purposes, it is customary to perform “forecast-only” experiments where forecasts are reintegrated using a modified configuration but with the same initial conditions and analysis increment from a control experiment conducted previously. These experiments are much faster to run since they can be launched in parallel. However, the overall impact of the feature being tested (here LHN) will be lower since the improvements obtained at one time will not make their way into the next forecasts.

5. Methodology

This research aims at documenting the overall impact of LHN in HRDPS-IC3 and to better understand the impact for some of the LHN components described in the previous section. The impacts of the following features are tested:

  • Applying LHN in the continuous assimilation cycle versus in forecast-only experiments

  • The use of idealized profiles

  • The conservation of relative humidity

Figure 6 provides the list of all the experiments conducted for this study. For each experiment, 110 forecasts were launched twice a day (at 0000 and 1200 UTC) between 2 July and 26 August 2016. The verification scores discussed in the following sections consist of average results for all the forecasts performed during this period.

Fig. 6.
Fig. 6.

Description of experiments being tested along with the associated changes in NWP index (%) compared to the control experiment. Blue (brown) bars represent NWP index changes for altitude (surface) observations.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

In verifications against conventional observations (radiosondes, aircraft, GPS delay, and surface observations from the SYNOP network) we evaluate the performance of the different experiments by computing the percentage change in root-mean-square error (RMSE) compared with control_no_LHN:
ΔRMSE(%)=1×100×RMSEexperimentRMSEcontrol_no_LHNRMSEcontrol_no_LHN.
The −1 multiplication factor is added to obtain a positive number when reduction of RMSE is obtained in experiment compared to control_no_LHN. An F test on variance is used to assess significance levels of ΔRMSE.

To condense verification results, we use an “NWP index,” which is simply the arithmetic average of change in ΔRMSE obtained for all observation types, at all altitudes and lead times. By doing so, the entire performance of a forecast is reduced to two numbers: one for altitude scores, another at the surface. The NWP indices are plotted in the second column of Fig. 6. Recognizing the limits to what this metric can represent, it nevertheless allows to evaluate the performance of an experiment at a glance.

The precipitation rates forecasted by the different experiments are evaluated against the precipitation rates inferred from the BALTRAD mosaics described in section 2. In this case, results from standard contingency scores are presented. These include the probability of detection (POD), false alarm ratio (FAR), the critical success index (CSI), and the frequency bias (FBIAS) as defined by Schaefer (1990) with nomenclature by Barnes et al. (2009). Other verification metrics such as the forecasting efficiency from the Pearson’s correlation coefficient (see appendix of Jacques et al. 2018) and the minimum length scale for a skillful forecast derived from the fraction skill score (Dixon et al. 2009) have also been examined but are not shown since the signal from these metrics is generally similar to that of the CSI.

6. Average results over a 2-month test period

a. Impact of including LHN within the assimilation cycle

Figures 7a–g show time–height cross sections of ΔRMSE that are obtained by comparing LHN_cycled to the control experiment control_no_LHN. Reduction of errors (larger ΔRMSE, in orange) on the order of 1%–4% are obtained for wind forecasts against aircrafts measurements (Figs. 7a,b) and 1%–2% against radiosondes (Figs. 7d,e). Temperatures (Figs. 7c,f) and dewpoint departures (Fig. 7g) are also generally improved but to a lesser extent. Verifications against dewpoint departures measured by aircrafts are not shown because these observations are not widely available in North America. The numbers that appear in some time–height bins are indicative of statistical confidence levels greater than 90%.

Fig. 7.
Fig. 7.

Average ΔRMSE [Eq. (10)] in LHN_cycled (color scale at right) compared to control_no_LHN for 110 forecasts conducted in July–August 2016. Changes in RMSE are estimated against (a)–(c) aircraft measurements and (d)–(g) radiosondes as a function of forecast lead time and in vertical bins of 100 hPa. Numbers indicate that the results are statistically significant at a confidence level greater than 90%.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

The spatial distribution of different observation types varies considerably and must be kept in mind when interpreting verification results. Figures 8a–c show how the observation density for radiosondes, aircrafts and the SYNOP network of surface stations measurements. For aircraft observations (Fig. 8a), the observation density also greatly varies with altitude (not shown) with most measurements below 500 hPa being close to major airports (roughly the colored areas) and measurements above 500 hPa being found along major air corridors (lower bin counts in brown). This difference in observation locations and altitude could explain why the wind improvements shown in Figs. 7a and 7b are mostly found above 500 hPa.

Fig. 8.
Fig. 8.

Color-coded observation count (July–August 2016) in ∼40 km × 40 km bins for (a) aircraft, (b) radiosondes, and (c) surface observations from SYNOP stations.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

To compare experiments against one another, it is convenient to use scorecards which summarize their performance compared to a common control experiment. Figure 9 shows two such scorecards indicating the performance of LHN_cycled and LHN_fcst_only each compared to control_no_LHN. Orange triangles pointing up indicate the average improvements in ΔRMSE for different variables and lead times. Solid colors indicate average results whose statistical significance is greater than 90%.

Fig. 9.
Fig. 9.

Scorecards comparing LHN_cycled and LHN_fcst_only to control_no_LHN. Triangles represent the average percentage change, in RMSE, for different observation types as a function of forecast lead time. The altitude observations of temperature (T), dewpoint departure (HU), and wind (U/V) are from radiosondes and aircraft. Surface observations of temperature (T 2m), dewpoint departures (Td 2m), wind (U/V 10m), and surface pressure (SP) are from the SYNOP network. Full triangles indicate statistically significant results.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

By comparing the two scorecards, we can assess the impact of applying LHN within the assimilation cycle. We can see that including LHN in the assimilation cycle generally increases the magnitude and duration of the improvements. Improved performance early in the forecast is expected since the cycled forecasts benefit from LHN applied in the previous assimilation cycle.

In Fig. 6, we can see that the NWP index for LHN_cycled is 1.50% in altitude and 0.81% at the surface. For LHN_fcst_only, improvements are smaller at 1.05% in altitude and 0.44% at the surface. Based on these numbers, we can say that including LHN in the cycled assimilation system accounts for a significant proportion of the improvements that are obtained with respect to observations other than precipitation.

In verifications against observed precipitation, Fig. 10, we observe the usual improvements in precipitation scores that lasts for approximately 6 h after the application of LHN between T0 − 3 h and T0 + 3 h. Including LHN within the assimilation cycle does not significantly improve the intensity or the duration of the improvements of precipitation in free forecasts (after T0 + 3 h). It can also be seen that the application of LHN in LHN_cycled and LHN_fcst_only increases FBIAS between T0 − 3 h and T0 + 9 h compared to control_no_LHN. This deterioration is not considered alarming because the increase in FBIAS in both LHN experiments is accompanied by a reduction of FAR compared to control_no_LHN. When we separate (not shown here) the evening forecasts (starting at T0 = 0000 UTC) from the morning forecasts (T0 = 1200 UTC), we can see that FBIAS is correlated with the diurnal cycle of precipitation. Work aimed at improving precipitation biases in HRDPS-IC3 is scheduled for the next operational upgrade.

Fig. 10.
Fig. 10.

Verification scores for 110 forecasts of precipitation rates during the application of LHN (grayed-out area) and in the subsequent free forecast (from T0 + 3 h to T0 + 12 h). The scores shown are the probability of detection (POD), the false alarm ratio (FAR), the critical success index (CSI), and the frequency bias (FBIAS) defined in section 5. Precipitation rates above 1 mm h−1 are considered as the threshold for the occurrence of precipitation (hits).

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

Including LHN within the assimilation cycle definitely improved the benefits that can be obtained. Nevertheless, to reduce computational time, the experiments presented next are forecast-only experiments whose performance should be compared against that of LHN_fcst_only.

b. Impact of idealized profiles

The idealized profiles introduced in section 4b have been used in research projects for a few years already (Jacques et al. 2018; Buehner and Jacques 2020). Here, the impacts of these profiles are tested in isolation. In experiment LHN_no_Iprofiles, idealized profiles are not used at all. In cases where precipitation is observed but not simulated, nothing is done. The inverse is true of LHN_only_Iprofiles where it is the “normal” scaling and reduction of heating profiles that are turned off. For this experiment, LHN is only active through idealized profiles. Conservation of relative humidity is active in both experiments.

Figure 11 shows verifications of precipitation forecasts for LHN_no_Iprofiles and LHN_only_Iprofiles. By comparing the performance of these two experiments, we can see that the idealized profiles are responsible for a good proportion of the impact that we observe with our implementation of LHN.

Fig. 11.
Fig. 11.

As in Fig. 10, but for control_no_LHN, LHN_fcst_only, LHN_no_moist, LHN_only_Iprofiles, and LHN_no_Iprofiles.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

In general, there is a relative balance between the warming/moistening brought by the idealized profiles and the cooling/drying brought by the scaling down of existing profiles in locations where precipitation is modeled but not observed. In the experiment LHN_only_Iprofiles, LHN does nothing to reduce precipitation such that only warming/moistening can occur. Consequently, LHN_only_Iprofiles is associated with the largest FBIAS of all experiments.

The simultaneous reduction in the FAR and increase in FBIAS can be explained by considering that FAR is calculated as
FAR=false alarmshits+false alarms.
It turns out that the introduction of idealized profiles significantly increases hits causing a reduction in FAR.

Results of verifications against other variables corroborate the large influence of idealized profiles on the forecast performance. In Fig. 6, the NWP indices for LHN_no_Iprofiles are slightly negative indicating deteriorations of the forecasts when LHN is activated without these profiles compared to control_no_LHN. As for LHN_only_Iprofiles, results in altitude are positive but not as good as LHN_fcst_only.

It is somewhat comforting that the full implementation of LHN including both the “normal” scaling and the idealized profiles give the best results. Nevertheless, LHN_no_Iprofiles and LHN_only_Iprofiles show that the idealized profiles are very important in our implementation of LHN.

c. Impact of conserving relative humidity

The impact of conserving relative humidity can be assessed by comparing experiment LHN_no_moist (in blue) to LHN_fcst_only (in orange) in Fig. 11. The POD, FAR and CSI of LHN_fcst_only are better and indicate that the conservation of relative humidity is responsible for approximately one-third of the improvements in precipitation forecast that are obtained with LHN. Similarly, the NWP indices of LHN_no_moist are ∼25% smaller than those of LHN_fcst_only in Fig. 6 demonstrating that it is beneficial to conserve relative humidity during the application of LHN. Adjustment of moisture is thus a feature which we want to conserve as part of the LHN implementation.

7. Impact of LHN on altitude winds

We wished to better understand the mechanism by which LHN, which only modifies vertical profiles of temperature and moisture, could lead to significant and long lasting improvements to winds above 500 hPa. To this end, we first examine Figs. 12a and 12b, which show the RMSE for the U component of the wind between 300 and 200 hPa for each individual forecasts performed in the 2-month test period.

Fig. 12.
Fig. 12.

RMSE of the U component of the wind between 300 and 200 hPa for control_no_LHN and LHN_cycled against (a) radiosondes and (b) aircraft observations. RMSE is plotted for individual forecasts launched at 12-h intervals and can be seen to increase as a function of lead time. Orange shading indicates better performance (smaller RMSE) for the forecasts with LHN, gray shading indicates better performance in the control experiment without LHN. The vertical arrows indicate the one forecast examined in Figs. 1314. (c) Areal coverage of radar-inferred precipitation during the same period is shown.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

In these figures, the RMSE of control_no_LHN appears as thin black lines while the RMSE of LHN_cycled appears in blue. At the beginning of each forecast, RMSEs start at approximately 2 m s−1 and increase with lead times to reach values between 4 and 8 m s−1 at lead times of 48 h. To highlight which experiment has the smallest errors, the area between the RMSE values of the two experiments is colored. Orange shading indicates better results due to LHN, and gray shadings indicate better results without.

At lead times shorter than 6 h, the model state is constrained by the 4D-EnVar assimilation, and the two experiments generally have very similar RMSEs. The impact of LHN is most noticeable later in the forecasts. In a majority of cases, it improves the wind forecasts as seen by the predominance of orange shading. Deteriorations are also observed, but less often and generally of smaller magnitude. Exceptions to this are the forecasts around 21 July where noticeable deteriorations are brought by LHN.

We wondered if the impact of LHN could be related to the general amount of precipitation in the domain. To see this, Fig. 12c shows the areal coverage of precipitation rates greater than 0.1 mm h−1 which can be used by LHN. We note that the period around 21 July, where LHN is generally detrimental, has very little precipitation. In general, however, the relationship between precipitation coverage and the impact of LHN on winds is not obvious. For example, the period around 5–7 August also has little precipitation yet LHN brings no obvious deterioration to winds.

It can be seen that the RMSE of both experiments grows larger in July than in August. During this period of lower predictability, the difference in RMSE between the two experiments also tends to be larger. The difference in the impact LHN can bring to forecast quality is likely due to changes in weather regimes, which is also observed by Gastaldo et al. (2021). Identifying the situation when LHN is expected to be most beneficial to forecast quality would be an interesting avenue for future work.

In an attempt to connect the action of LHN with winds as high as 200 hPa, we will look more closely at one case where LHN brought large improvements in altitude winds for a 12-h forecast. A very good case is chosen here to make the differences between the two forecasts more visible. The hope is that the insight we can gain from this example should be applicable more generally. The forecast that we choose is initialized at 1200 UTC 10 July 2016 and is identified in Figs. 12a and 12b by vertically pointing black arrows.

a. Impact on precipitation

The model integration for this forecast starts at 0900 UTC (T0 − 3 h) with LHN and analysis increment being applied during a 6-h period ending at 1500 UTC. In terms of precipitation, the most visible difference brought by LHN is found around a squall line observed in the southern part of Minnesota and Iowa. Figure 13, shows a closeup of precipitation rates in this area. For this one case, we can observe that the use of LHN within the assimilation cycle (Figs. 13g–l) does lead to the simulation of precipitation that is in much better agreement to radar observations than the control experiment.

Fig. 13.
Fig. 13.

(a)–(f) Precipitation rates as observed by radar, (g)–(l) forecasted in LHN_cycled, (m)–(r) in LHN_fcst_only, and (s)–(x) in control_no_LHN. The center time of the analysis window (T0) for this case is at 1200 UTC 10 Jul 2016.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

It is worth pointing out that, of all experiments described in Fig. 6, LHN_cycled is the only one where organized convection is already going on at the onset of the forecast. In Figs. 13m–r we can see that applying LHN in LHN_fcst_only eventually leads to the generation of convection in this area but with a delay of few hours compared to observations. Note also how the structure and evolution of the precipitation that is generated does not correspond very well to observations.

The clear improvement of precipitation resulting from LHN in LHN_cycled is not typical and this example should not be considered as representative of the general performance of LHN. The interesting aspect of this forecast is not the improvement to precipitation itself, but instead the fact that we could find such an improvement in precipitation based on improvements to altitude winds later in the forecast.

b. Impact on wind at 250 hPa

Figure 14a shows the 250-hPa wind velocity (black and white shadings) and direction (arrows) that is found in control_no_LHN at T0 + 0 h. Figure 14b also shows 250-hPa wind velocity, this time for LHN_cycled. Purple shadings have been added to highlight where the differences in wind velocities between the two experiments are greater than 10 m s−1. These differences in wind velocity are notably large in the wake of the squall line discussed above and indicated by the white dashed line labeled “A.” In this location, the texture of the differences in wind velocity is rough and can be directly related to differences in the convective plumes/bubbles found in the two experiments.

Fig. 14.
Fig. 14.

(a)–(f) Impact of LHN on altitude winds. The 250-hPa wind modulus (black and white shading) and direction (arrows) in control_no_LHN at 1200 UTC 10 Jul 2016 is shown in (a). The same field as simulated in LHN_cycled in shown in (b). The purple shading in (b)–(f) indicates places where the difference in wind modulus between the two experiments is greater than 10 m s−1. The small dots in this figure indicate the difference in forecast errors (aircraft and radiosondes between 300 and 200 hPa) between the two experiments.

Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-22-0028.1

There is no precipitation to the north and east of the squall line, and LHN is inactive there. At locations labeled “B” and “C” the differences in wind velocities are smoother and indicate displacement of larger-scale wind patterns due to LHN applied in this, and previous, assimilation cycles. These displacements provide some evidence that the application of LHN can modify atmospheric fields several hundred kilometers away from where it is actively ongoing. These differences are important as they persist and evolve throughout the model integration.

Naturally, it is important that LHN demonstrates not just different, but improved, wind forecasts before it is accepted. To help determining whether this is the case, we added scattered dots showing the differences in forecast errors for the U component of the wind between 300 and 200 hPa for control_no_LHN and LHN_cycled. The dot’s size and color indicate which experiment has the smallest error and by how much. The color orange indicates better results (smaller errors) with LHN, the color blue indicates better results in the control.

When we look at these error differences, we can see that the initially small difference in wind labeled “C” ends up being the one location where the largest reductions in forecast errors are observed at T0 + 12 h. Even if only a small proportion of observations show large improvements, they end up dominating the RMSE for this time and altitude. Elsewhere, the predominance of improvements by LHN (i.e., the predominance of orange dots over blue dots) is not discernible.

If the improvements in winds can be attributed to LHN, they are also caused by the lucky fact that a lot of aircraft measurements were available in the relatively small area where the wind has clearly been improved by LHN. This case demonstrates how, the changes to the wind field brought by LHN will be difficult to perceive by simply comparing forecasts. It is only the recurrence of such improvements over the entire verification period that can assure us of the generally positive impact of LHN. In this respect, the impact of LHN on HRDPS-IC3 is not different from those from other observations, each bringing its small contribution to the overall improvement of the system.

8. Discussion and conclusions

This study documents the impact of latent heat nudging (LHN) in the operational 2.5-km High-Resolution Deterministic Prediction System (HRDPS). On average, for a period of two months in the summer of 2016, LHN is shown to improve precipitation forecasts for up to 6 h after the assimilation period. The use of LHN also reduces errors for winds and temperature forecasts. Compared to a control experiment with no LHN, error reduction on the order of 0.5%–1.5% are obtained on an NWP index measuring errors across many forecasted variables and for different observation types. Above 500 hPa, improvements for wind, temperature and moisture are shown to persist for lead times of 36–48 h.

The most beneficial aspect of our LHN implementation is its inclusion within the continuous assimilation cycle. For surface variables, including LHN in the cycled system yields average improvements that are approximately twice as large as those observed in a forecast-only experiment. For higher altitude measurements, the improvements are approximately 25% larger. The conservation of relative humidity along with the adjustments to temperature made by LHN is also significantly beneficial. It is found to account for approximately one-third of the overall impact of LHN on precipitation scores.

When we compare precipitation scores for experiments conducted with different LHN configurations, it is found that the magnitude of forecasting skill for precipitation can be improved but not the duration. While some experiments have better precipitation scores at short lead times, the skill decreases rapidly such that all experiments are found to have negligible impact on precipitation forecasts between 6 and 9 h after the application of LHN.

This contrasts with verification scores obtained for other observation types for which the improvements lasts longer, up to 36–48 h for the best configuration. It is not easy to reconcile the long-lasting improvement obtained against nonradar observations to the shorter-lived improvements that are obtained for precipitation. One possible explanation would be that the high-intensity/small-scale precipitation features associated with convection dominate precipitation errors for the summer periods considered. At these scales, predictability is quite short and does not extend beyond a few hours. The small improvement on altitude variables brought by LHN are not sufficient to significantly improve the location and intensity of precipitation such that the precipitation forecasts from any experiment become equally distant from the radar observations at lead times beyond a few hours.

A case study was conducted to give some insight for the mechanism by which the changes in ongoing convection brought by LHN can be associated with long-lasting changes to the altitude wind that result in improved forecast skill. The exact mechanism by which LHN leads to improvements for wind forecasts above 500 hPa remains unknown. One hypothesis is that the vertical transport of horizontal momentum associated with the convection triggered by LHN projects on synoptic-scale atmospheric features (and balances) which evolve on longer time scales. Support for this hypothesis is provided in Figs. 14b and 14c which illustrate how the individual convective plumes/bubbles that were triggered by LHN have a noticeable impact on horizontal wind as high as 250 hPa.

Finally, this study demonstrated that the use of idealized heating profiles, alone, were responsible for approximately 75% of the improvements obtained with LHN on precipitation. In the experiment without these profiles, LHN did very little for improving precipitation and even brought small deteriorations when compared to surface and altitude observations. Because of the significant impact of idealized profiles, this feature will be the object of future work for improving LHN. In particular, the ad hoc approach for building these profiles (section 4b) should be improved. It would also be interesting to conduct a comparison with the more traditional approach of selecting neighboring latent heating profiles.

Acknowledgments.

We wish to thank Stéphane Laroche for providing an in-depth and insightful review of a preliminary version of this manuscript. Great thanks also to Thomas Milewski for his help running forecast experiments with the HRDPS.

Data availability statement.

The code for most of the data analysis presented here is made available in a Zenodo archive at https://doi.org/10.5281/zenodo.5942091. Due to the large volume of space requires, model outputs and observation files are archived for a period of five years and can be made available to anyone upon request.

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Save
  • Barnes, L. R., D. M. Schultz, E. C. Gruntfest, M. H. Hayden, and C. C. Benight, 2009: CORRIGENDUM: False alarm rate or false alarm ratio? Wea. Forecasting, 24, 14521454, https://doi.org/10.1175/2009WAF2222300.1.

    • Search Google Scholar
    • Export Citation
  • Beljaars, A. C. M., A. R. Brown, and N. Wood, 2004: A new parametrization of turbulent orographic form drag. Quart. J. Roy. Meteor. Soc., 130, 13271347, https://doi.org/10.1256/qj.03.73.

    • Search Google Scholar
    • Export Citation
  • Benjamin, S. G., and Coauthors, 2016: A North American hourly assimilation and model forecast cycle: The Rapid Refresh. Mon. Wea. Rev., 144, 16691694, https://doi.org/10.1175/MWR-D-15-0242.1.

    • Search Google Scholar
    • Export Citation
  • Bick, T., and Coauthors, 2016: Assimilation of 3D radar reflectivities with an ensemble Kalman filter on the convective scale. Quart. J. Roy. Meteor. Soc., 142, 14901504, https://doi.org/10.1002/qj.2751.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., and D. Jacques, 2020: Non-Gaussian deterministic assimilation of radar-derived precipitation accumulations. Mon. Wea. Rev., 148, 783808, https://doi.org/10.1175/MWR-D-19-0199.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., and Coauthors, 2015: Implementation of deterministic weather forecasting systems based on ensemble–variational data assimilation at environment Canada. Part I: The global system. Mon. Wea. Rev., 143, 25322559, https://doi.org/10.1175/MWR-D-14-00354.1.

    • Search Google Scholar
    • Export Citation
  • Caron, J.-F., T. Milewski, M. Buehner, L. Fillion, M. Reszka, S. Macpherson, and J. St-James, 2015: Implementation of deterministic weather forecasting systems based on ensemble–variational data assimilation at Environment Canada. Part II: The regional system. Mon. Wea. Rev., 143, 25602580, https://doi.org/10.1175/MWR-D-14-00353.1.

    • Search Google Scholar
    • Export Citation
  • Denis, B., J. Côté, and R. Laprise, 2002: Spectral decomposition of two-dimensional atmospheric fields on limited-area domains using the discrete cosine transform (DCT). Mon. Wea. Rev., 130, 18121829, https://doi.org/10.1175/1520-0493(2002)130<1812:SDOTDA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dixon, M., Z. Li, H. Lean, N. Roberts, and S. Ballard, 2009: Impact of data assimilation on forecasting convection over the United Kingdom using a high-resolution version of the Met Office Unified Model. Mon. Wea. Rev., 137, 15621584, https://doi.org/10.1175/2008MWR2561.1.

    • Search Google Scholar
    • Export Citation
  • Gastaldo, T., V. Poli, C. Marsigli, D. Cesari, P. P. Alberoni, and T. Paccagnella, 2021: Assimilation of radar reflectivity volumes in a pre-operational framework. Quart. J. Roy. Meteor. Soc., 147, 10311054, https://doi.org/10.1002/qj.3957.

    • Search Google Scholar
    • Export Citation
  • Gustafsson, N., and Coauthors, 2018: Survey of data assimilation methods for convective-scale numerical weather prediction at operational centres. Quart. J. Roy. Meteor. Soc., 144, 12181256, https://doi.org/10.1002/qj.3179.

    • Search Google Scholar
    • Export Citation
  • Hawkness-Smith, L. D., and D. Simonin, 2021: Radar reflectivity assimilation using hourly cycling 4D-Var in the Met Office Unified Model. Quart. J. Roy. Meteor. Soc., 147, 15161538, https://doi.org/10.1002/qj.3977.

    • Search Google Scholar
    • Export Citation
  • Jacques, D., D. Michelson, J.-F. Caron, and L. Fillion, 2018: Latent heat nudging in the Canadian regional deterministic prediction system. Mon. Wea. Rev., 146, 39954014, https://doi.org/10.1175/MWR-D-18-0118.1.

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  • Fig. 1.

    The 2.5-km “high-resolution” HRDPS is nested within the 10-km regional system that is itself nested in the 15-km global system. Measurements from the Canadian radars (red outlines) and the American radars (white outlines) that are within the HRDPS domain are assimilated.

  • Fig. 2.

    (a),(b) BALTRAD composites are smoothed to remove the small-scale features that the model is not capable of representing. This is done by using a circular smoothing stencil in (a) and producing fields of precipitation rates in (b) whose spectral density match more closely with those simulated by the model. By eye, (d) the filtered observations have a texture that better resembles that of the (e) model than (c) its unfiltered counterpar. (f),(g) BALTRAD’s quality index is filtered using the same process.

  • Fig. 3.

    Diagram representing the concurrent but independent application of IAU and LHN during the first 6 h of model integration.

  • Fig. 4.

    When binned in different precipitation rate categories, profiles of latent heating/cooling (in gray) show great variability. This variability can be reduced by selecting only the profiles displaying low-level heating (in blue). The idealized profiles in red are used by LHN in cases where there is precipitation in the observations but not in the model.

  • Fig. 5.

    Color-coded histograms for the column sum of latent heat release (+ve) and cooling (−ve) as a function of precipitation rates. (a) At a resolution of 10 km, coarsely parameterized microphysics enforce a good relation between latent heating above and the precipitation at the ground. (b) At 2.5 km, the added complexity deteriorates this relationship. (c) Horizontal smoothing of both the precipitation rates and latent heating helps to improve the correspondence between the two.

  • Fig. 6.

    Description of experiments being tested along with the associated changes in NWP index (%) compared to the control experiment. Blue (brown) bars represent NWP index changes for altitude (surface) observations.

  • Fig. 7.

    Average ΔRMSE [Eq. (10)] in LHN_cycled (color scale at right) compared to control_no_LHN for 110 forecasts conducted in July–August 2016. Changes in RMSE are estimated against (a)–(c) aircraft measurements and (d)–(g) radiosondes as a function of forecast lead time and in vertical bins of 100 hPa. Numbers indicate that the results are statistically significant at a confidence level greater than 90%.

  • Fig. 8.

    Color-coded observation count (July–August 2016) in ∼40 km × 40 km bins for (a) aircraft, (b) radiosondes, and (c) surface observations from SYNOP stations.

  • Fig. 9.

    Scorecards comparing LHN_cycled and LHN_fcst_only to control_no_LHN. Triangles represent the average percentage change, in RMSE, for different observation types as a function of forecast lead time. The altitude observations of temperature (T), dewpoint departure (HU), and wind (U/V) are from radiosondes and aircraft. Surface observations of temperature (T 2m), dewpoint departures (Td 2m), wind (U/V 10m), and surface pressure (SP) are from the SYNOP network. Full triangles indicate statistically significant results.

  • Fig. 10.

    Verification scores for 110 forecasts of precipitation rates during the application of LHN (grayed-out area) and in the subsequent free forecast (from T0 + 3 h to T0 + 12 h). The scores shown are the probability of detection (POD), the false alarm ratio (FAR), the critical success index (CSI), and the frequency bias (FBIAS) defined in section 5. Precipitation rates above 1 mm h−1 are considered as the threshold for the occurrence of precipitation (hits).

  • Fig. 11.

    As in Fig. 10, but for control_no_LHN, LHN_fcst_only, LHN_no_moist, LHN_only_Iprofiles, and LHN_no_Iprofiles.

  • Fig. 12.

    RMSE of the U component of the wind between 300 and 200 hPa for control_no_LHN and LHN_cycled against (a) radiosondes and (b) aircraft observations. RMSE is plotted for individual forecasts launched at 12-h intervals and can be seen to increase as a function of lead time. Orange shading indicates better performance (smaller RMSE) for the forecasts with LHN, gray shading indicates better performance in the control experiment without LHN. The vertical arrows indicate the one forecast examined in Figs. 1314. (c) Areal coverage of radar-inferred precipitation during the same period is shown.

  • Fig. 13.

    (a)–(f) Precipitation rates as observed by radar, (g)–(l) forecasted in LHN_cycled, (m)–(r) in LHN_fcst_only, and (s)–(x) in control_no_LHN. The center time of the analysis window (T0) for this case is at 1200 UTC 10 Jul 2016.

  • Fig. 14.

    (a)–(f) Impact of LHN on altitude winds. The 250-hPa wind modulus (black and white shading) and direction (arrows) in control_no_LHN at 1200 UTC 10 Jul 2016 is shown in (a). The same field as simulated in LHN_cycled in shown in (b). The purple shading in (b)–(f) indicates places where the difference in wind modulus between the two experiments is greater than 10 m s−1. The small dots in this figure indicate the difference in forecast errors (aircraft and radiosondes between 300 and 200 hPa) between the two experiments.

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